This study concentrates on adaptive event-triggered control of complex dynamical networks with unpredictable coupling delays and stochastic deception attacks. The adaptive event-triggered mechanism is used to avoid the wasting of limited bandwidth. The probability of data communicated by the network is established by statistical properties and Bernoulli stochastic variables with an uncertain occurrence probability. Stability analysis based on Lyapunov–Krasovskii functional and the stability of the closed-loop system is guaranteed. Using the LMI technique, we obtain triggered parameters. To demonstrate (...) the feasibility and usefulness of the suggested methodology, two examples are shown. (shrink)

Assumptions of stochastic independence are crucial to statistical models in science. Under what circumstances is it reasonable to suppose that two events are independent? When they are not causally or logically connected, so the standard story goes. But scientific models frequently treat causally dependent events as stochastically independent, raising the question whether there are kinds of causal connection that do not undermine stochastic independence. This paper provides one piece of an answer to this question, treating the (...) simple case of two tossed coins with and without a midair collision. (shrink)

The paper extends the framework of outcomes in branching space-time (Kowalski and Placek [1999]) by assigning probabilities to outcomes of events, where these probabilities are interpreted either epistemically or as weighted possibilities. In resulting models I define the notion of common cause of correlated outcomes of a single event, and investigate which setups allow for the introduction of common causes. It turns out that a deterministic common cause can always be introduced, but (surprisingly) only special setups permit the introduction (...) of truly stochastic common causes. I analyse next the Bell-Aspect experiment and derive the Bell-CH inequalities. I observe that we postulate there not a common cause for outcomes of a single event but rather a common common cause that accounts for outcomes of many events, where 'events' mean 'measurements with (different) directions of polarization'. Since the inequalities are violated, I claim that no causal story can be told about the Bell correlations, where causality is subliminal and restricted by screening-off condition. Similarly, given certain intuitive principles, no deterministic story can be told about these correlations. (shrink)

The measurement of one or more observables can be considered to yield sample points which are in general fuzzy sets. Operationally these fuzzy sample points are the outcomes of calibration procedures undertaken to ensure the internal consistency of a scheme of measurement. By introducing generalized probability measures on σ-semifields of fuzzy events, one can view a quantum mechanical state as an ensemble of probability measures which specify the likelihood of occurrence of any specific fuzzy sample point at some instant. (...) These sample points are the possible outcomes of any infinitely rapid succession of measurements at that instant of any sequence of observables of the system. (shrink)

One of the most important methods in dealing with the optimization of large, complex systems is that of hierarchical decomposition. The idea is to reduce the overall complex problem into manageable approximate problems or subproblems, to solve these problems, and to construct a solution of the original problem from the solutions of these simpler prob lems. Development of such approaches for large complex systems has been identified as a particularly fruitful area by the Committee on the Next Decade in Operations (...) Research (1988) [42] as well as by the Panel on Future Directions in Control Theory (1988) [65]. Most manufacturing firms are complex systems characterized by sev eral decision subsystems, such as finance, personnel, marketing, and op erations. They may have several plants and warehouses and a wide variety of machines and equipment devoted to producing a large number of different products. Moreover, they are subject to deterministic as well as stochastic discrete events, such as purchasing new equipment, hiring and layoff of personnel, and machine setups, failures, and repairs. (shrink)

The problem of getting a relativistic generalization of the CSL dynamical reduction model, which has been presented in part I, is discussed. In so doing we have the opportunity to introduce the idea of a stochastically invariant theory. The theoretical model we present, that satisfies this kind of invariance requirement, offers us the possibility to reconsider, from a new point of view, some conceptually relevant issues such as nonlocality, the legitimacy of attributing elements of physical reality to physical systems and (...) the problem of establishing causal relations between physical events. (shrink)

ObjectiveNoisy galvanic vestibular stimulation (nGVS) is often used to improve postural stability in disorders, such as neurorehabilitation montage. For the safe use of nGVS, we investigated whether arterial pressure (AP) and heart rate vary during static supine and slow whole-body tilt with random nGVS (0.4 mA, 0.1–640 Hz, gaussian distribution) in a healthy elderly population.MethodsThis study was conducted with a double-blind, sham-controlled, cross-over design. Seventeen healthy older adults were recruited. They were asked to maintain a static supine position on a (...) bed for 10 min, and the bed was tilted up (TU) to 70 degrees within 30 s. After maintaining this position for 3 min, the bed was passively tilted down (TD) within 30 s. Real-nGVS or sham-nGVS was applied from 4 to 15 min. The time course of mean arterial pressure (MAP) and RR interval variability (RRIV) were analyzed to estimate the autonomic nervous activity.ResultnGVS and/or time, including pre-/post-event (nGVS-start, TU, and TD), had no impact on MAP and RRIV-related parameters. Further, there was no evidence supporting the argument that nGVS induces pain, vertigo/dizziness, and uncomfortable feeling.ConclusionnGVS may not affect the AP and RRIV during static position and whole-body tilting or cause pain, vertigo/dizziness, and discomfort in the elderly. (shrink)

This paper concentrates on the event-triggered H ∞ filter design for the discrete-time Markovian jump neural networks under random missing measurements and cyber attacks. Considering that the controlled system and the filtering can exchange information over a shared communication network which is vulnerable to the cyber attacks and has limited bandwidth, the event-triggered mechanism is proposed to relieve the communication burden of data transmission. A variable conforming to Bernoulli distribution is exploited to describe the stochastic phenomenon since the missing (...) measurements occur with random probability. Furthermore, seeing that the communication networks are vulnerable to external malicious attacks, the transferred information via the shared communication network may be changed by the injected false information from the attackers. Based on the above consideration, sufficient conditions for the filtering error system to maintain asymptotically stable are provided with predefined H ∞ performance. In the end, three numerical examples are given to verify the proposed theoretical results. (shrink)

I compare the failure of counterfactual dependence as a criterion of event causation to the failure of stochastic dependence as a criterion of causal law. Counterexamples to the stochastic analysis arise from cases of Simpson's Paradox, and Nancy Cartwright has suggested a way of transforming the stochastic analysis into something that avoids these counterexample. There is an analogical relationship between cases of Simpson's Paradox and cases of causal overdetermination. I exploit this analogical relationship to motivate my own (...) view about the connection between counterfactuals and event causation. According to my view, counterfactuals and event causation are intimately connected by a principle which falls short of being an analysis but which, as I show, correctly handles not only overdetermination but common causes as well. (shrink)

The paper develops models of statistical experiments that combine propensities with frequencies, the underlying theory being the branching space-times (BST) of Belnap (1992). The models are then applied to analyze Bell's theorem. We prove the so-called Bell-CH inequality via the assumptions of a BST version of Outcome Independence and of (non-probabilistic) No Conspiracy. Notably, neither the condition of probabilistic No Conspiracy nor the condition of Parameter Independence is needed in the proof. As the Bell-CH inequality is most likely experimentally falsified, (...) the choice is this: contrary to the appearances, experimenters cannot choose some measurement settings, or some transitions, with spacelike related initial events, are correlated; or both. (shrink)

From its beginnings religious philosophy confronted the challenge to reconcile Divine or natural determinism with man's moral freedom. In ancient Jewish thought, this gave rise to statistical ideas. In some Rabbinic texts, necessity is seen as inhering in collectives rather than in individuals. This is a statistical conception. Some miracles too were understood as highly improbable events, and remarkable phenomena were distinguished from usual ones. Medieval thinkers amplified and developed these ideas. Providential as well as natural determinism were explained (...) as operating in large numbers of individual acts of free will, an idea later taken up by Kant. (shrink)

Starting from a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity, whose set of possible values normally contains the probabilities assessed for the two conditional events. We examine some cases of logical dependencies, where the conjunction is a conditional event; moreover, we (...) give the lower and upper bounds on the conjunction. We also examine an apparent paradox concerning stochastic independence which can actually be explained in terms of uncorrelation. We briefly introduce the notions of disjunction and iterated conditioning and we show that the usual probabilistic properties still hold. (shrink)

This work is devoted to studying the stochastic stabilization of a class of neutral-type complex-valued neural networks with partly unknown Markov jump. Firstly, in order to reduce the conservation of our stability conditions, two integral inequalities are generalized to the complex-valued domain. Secondly, a state-feedback controller is designed to investigate the stability of the neutral-type CVNNs with H ∞ performance, making the stability problem a further extension, and then, the stabilization of the CVNNs with H ∞ performance is investigated (...) through a sampling-based event-triggered control for the first time that the transmission event is not triggered except when it violates the event-triggered condition. Finally, two examples are given to illustrate the validity and correctness of our obtained theorems. (shrink)

In an earlier paper the present author proved that de Finetti coherence is preserved under taking products of coherent books on two finite sets of independent events. Conversely, in this note it is proved that product is the only coherence preserving operation on coherent books. Our proof shows that the traditional definition of stochastically independent classes of events actually follows from the combination of two more basic notions: boolean algebraic independence and de Finetti coherent betting system.

Cell interdivision periods (IDP) in homogenous cell populations vary stochastically. Another aspect of probabilistic cell behavior is randomness in cell differentiation. These features are suggested to result from competing stochastic events of assembly/disassembly of the transcription pre‐initiation complex (PIC) at gene promoters. The time needed to assemble a proper PIC from different proteins, which must be numerous enough to make their combination gene specific, may be comparable to the IDP. Nascent mRNA visualization at defined genes and inferences from (...) protein level fluctuations in single cells suggest that some genes do operate in this way. The onset of mRNA production by such genes may miss the time windows provided by the cell cycle, resulting in cells differentiating into those in which the respective mRNAs are either present or absent. This creates a way to generate cell phenotype diversity in multicellular organisms. (shrink)

Population genetics is often taught in introductory biology classes, starting with the Hardy–Weinberg principle (HWP) and genetic drift. Here I argue that teaching these two topics first aligns neither with current expert knowledge, nor with good pedagogy. Student difficulties with mathematics in general, and probability in particular, make population genetics difficult to teach and learn. I recommend an alternative, historically inspired ordering of population genetics topics, based on progressively increasing mathematical difficulty. This progression can facilitate just‐in‐time math instruction. This alternative (...) ordering includes, but does not privilege, the HWP and genetic drift. Stochastic events whose consequences are felt within a single generation, and the deterministic accumulation of the effects of selection across multiple generations, are both taught before tackling the stochastic accumulation of the effects of accidents of sampling. (shrink)

It is shown that the uncertainty connected with a `random in a broad sense' (not necessarily stochastic) event always has some `statistical regularity' (SR) in the form of a family of finite-additive probability distributions. The specific principle of guaranteed result in decision making is introduced. It is shown that observing this principle of guaranteed result leads to determine the one optimality criterion corresponding to a decision system with a given `statistical regularity'.

The study of biomechanics most often takes a classic adaptationist approach, examining the functional abilities of organisms in relation to what is allowed by physical parameters. This approach generally assumes strong selection and is less concerned with evolutionary stochasticity in determining the presence of biological traits. It is equally important, however, to consider the importance of constraint in determining the form of organisms. If selection is relatively weak compared to stochastic events, then the observed forms in living systems (...) can be taken not as those shapes that were strongly selected for, so much as those forms that do not violate physical rules and therefore persist. Using the problem of maximum animal size as a case study for this alternative biomechanical philosophy, I demonstrate one example of how biomechanical approaches can be used to study constraint and consider the concept of absent forms. This alternative mindset and approach produces a complementary system to the traditional form and function approach in biomechanics. The two philosophies can be used in conjunction to better understand biological systems. I focus particularly on the maximum size of flying animals, as they are a heavily constrained class of system that has also been shaped by substantial stochasticity. (shrink)

Stochastic forecasts in complex environments can benefit from combining the estimates of large groups of forecasters (“judges”). But aggregating multiple opinions faces several challenges. First, human judges are notoriously incoherent when their forecasts involve logically complex events. Second, individual judges may have specialized knowledge, so different judges may produce forecasts for different events. Third, the credibility of individual judges might vary, and one would like to pay greater attention to more trustworthy forecasts. These considerations limit the value (...) of simple aggregation methods like linear averaging. In this paper, a new algorithm is proposed for combining probabilistic assessments from a large pool of judges. Two measures of a judge’s likely credibility are introduced and used in the algorithm to determine the judge’s weight in aggregation. The algorithm was tested on a data set of nearly half a million probability estimates of events related to the 2008 U.S. presidential election (∼ 16000 judges). (shrink)

I compare deterministic and stochastic hidden variable models of the Bell experiment, exphasising philosophical distinctions between the various ways of combining conditionals and probabilities. I make four main claims. (1) Under natural assumptions, locality as it occurs in these models is equivalent to causal independence, as analysed (in the spirit of Lewis) in terms of probabilities and conditionals. (2) Stochastic models are indeed more general than deterministic ones. (3) For factorizable stochastic models, relativity's lack of superluminal causation (...) does not favour locality over completeness. (4) If we prohibit all superluminal causation, then the violation of the Bell inequality teaches us a lesson, besides quantum mechanics' familiar ones that quantities can lack precise values and that pairs of quantities can lack joint probabilities: namely, some pairs of events are not screened off by their common past. (shrink)

Accepted quantum description is stochastic, yet history is nonstochastic, i.e., not representable by a probability distribution. Therefore ordinary quantum mechanics is unsuited to describe history. This is a limitation of the accepted quantum theory, rather than a failing of mechanics in general. To remove the limitation, it would be desirable to find a form of quantum mechanics that describes the future stochastically and the past nonstochastically. For this purpose it proves sufficient to introduce into quantum mechanics, by means of (...) a perfected formal correspondence, certain analogs of the classical initial-condition constants. Through the restoration of such parameters at the quantum level one accomplishes a natural accommodation of time anisotropy, wave-function reduction, and “event” description by quantum mechanical equations of motion alone, without the need for extra postulates (e.g., a projection postulate). This requires a complete restructuring of quantum measurement theory. (shrink)

We demonstrate in this paper that the probabilities for sequential measurements have features very different from those of single-time measurements. First, they cannot be modelled by a classical stochastic process. Second, they are contextual, namely they depend strongly on the specific measurement scheme through which they are determined. We construct Positive-Operator-Valued measures (POVM) that provide such probabilities. For observables with continuous spectrum, the constructed POVMs depend strongly on the resolution of the measurement device, a conclusion that persists even if (...) we consider a quantum mechanical measurement device or the presence of an environment. We then examine the same issues in alternative interpretations of quantum theory. We first show that multi-time probabilities cannot be naturally defined in terms of a frequency operator. We next prove that local hidden variable theories cannot reproduce the predictions of quantum theory for sequential measurements, even when the degrees of freedom of the measuring apparatus are taken into account. Bohmian mechanics, however, does not fall in this category. We finally examine an alternative proposal that sequential measurements can be modeled by a process that does not satisfy the Kolmogorov axioms of probability. This removes contextuality without introducing non-locality, but implies that the empirical probabilities cannot be always defined (the event frequencies do not converge). We argue that the predictions of this hypothesis are not ruled out by existing experimental results (examining in particular the “which way” experiments); they are, however, distinguishable in principle. (shrink)

Unification of natural science and social science is a centuries-old, unmitigated debate. Natural science has a chronological advantage over social science because the latter took time to include many social phenomena in its fold. History of science witnessed quite a number of efforts by social scientists to fit this discipline in a rational if not mathematical framework. On the other hand a tendency among some physicists has been observed especially since the last century to recast a number of social phenomena (...) in the mould of events taking place in physical world and governed by well-known systems and equations of physics. It necessitated the introduction of social physics as a new inter-disciplinary subject. Obviously this attempt is aimed at explaining hitherto unsolved or highly debated issues of social science. Physicists are showing special interest on problems on economics, ranging from some topics of normative economics to the movement of prices of derivatives. Statistics has been widely used in these attempts and at least two sub-disciplines of the subject, namely, stochastic process and time series analysis deserve special mention. All these research activities gave birth to another inter-disciplinary subject named as econophysics. Interestingly, global financial crisis of 2007–08 has revived the need of determination of prices of derivatives in a more accurate manner. This article adumbrates a sketch of the theoretical synthesis between physics and economics and the role played by statistics in this process. (shrink)

A sense of agency (SoA) is the experience of subjective awareness regarding the control of one’s actions. Humans have a natural tendency to generate prediction models of the environment and adapt their models according to changes in the environment. The SoA is associated with the degree of the adaptation of the prediction models, e.g., insufficient adaptation causes low predictability and lowers the SoA over the environment. Thus, identifying the mechanisms behind the adaptation process of a prediction model related to the (...) SoA is essential for understanding the generative process of the SoA. In the first half of the current study, we constructed a mathematical model in which the SoA represents a likelihood value for a given observation (sensory feedback) in a prediction model of the environment and in which the prediction model is updated according to the likelihood value. From our mathematical model, we theoretically derived a testable hypothesis that the prediction model is updated according to a Bayesian rule or a stochastic gradient. In the second half of our study, we focused on the experimental examination of this hypothesis. In our experiment, human subjects were repeatedly asked to observe a moving square on a computer screen and press a button after a beep sound. The button press resulted in an abrupt jump of the moving square on the screen. Experiencing the various stochastic time intervals between the action execution button-press) and the consequent event square jumping caused gradual changes in the subjects' degree of their SoA. By comparing the above theoretical hypothesis with the experimental results, we concluded that the update (adaptation) rule of the prediction model based on the SoA is better described by a Bayesian update than by a stochastic gradient descent. (shrink)

Learning the structure of event sequences is a ubiquitous problem in cognition and particularly in language. One possible solution is to learn a probabilistic generative model of sequences that allows making predictions about upcoming events. Though appealing from a neurobiological standpoint, this approach is typically not pursued in connectionist modeling. Here, we investigated a sequential version of the restricted Boltzmann machine, a stochastic recurrent neural network that extracts high-order structure from sensory data through unsupervised generative learning and can (...) encode contextual information in the form of internal, distributed representations. We assessed whether this type of network can extract the orthographic structure of English monosyllables by learning a generative model of the letter sequences forming a word training corpus. We show that the network learned an accurate probabilistic model of English graphotactics, which can be used to make predictions about the letter following a given context as well as to autonomously generate high-quality pseudowords. The model was compared to an extended version of simple recurrent networks, augmented with a stochastic process that allows autonomous generation of sequences, and to non-connectionist probabilistic models. We conclude that sequential RBMs and stochastic simple recurrent networks are promising candidates for modeling cognition in the temporal domain. (shrink)

The paper intends to provide an algebraic framework in which subluminal causation can be analysed. The framework merges Belnap's 'outcomes in branching time' with his 'branching space-time' (BST). it is shown that an important structure in BST, called 'family of outcomes of an event', is a boolean algebra. We define next non-stochastic common cause and analyse GHZ-Bell theorems. We prove that there is no common cause that accounts for results of GHZ-Bell experiment but construct common causes for two other (...) quantum mechanical setups. Finally, we investigate why some setups allow for common causes whereas other setups do not. (shrink)

Evolution exploits the physics of non‐neural bioelectricity to implement anatomical homeostasis: a process in which embryonic patterning, remodeling, and regeneration achieve invariant anatomical outcomes despite external interventions. Linear “developmental pathways” are often inadequate explanations for dynamic large‐scale pattern regulation, even when they accurately capture relationships between molecular components. Biophysical and computational aspects of collective cell activity toward a target morphology reveal interesting aspects of causation in biology. This is critical not only for unraveling evolutionary and developmental events, but also (...) for the design of effective strategies for biomedical intervention. Bioelectrical controls of growth and form, including stochastic behavior in such circuits, highlight the need for the formulation of nuanced views of pathways, drivers of system‐level outcomes, and modularity, borrowing from concepts in related disciplines such as cybernetics, control theory, computational neuroscience, and information theory. This approach has numerous practical implications for basic research and for applications in regenerative medicine and synthetic bioengineering. (shrink)

In what follows, I propose to evaluate Giere's analysis by applying it to a causal process considered in evolutionary theory, namely, natural selection. To say that there is selection for a given trait is to say that possessing that trait causes differential reproductive success. If there is selection for a trait and if no other evolutionary forces impinge and there is no "sampling error" due to random drift, individuals with the trait will on average have more offspring than individuals without (...) it. But sampling error can't be discounted for finite populations; so the combined effect of selection and drift will be a probability distribution of numbers of offspring. In this event, selection for a trait will imply that the mean value of the distribution associated with the individuals possessing the trait exceeds the mean value for individuals without the trait. Evolutionary theory assigns a probability distribution of possible reproductive outputs to each organism and, thereby, views organisms as stochastic systems. This implies no commitment to indeterminacy at the microlevel, of course. (shrink)

‘Gouldian arguments’ appeal to the contingency of a scientific domain to establish that domain’s autonomy from some body of theory. For instance, pointing to evolutionary contingency, Stephen Jay Gould suggested that natural selection alone is insufficient to explain life on the macroevolutionary scale. In analysing contingency, philosophers have provided source-independent accounts, understanding how events and processes structure history without attending to the nature of those events and processes. But Gouldian Arguments require source-dependent notions of contingency. An account of (...) contingency is source-dependent when it is indexed to some pattern and some process. Positions like Gould’s do not turn on the mere fact of life’s contingency—that life’s shape could have been different due to its sensitivity to initial conditions, path-dependence or stochasticity. Rather, Gouldian arguments require that the contingency is due to particular kinds of processes: in this case, those which microevolutionary theory cannot account for. This source-dependent perspective clarifies both debates about the nature and importance of contingency, and empirical routes for testing Gould’s thesis. (shrink)

A quantum measurement-like event can produce any of a number of macroscopically distinct results, with corresponding macroscopically distinct gravitational fields, from the same initial state. Hence the probabilistically evolving large-scale structure of space-time is not precisely or even always approximately described by the deterministic Einstein equations.Since the standard treatment of gravitational wave propagation assumes the validity of the Einstein equations, it is questionable whether we should expect all its predictions to be empirically verified. In particular, one might expect the stochasticity (...) of amplified quantum indeterminacy to cause coherent gravitational wave signals to decay faster than standard predictions suggest. This need not imply that the radiated energy flux from gravitational wave sources differs from standard theoretical predictions. An underappreciated bonus of gravitational wave astronomy is that either detecting or failing to detect predicted gravitational wave signals would constrain the form of the semi-classical theory of gravity that we presently lack. (shrink)

Speciation is an aspect of evolutionary biology that has received little philosophical attention apart from articles mainly by biologists such as Mayr (1988). The role of speciation as a terminus a quo for the individuality of species or in the context of punctuated equilibrium theory has been discussed, but not the nature of speciation events themselves. It is the task of this paper to attempt to bring speciation events into some kind of general scheme, based primarily upon the (...) work of Sergey Gavrilets on adaptive landscapes, using migration rate, or gene flow, as the primary scale, and concluding that adaptive and drift explanations are complementary rather than competing. I propose a distinction between intrinsic and extrinsic selection, and the notion of reproductive reach and argue that speciation modes should be discriminated in terms of gene flow, the nature of selection maintaining reproductive reach, and whether the predominant cause is selective or stochastic. I also suggest that the notion of an adaptive “quasispecies” for asexual species is the primitive notion of species, and that members of reproductively coherent sexual species are additionally coadapted to their mating partners. (shrink)

Spontaneous localization theory is a quantum theory proposed by GianCarlo Ghirardi, together with Alberto Rimini and Tullio Weber in 1986. However, soon it became clear to Ghirardi that his work was more than just one theory: he actually developed a framework, a family of theories in which the wavefunction jumps, but where the ontology of the theory is underdetermined. After acknowledging that the wavefunction did not provide a satisfactory ontology, he assumed that matter was described by a continuous matter density (...) field in three-dimensional space, whose evolution is governed by a stochastic wavefunction evolution. Alternatively, Bell assumed that the wavefunction would govern a spatiotemporal event ontology, dubbed ‘flashes.’ However, not much work has been done with the perhaps most obvious possibility, namely that physical objects are made of particles. This paper has two aims. First to explain the reason why people require spontaneous localization theory to be more than just a theory about the wavefunction. This is done by showing how the problem everyone in the foundation of quantum mechanics take to be the fundamental problem of quantum mechanics, namely the measurement problem, is a red herring. Then, the paper explores the possibility of spontaneous localization theories of particles. I argue that this discussion is not a mere exercise, as spontaneous localization theories of particles may be amenable to a relativistic extension which does not require a foliation, and because in general the peculiar type of indeterminism of spontaneous localization theories may help shedding new light on the nature of the tension between quantum theory and relativity. (shrink)

This paper characterizes the role of the experimenter in causal explanations of laboratory phenomena. Causal explanation rests on appeals to the experimenter's efficacy as a causal agent. I contrast "demographic" and "genetic" explanations of stochastic outcomes in a set of competition experiments in ecology. The demographic view ascribes causes to the experimenter's agency in setting up the experiment and to events within the experimental set-up. The genetic view ascribes causes to an unrecognized effect of the experimenter's sampling process (...) prior to the experimental set-up. (shrink)

THE ART OF CAUSAL CONJECTURE Glenn Shafer Table of Contents Chapter 1. Introduction........................................................................................ ...........1 1.1. Probability Trees..........................................................................................3 1.2. Many Observers, Many Stances, Many Natures..........................................8 1.3. Causal Relations as Relations in Nature’s Tree...........................................9 1.4. Evidence............................................................................................ ...........13 1.5. Measuring the Average Effect of a Cause....................................................17 1.6. Causal Diagrams..........................................................................................20 1.7. Humean Events............................................................................................23 1.8. Three Levels of Causal Language................................................................27 1.9. An Outline of the Book................................................................................27 Chapter 2. Event Trees............................................................................................... .....31 2.1. Situations and Events...................................................................................32 2.2. The Ordering of Situations and Moivrean Events.......................................35 2.3. Cuts................................................................................................ ..............39 2.4. (...) Humean Events............................................................................................43 2.5. Moivrean Variables......................................................................................49 2.6. Humean Variables........................................................................................53 2.7. Event Trees for Stochastic Processes...........................................................54 2.8. Timing in Event Trees.................................................................................56 2.9. Intersecting Event Trees...............................................................................60 2.10. Notes on the Literature...............................................................................61 Chapter 3. Probability Trees...........................................................................................63 3.1. Some Types of Probability Trees.................................................................64 ii 3.2. Axioms for the Probabilities of Moivrean Events.......................................68 3.3. Zero Probabilities....................................................................................... ..70 3.4. A Sample-Space Analysis of the Event-Tree Axioms.................................72 3.5. Probabilities and Expected Values for Variables.........................................74 3.6. Martingales......................................................................................... .........79 3.7. The Expectation of a Variable in a Cut........................................................83 3.8. Conditional Expected Value and Conditional Expectation.........................87 Chapter 4. The Meaning of Probability...........................................................................91 4.1. The Interpretation of Expected Value..........................................................92 4.2. The Interpretation of Expectation................................................................95 4.3. The Long Run..............................................................................................98 4.4. Changes in Belief.........................................................................................101 4.5. The Empirical Validation of Probability......................................................106 4.6. The Diversity of Uses of Probability...........................................................108 4.7. Notes on the Literature.................................................................................110 Chapter 5. Independent Events.......................................................................................113 5.1. Independence........................................................................................ .......114 5.2. Weak Independence.....................................................................................118 5.3. The Principle of the Common Cause...........................................................121 5.4. Conditional Independence............................................................................128 5.5. Notes on the Literature.................................................................................133 Chapter 6. Events Tracking Events.................................................................................135 6.1. Tracking............................................................................................ ...........137 6.2. Tracking and Conditional Independence.....................................................142 6.3. Stochastic Subsequence...............................................................................143 6.4. Singular Diagrams for Stochastic Subsequence...........................................147 6.5. Conjunctive and Interactive Forks...............................................................149 Chapter 7. Events as Signs of Events..............................................................................153 iii 7.1. Sign................................................................................................ ..............154 7.2. Weak Sign................................................................................................ ....159 7.3. The Ethics of Causal Talk............................................................................160 7.4. Screening Off...............................................................................................16 2 Chapter 8. Independent Variables...................................................................................167 8.1. Unconditional Independence........................................................................170 8.2. Conditional Independence............................................................................175 8.3. Independence for Partitions.........................................................................177 8.4. Independence for Families of Variables......................................................182 8.5. Individual Properties of the Independence Relations...................................186 Chapter 9. Variables Tracking Variables........................................................................189 9.1. Tracking and Conditional Independence: A Summary...............................190 9.2. Strong Tracking............................................................................................ 192 9.3. Strong Tracking and Conditional Independence..........................................198 9.4. Stochastic Subsequence...............................................................................201 9.5. Functional Dependence................................................................................203 9.6. Tracking in Mean.........................................................................................204 9.7. Linear Tracking............................................................................................ 207 9.8. Tracking by Partitions..................................................................................210 9.9. Tracking by Families of Variables...............................................................212 Chapter 10. Variables as Signs of Variables...................................................................215 10.1. Sign................................................................................................ ............219 10.2. Linear Sign................................................................................................ .222 10.3. Scored Sign................................................................................................ 225 10.4. Families of Variables.................................................................................227 Chapter 11. AnTheory of Event Trees.............................................................229 11.1. Event Trees as Sets of Sets........................................................................230 11.2. Event Trees as Partially Ordered Sets........................................................232 iv 11.3. Regular Event Trees...................................................................................240 11.4. The Resolution of Moivrean Variables......................................................244 11.5. Humean Events and Variables...................................................................246 Chapter 12. Martingale Trees..........................................................................................247 12.1. Examples of Decision Trees......................................................................249 12.2. The Meaning of Probability in a Decision Tree.........................................253 12.3. Martingales......................................................................................... .......257 12.4. The Structure of Martingale Trees.............................................................261 12.5. Probability and Causality...........................................................................265 12.6. Lower and Upper Probability.....................................................................269 12.7. The Law of Large Numbers.......................................................................272 12.8. Notes on the Literature...............................................................................274 Chapter 13. Refining............................................................................................ ...........275 13.1. Examples of Refinement............................................................................277 13.2. A Constructive Definition of Finite Refinement.......................................281 13.3. Axioms for Refinement..............................................................................282 13.4. Lifting Moivrean Events and Variables.....................................................288 13.5. Refining Martingale Trees.........................................................................288 13.6. Grounding........................................................................................... .......294 Chapter 14. Principles of Causal Conjecture..................................................................299 14.1. The Diversity of Causal Explanation.........................................................302 14.2. The Mean Effect of the Happening of a Moivrean Event..........................305 14.3. The Effect of a Humean Variable..............................................................311 14.4. Attribution and Generality.........................................................................316 14.5. The Statistical Measurement of the Effect of a Cause...............................319 14.6. Measurement by Experiment.....................................................................320 14.7. Using Our Knowledge of How Things Work............................................322 v 14.8. Sampling Error...........................................................................................329 14.9. The Sampling Frame..................................................................................329 14.10. Notes on the Literature.............................................................................330 Chapter 15. Causal Models.............................................................................................3 31 15.1. The Causal Interpretation of Statistical Prediction....................................333 15.2. Generalizing to a Family of Exogenous Variables....................................337 15.3 Some Joint Causal Diagrams......................................................................339 15.4. Causal Path Diagrams................................................................................342 15.5. Causal Relevance Diagrams.......................................................................346 15.6. The Meaning of Latent Variables..............................................................352 15.7. Notes on the Literature...............................................................................357 Chapter 16. Representing Probability Trees...................................................................359 16.1. Three Graphical Representations...............................................................361 16.2. Skeletal Simplifications.............................................................................368 16.3. Martingale Trees in Type Theory...............................................................371 Appendix A. Huygens’s Probability Trees.....................................................................379 Huygens’s Manuscript in Translation..................................................................380 Appendix B. Some Elements of Graph Theory..............................................................385 B1. Undirected Graphs........................................................................................385 B2. Directed Graphs............................................................................................38 6 Appendix C. Some Elements of Order Theory...............................................................393 C1. Partial and Quasi Orderings.........................................................................393 C2. Singular and Joint Diagrams for Binary Relations.......................................394 C3. Lattices............................................................................................ .............395 C4. The Lattice of Partitions of a Set..................................................................396 Appendix D. The Sample-Space Framework for Probability.........................................399 D1. Probability Measures....................................................................................399 D2. Variables........................................................................................... ...........400 vi D3. Families of Variables...................................................................................401 D4. Expected Value............................................................................................402 D5. The Law of Large Numbers.........................................................................405 D6. Conditional Probability................................................................................406 D7. Conditional Expected Value........................................................................407 Appendix E. Prediction in Probability Spaces................................................................409 E1. Conditional Distribution...............................................................................411 E2. Regression on a Single Variable...................................................................412 E3. Regression on a Partition or a Family of Variables......................................415 E4. Linear Regression on a Single Variable.......................................................418 E5. Linear Regression on a Family of Variables................................................422 Appendix F. Sample-Space Concepts of Independence.................................................425 F1. Overview............................................................................................ ...........426 F2. Independence Proper.....................................................................................432 F3. Unpredictability in Mean..............................................................................434 F4. Simple Uncorrelatedness..............................................................................437 F5. Mixed Uncorrelatedness...............................................................................438 F6. Partial Uncorrelatedness...............................................................................440 F7. Independence for Partitions..........................................................................442 F8. Independence for Families of Variables.......................................................445 F9. The Basic Role of Uncorrelatedness.............................................................448 F10. Dawid’s Axioms.........................................................................................449 Appendix G. Prediction Diagrams..................................................................................453 G1. Path Diagrams............................................................................................ ..454 G2. Generalized Path Diagrams..........................................................................462 G3. Relevance Diagrams.....................................................................................466 G4. Bubbled Relevance Diagrams......................................................................475 Appendix H. Abstract Stochastic Processes...................................................................479 vii H1. Probability Conditionals and Probability Distributions...............................477 H2. Abstract Stochastic Processes......................................................................479 H3. Embedding Variables and Processes in a Sample Space.............................480 References.......................................................................................... ..............................491. (shrink)

Recent research into human origins has largely focused on deducing past events and processes from current patterns of genetic variation. Some human genes possess unexpectedly low diversity, seemingly resulting from events of the late Pleistocene. Such anomalies have previously been ascribed to population bottlenecks or selection on genes. For four species of matrilineal whale, evidence suggests that cultural evolution may have reduced the diversity of genes which have similar transmission characteristics to selective cultural traits, through a process called (...) cultural hitchhiking. Cultural evolution is characteristic of human societies and so should be considered as a potential determinant of human genetic diversity. A stochastic simulation of gene and cultural dynamics in an array of hunter-gatherer tribes shows that cultural selection has the potential to severely reduce genetic diversity if: inter-tribe gene flows are reasonably low (<~0.6-15 genes/tribe/generation); cultural evolution changes fitness by >~0.3-3%/generation; and fitness is changed more by cultural innovation within a tribe than cultural assimilation from neighboring tribes. Thus cultural hitchhiking may explain low diversity and short coalescence times in mitochondrial and, especially, Y-linked human genes. (shrink)

The de‐repression of transposable elements (TEs) in mammalian genomes is thought to contribute to genome instability, inflammation, and ageing, yet is viewed as a cell‐autonomous event. In contrast to mammalian cells, prokaryotes constantly exchange genetic material through TEs, crossing both cell and species barriers, contributing to rapid microbial evolution and diversity in complex communities such as the mammalian gut. Here, it is proposed that TEs released from prokaryotes in the microbiome or from pathogenic infections regularly cross the kingdom barrier to (...) the somatic cells of their eukaryotic hosts. It is proposed this horizontal transfer of TEs from microbe to host is a stochastic, ongoing catalyst of genome destabilization, resulting in structural and epigenetic variations, and activation of well‐evolved host defense mechanisms contributing to inflammation, senescence, and biological ageing. It is proposed that innate immunity pathways defend against the horizontal acquisition of microbial TEs, and that activation of this pathway during horizontal transposon transfer promotes chronic inflammation during ageing. Finally, it is suggested that horizontal acquisition of prokaryotic TEs into mammalian genomes has been masked and subsequently under‐reported due to flaws in current sequencing pipelines, and new strategies to uncover these events are proposed. (shrink)

��The Coherent Approximation Principle (CAP) is a method for aggregating forecasts of probability from a group of judges by enforcing coherence with minimal adjustment. This paper explores two methods to further improve the forecasting accuracy within the CAP framework and proposes practical algorithms that implement them. These methods allow flexibility to add fixed constraints to the coherentization process and compensate for the psychological bias present in probability estimates from human judges. The algorithms were tested on a data set of nearly (...) half a million probability estimates of events related to the 2008 U.S. presidential election (from about 16000 judges). The results show that both methods improve the stochastic accuracy of the aggregated forecasts compared to using simple CAP. (shrink)

In his recent book Scientific Explanation and the Causal Structure of the World Wesley Salmon provides a detailed explanation of objective homogeneity, a concept which is central to his S-R model of explanation. 1 propose a modification of Salmon's definition which both simplifies and (in minor ways) corrects it, while at the same time generalizes it by including an important temporal factor that is missing from the original. I argue that if the world is irreducibly stochastic, then objective probabilities (...) (determined by objective homogeneous reference classes) must be temporally relativized. We can speak coherently of the objective probability of a particular event relative to a given point in time, but not of the objective probability of the event simpliciter. I briefly explore the consequences, of the temporal relativity of objective homogeneity for Salmon's attempt to secure an objective (nonepistemic, nonpraagmatic) S-R basis for causal explanation. (shrink)

In his constructive and well-informed commentary, Andrei Khrennikov acknowledges a privileged status of classical probability theory with respect to statistical analysis. He also sees advantages offered by the Contextuality-by-Default theory, notably, that it “demystifies quantum mechanics by highlighting the role of contextuality,” and that it can detect and measure contextuality in inconsistently connected systems. He argues, however, that classical probability theory may have difficulties in describing empirical phenomena if they are described entirely in terms of observable events. We disagree: (...) contexts in which random variables are recorded are as observable as the variables’ values. Khrennikov also argues that the Contextuality-by-Default theory suffers the problem of non-uniqueness of couplings. We disagree that this is a problem: couplings are all possible ways of imposing counterfactual joint distributions on random variables that de facto are not jointly distributed. The uniqueness of modeling experiments by means of quantum formalisms brought up by Khrennikov is achieved for the price of additional, substantive assumptions. This is consistent with our view of quantum theory as a special-purpose generator of classical probabilities. Khrennikov raises the issue of “mental signaling,” by which he means inconsistent connectedness in behavioral systems. Our position is that it is as inherent to behavioral systems as their stochasticity. (shrink)

In his book “Medical Philosophy: Conceptual issues in Medicine”, Mario Bunge provides a unique account of medical philosophy that is deeply rooted in a realist ontology he calls “systemism”. According to systemism, the world consists of systems and their parts, and systems possess emergent properties that their parts lack. Events within systems may form causes and effects that are constantly conjoined via particular mechanisms. Bunge supports the views of the evidence-based medicine movement that randomized controlled trials (RCTs) provide the (...) best evidence to establish the truth of causal hypothesis; in fact, he argues that _only_ RCTs have this ability. Here, we argue that Bunge neglects the important feature of patients being open systems which are in steady interaction with their environment. We show that accepting this feature leads to counter-intuitive consequences for his account of medical hypothesis testing. In particular, we point out that (i) the confirmation of hypotheses is inherently stochastic and affords a probabilistic account of both confirmation and evidence which we provide here; (ii) RCTs are neither necessary nor sufficient to establish the truth of a causal claim; (iii) testing of causal hypotheses requires taking into account background knowledge and the context within which an intervention is applied. We conclude that there is no “best” research methodology in medicine, but that different methodologies should coexist in a complementary fashion. (shrink)

Process physics2 is, like all physics, a model of reality. However, unlike traditional substance-based versions, process physics implements many process philosophical concepts, perhaps most notably, the notion of internal relations. It argues that the universe can best be understood in terms of selfreferential semantic information that is remarkably similar to mathematical stochastic neural networks research in biology. It argues that information patterns generate new information through causal efficacy and, ultimately, internal integration, generating self-organising patterns of relationships. These patterns or (...) relations have an intrinsic value inherent in their self-actualisation and thereby experience a subjective unity in response to influences from the totality of their past. The result is an internally related self-organising stream of experiences that provides a defining essence objectively distinguishable in abstraction and as exhibiting all the characteristics of a quantum space and quantum matter. In process physics, therefore, quantum phenomena emerge where no prior assumption regarding their existence is made or prescribed at the start. Rather, they are internally generated as an inherent feature of an experientially becoming reality, growing in size over time and thus having an observable key feature — i.e. a ‘defining essence’ — of an expanding universe. Reality itself is now understood — and modeled — as having a primitive form of self awareness. By this we mean that it has, in the process philosopher Alfred North Whitehead’s words, prehensions of other actualities as objects in terms of their ‘provocation of some special activity within the subject’.3 In more biologically complex information systems these ultimately lead to experiential integration as conscious discrimination of contrasts in prior experiences. Reality is, ultimately, not about the identification of isolated individuals through externality, but related individuals through internality. The purpose of this paper is to arrive at a point whereby we might apply these ultimate principles of reality to management. To do this, we shall start by considering Whitehead’s own renderings of management issues, before turning to the use management studies has or has not made of his work. In the light of this discussion, we shall question the principle of deconstructive postmodernism that underpins this body of work. We shall then ask whether and to what extent Whiteheadian principles might help explain organisations as ‘event fields’ 4 within which ‘persons-in-communities’5 reside. This will then allow us to consider organisations in terms of a process reinterpretation of physics. In so doing, we shall uncover a final contradiction, between Whitehead’s understanding of organisation and his principles concerning the application of metaphysics, to which we shall at least indicate a solution. (shrink)

A structuralist “reconstruction sketch” of an idealized theory is provided. This theory, QM, has some essential features of quantum mechanics. QM is a theory about abstract “result-observation events”, formal characterizations of interactions among physical systems and their results. QM is a stochastic theory and in the stochastic apparatus some features of “real life” quantum mechanics are recognizable. The result-observation events themselves exhibit neither essentially quantum mechanical features nor essentially physical features. At the level of the basic (...) theory element QM is more like a specialization of probability theory than a physical theory. It is only at the level of specialization of the basic theory element that essentially physical and quantum mechanical features may be introduced. The account provides a “reconstruction sketch” rather than a reconstruction largely in that no account is given of physically interesting specializations. It also falls short of a full reconstruction in that the mathematical apparatus is restricted to finite structures. (shrink)

Prediction of daily rainfall is important for flood forecasting, reservoir operation, and many other hydrological applications. The artificial intelligence algorithm is generally used for stochastic forecasting rainfall which is not capable to simulate unseen extreme rainfall events which become common due to climate change. A new model is developed in this study for prediction of daily rainfall for different lead times based on sea level pressure which is physically related to rainfall on land and thus able to predict (...) unseen rainfall events. Daily rainfall of east coast of Peninsular Malaysia was predicted using SLP data over the climate domain. Five advanced AI algorithms such as extreme learning machine, Bayesian regularized neural networks, Bayesian additive regression trees, extreme gradient boosting, and hybrid neural fuzzy inference system were used considering the complex relationship of rainfall with sea level pressure. Principle components of SLP domain correlated with daily rainfall were used as predictors. The results revealed that the efficacy of AI models is predicting daily rainfall one day before. The relative performance of the models revealed the higher performance of BRNN with normalized root mean square error of 0.678 compared with HNFIS, BART, xgBoost, and ELM. Visual inspection of predicted rainfall during model validation using density-scatter plot and other novel ways of visual comparison revealed the ability of BRNN to predict daily rainfall one day before reliably. (shrink)

Cytoplasmic messenger ribonucleoprotein particles (mRNPs) represent the cellular transcriptome, and recent data have challenged our current understanding of their architecture, transport, and complexity before translation. Pre‐translational mRNPs are composed of a single transcript, whereas P‐bodies and stress granules are condensates. Both pre‐translational mRNPs and actively translating mRNPs seem to adopt a linear rather than a closed‐loop configuration. Moreover, assembly of pre‐translational mRNPs in physical RNA regulons is an unlikely event, and co‐regulated translation may occur locally following extracellular cues. We envisage (...) a stochastic mRNP transport mechanism where translational repression of single mRNPs—in combination with microtubule‐mediated cytoplasmic streaming and docking events—are prerequisites for local translation, rather than direct transport. (shrink)

The placenta arose during mammalian evolution, which is recent in evolutionary terms. Genetic changes underlying placental development remain identifiable by the new science of comparative genomics (approximately post‐2000). Randomly arising features of genomes including endogenous retroviruses and transposable elements have provided structural genes and gene‐regulatory motifs responsible for innovations in placental biology. Stochastic genetic events indeed contribute to new functionality. Theologically, random mutations are part of the strategy by which the divine purpose for humanity is attained. Placental function (...) critically underlies human brain development, and suboptimal function, associated with environmental conditions and maternal distress, contributes to mental health deficits in the offspring. Many enter life with handicaps arising from contingent events in utero, mandating understanding, compassion, and socioemotional support, imperatives native to moral including biblical values. The extended period of development afforded by placentation enables prenatal parenting, with implications for sensitive and devoted parental commitment. (shrink)

The following paper is based on a broad understanding of communication that considers as text basically anything that has been created within the framework of a cultural interaction by an author and that is perceived by a recipient. The first part of the paper introduces, explains and follows mostly cases in which the author’s violations of the recipient’s expectations have a communication value, i.e. provoke, in the recipient, a communication effect that matches the author’s intentions. In such cases, this effect (...) results as a consequence of an violation of the communication „cooperative“ principles. This, at the recipient’s end, translates into an event of expectancy violation. Each of such violations provokes an arousal in the recipient, which further motivates him/her to search for its cause. Finding this cause, and being “confronted” with the related violation pertaining to it with the norm equals, for the recipient, getting to the meaning of the text, or identifying its communication value etc. As part of the conclusion, a commented scheme is presented which offers a spectrum of possible communication outcomes “positioned” between the predictability of each textual element and the stochasticity of choice. The effort to illustrate all the explained facts results, in the paper, in a rich set of examples stemming from miscellaneous spheres of human activity – from “high styles” to rather day-to-day activities, to pop-culture. The objective is to show that the described principles, if not valid in general, permeate at least all forms of interaction. (shrink)

To ground judgments of credal probability on knowledge of chance via direct inference, one should appeal to the information about chances available relative to the most specific description known to be true of the trial event.Thus, to obtain a judgment of credal probability concerning the hypothesis that coin a landed heads at t given that it is known that at t it is known that a was tossed by Levi in 728 Philosophy Hall, the pertinent knowledge of chances concerns the (...) chances of coin a landing heads on a toss of coin a which is a toss at t, a toss in 728 Philosophy Hall and a toss by Levi. In many contexts, appeal is made to knowledge of the chance of coin a landing heads on a toss. This appeal, when legitimate, takes for granted that the additional information about the specific tossing listed in, and is stochastically irrelevant to landing heads and, hence, may be ignored. Such an assumption is a substantive presupposition about chances and not an a priori, self evident or pragmatic principle of methodology. (shrink)

This paper considers the nature of time and temporality in Homer. It argues that any exploration of narrative and time must, as its central tenet, take into account the irreducible plurality and interconnectedness of memory, the event, and experienced time. Drawing on notions of complexity, emergence, and stochastic behavior in science as well as phenomenological traditions in the discussion and analysis of time, temporality, and change, and offering extensive readings of Homer, of Homeric epithets and formulae, and of key (...) passages in the Iliad and Odyssey, the paper argues against chronological notions of linear time and progression and in favor of a complex, dynamic temporal “geometries” of Homeric temporality. The paper concludes by briefly extending the argument to the wider domain of ancient time in general. Homer is a fundamental point of reference in the ancient world. Thus, Homeric temporality—irreducibly complex—affects the cognition and perception of time throughout the whole of antiquity. (shrink)

The astonishing efficiency and accuracy of DNA replication has long suggested that refined rules enforce a single highly reproducible sequence of molecular events during the process. This view was solidified by early demonstrations that DNA unwinding and synthesis are coupled within a stable molecular factory, known as the replisome, which consists of conserved components that each play unique and complementary roles. However, recent single-molecule observations of replisome dynamics have begun to challenge this view, revealing that replication may not be (...) defined by a uniform sequence of events. Instead, multiple exchange pathways, pauses, and DNA loop types appear to dominate replisome function. These observations suggest we must rethink our fundamental assumptions and acknowledge that each replication cycle may involve sampling of alternative, sometimes parallel, pathways. Here, we review our current mechanistic understanding of DNA replication while highlighting findings that exemplify multi-pathway aspects of replisome function and considering the broader implications. Recent single-molecule studies have revealed that replisome function is dominated by stochastic sampling of multiple molecular pathways. In the context of these new findings, we re-examine the foundational assumptions and seminal experiments that have guided our understanding of replication mechanism and reconcile several long-debated coordination models. (shrink)