Gut microbiome plays a significant role in defining the health status of subjects, and recent studies highlight the importance of using time series strategies to analyse microbiome dynamics. In this paper, we develop a Bayesian model for microbiota longitudinal data, based on Dirichlet distribution with time-varying parameters, that take into account the compositional paradigm and consider principal balances. The proposed model can be effective for predicting the future dynamics of a microbial community in the short term and for analysing (...) the microbial interactions using the value of the estimated parameters. The usefulness of the proposed model is illustrated with six different datasets, and a comparison study with four alternative models is provided. (shrink)

Since the seminal paper of Nash (Proc Natl Acad Sci USA 36:48–49, 1950) game theoretic literature has focused mostly on equilibrium and not on maximin (minimax) strategies. In a recent paper of Pruzhansky (Int J Game Theory 40:351–365, 2011) it was shown that under fairy general conditions maximin strategies in completely mixed games can guarantee the same expected payoff as completely mixed Nash equilibrium strategies. Based on this finding, the current paper argues that maximin strategies have important properties. For instance, (...) maximin strategies may refine Nash equilibria in subjective mixed strategies. Further, Bayesian rationality of the players may favor maximin strategies more often than Nash equilibrium strategies. The paper concludes with several suggestions for further experimental research that may shed more light on whether maximin behavior can explain reality better than Nash equilibrium. (shrink)

Disputes between advocates of Bayesians and more orthodox approaches to statistical inference presuppose that Bayesians must regard must regard stopping rules, which play an important role in orthodox statistical methods, as evidentially irrelevant.In this essay, I show that this is not the case and that the stopping rule is evidentially relevant given some Bayesian confirmation measures that have been seriously proposed. However, I show that accepting a confirmation measure of this sort comes at the cost of rejecting two (...) useful ancillaryBayesian principles. (shrink)

Occam's razor—the idea that all else being equal, we should pick the simpler hypothesis—plays a prominent role in ordinary and scientific inference. But why are simpler hypotheses better? One attractive hypothesis known as Bayesian Occam's razor is that more complex hypotheses tend to be more flexible—they can accommodate a wider range of possible data—and that flexibility is automatically penalized by Bayesian inference. In two experiments, we provide evidence that people's intuitive probabilistic and explanatory judgments follow the prescriptions of (...) BOR. In particular, people's judgments are consistent with the two most distinctive characteristics of BOR: They penalize hypotheses as a function not only of their numbers of free parameters but also as a function of the size of the parameter space, and they penalize those hypotheses even when their parameters can be “tuned” to fit the data better than comparatively simpler hypotheses. (shrink)

Debunking arguments in ethics contend that our moral beliefs have dubious evolutionary, cultural, or psychological origins—hence concluding that we should doubt such beliefs. Debates about debunking are often couched in coarse-grained terms—about whether our moral beliefs are justified or not, for instance. In this paper, I propose a more detailed Bayesian analysis of debunking arguments, which proceeds in the fine-grained framework of rational confidence. Such analysis promises several payoffs: it highlights how debunking arguments don’t affect all agents, but rather (...) only those agents who updated on their intuitions using a specific range of evidentiary weights; it underscores how the debunkers shouldn’t conclude that we should reduce confidence beyond some threshold, but rather only that we should reduce confidence by some amount; and it proposes a method of integrating different kinds of evidence—about the kinds of epistemic flaws at play, about the different possible origins of our moral beliefs, about the background normative assumptions we’re entitled to make—in order to arrive at a rational moral credence in light of debunking. (shrink)

Gordon Belot argues that Bayesian theory is epistemologically immodest. In response, we show that the topological conditions that underpin his criticisms of asymptotic Bayesian conditioning are self-defeating. They require extreme a priori credences regarding, for example, the limiting behavior of observed relative frequencies. We offer a different explication of Bayesian modesty using a goal of consensus: rival scientific opinions should be responsive to new facts as a way to resolve their disputes. Also we address Adam Elga’s rebuttal (...) to Belot’s analysis, which focuses attention on the role that the assumption of countable additivity plays in Belot’s criticisms. (shrink)

In An Introduction to Probability Theory and its Applications, W. Feller established a way of ending the St. Petersburg paradox by the introduction of an entrance fee, and provided it for the case in which the game is played with a fair coin. A natural generalization of his method is to establish the entrance fee for the case in which the probability of heads is θ. The deduction of those fees is the main result of Section 2. We then propose (...) a Bayesian approach to the problem. When the probability of heads is θ the expected gain of the St. Petersburg game is finite, therefore there is no paradox. However, if one takes θ as a random variable assuming values in the paradox may hold, which is counter-intuitive. In Section 3 we determine necessary conditions for the absence of paradox in the Bayesian approach and in Section 4 we establish the entrance fee for the case in which θ is uniformly distributed in, for in this case there is a paradox. (shrink)

The unit root problem plays a central role in empirical applications in the time series econometric literature. However, significance tests developed under the frequentist tradition present various conceptual problems that jeopardize the power of these tests, especially for small samples. Bayesian alternatives, although having interesting interpretations and being precisely defined, experience problems due to the fact that that the hypothesis of interest in this case is sharp or precise. The Bayesian significance test used in this article, for the (...) unit root hypothesis, is based solely on the posterior density function, without the need of imposing positive probabilities to sets of zero Lebesgue measure. Furthermore, it is conducted under strict observance of the likelihood principle. It was designed mainly for testing sharp null hypotheses and it is called FBST for Full Bayesian Significance Test. (shrink)

Young children spend a large portion of their time pretending about non-real situations. Why? We answer this question by using the framework of Bayesian causal models to argue that pretending and counterfactual reasoning engage the same component cognitive abilities: disengaging with current reality, making inferences about an alternative representation of reality, and keeping this representation separate from reality. In turn, according to causal models accounts, counterfactual reasoning is a crucial tool that children need to plan for the future and (...) learn about the world. Both planning with causal models and learning about them require the ability to create false premises and generate conclusions from these premises. We argue that pretending allows children to practice these important cognitive skills. We also consider the prevalence of unrealistic scenarios in children's play and explain how they can be useful in learning, despite appearances to the contrary. (shrink)

Bayesian approaches to rationality require that a person’s degrees of belief be coherent. Among other implications, coherence requires that a person has the same degree of belief in every logically equivalent proposition. However, a person can have evidence for a claim without having evidence for all its propositional equivalences. This paper explores this conflict and argues that a person may be perfectly rational by virtue of responding to their evidence, even if their credences are not coherent. The paper also (...) challenges the idea that it is always better to have more coherent credence, highlighting the fundamental role that evidence plays in rational belief. (shrink)

Bayes’ inference cannot reliably account for uncertainty in mental processes. The reason is that Bayes’ inference is based on the assumption that the order in which the relevant features are evaluated is indifferent, which is not the case in most of mental processes. Instead of Bayes’ rule, a more general, probabilistic rule of inference capable of accounting for these order effects is established. This new rule of inference can be used to improve the current Bayesian models of cognition. Moreover, (...) it should play an essential role in the search for artificial emotional intelligence. (shrink)

The objective Bayesian view of proof (or logical probability, or evidential support) is explained and defended: that the relation of evidence to hypothesis (in legal trials, science etc) is a strictly logical one, comparable to deductive logic. This view is distinguished from the thesis, which had some popularity in law in the 1980s, that legal evidence ought to be evaluated using numerical probabilities and formulas. While numbers are not always useful, a central role is played in uncertain reasoning by (...) the ‘proportional syllogism’, or argument from frequencies, such as ‘nearly all aeroplane flights arrive safely, so my flight is very likely to arrive safely’. Such arguments raise the ‘problem of the reference class’, arising from the fact that an individual case may be a member of many different classes in which frequencies differ. For example, if 15 per cent of swans are black and 60 per cent of fauna in the zoo is black, what should I think about the likelihood of a swan in the zoo being black? The nature of the problem is explained, and legal cases where it arises are given. It is explained how recent work in data mining on the relevance of features for prediction provides a solution to the reference class problem. (shrink)

This work provides a conceptual foundation for a Bayesian approach to artificial inference and learning. I argue that Bayesian confirmation theory provides a general normative theory of inductive learning and therefore should have a role in any artificially intelligent system that is to learn inductively about its world. I modify the usual Bayesian theory in three ways directly pertinent to an eventual research program in artificial intelligence. First, I construe Bayesian inference rules as defeasible, allowing them (...) to be overridden in certain contexts and therefore allowing them to play a part in a hybrid system, coexisting with non-Bayesian modes of inference. I take seriously the need to find meaningful prior probabilities for hypotheses, and elaborate means for supplying an artificial intelligence with such. And I address the computational complexity of Bayesian inference by reference to simplifications using causal networks and by allowing the probabilistic acceptance of hypotheses and subsequent qualitative inference to supplement Bayesian reasoning. The result is a Pragmatic Bayesian model of induction. (shrink)

The goal of the paper is to review existing work on consciousness within the frameworks of Predictive Processing, Active Inference, and Free Energy Principle. The emphasis is put on the role played by the precision and complexity of the internal generative model. In the light of those proposals, these two properties appear to be the minimal necessary components for the emergence of conscious experience—a Minimal Unifying Model of consciousness.

In this paper, a problem for utility theory - that it would have an agent who was compelled to play “Russian Roulette’ with one revolver or another, to pay as much to have a six-shooter with four bullets relieved of one bullet before playing with it, as he would be willing to pay to have a six-shooter with two bullets emptied - is reviewed. A less demanding Bayesian theory is described, that would have an agent maximize expected values (...) of possible total consequence of his actions. And utility theory is located within that theory as valid for agents who satisfy certain formal conditions, that is, for agents who are, in terms of that more general theory, indifferent to certain dimensions of ‘risk’. Raiffa- and Savage-style arguments for its more general validity are then resisted. Addenda are concerned with implications for game theory, and relations between ‘utilities’ and ‘values’. (shrink)

Bayesian reasoning, defined here as the updating of a posterior probability following new information, has historically been problematic for humans. Classic psychology experiments have tested human Bayesian reasoning through the use of word problems and have evaluated each participant’s performance against the normatively correct answer provided by Bayes’ theorem. The standard finding is of generally poor performance. Over the past two decades, though, progress has been made on how to improve Bayesian reasoning. Most notably, research has demonstrated (...) that the use of frequencies in a natural sampling framework —as opposed to single-event probabilities—can improve participants’ Bayesian estimates. Furthermore, pictorial aids and certain individual difference factors also can play significant roles in Bayesian reasoning success. The mechanics of how to build tasks which show these improvements is not under much debate. The explanations for why naturally-sampled frequencies and pictures help Bayesian reasoning remain hotly contested, however, with many researchers falling into ingrained “camps” organized around two dominant theoretical perspectives. The present paper evaluates the merits of these theoretical perspectives, including the weight of empirical evidence, theoretical coherence, and predictive power. By these criteria, the ecological rationality approach is clearly better than the heuristics and biases view. Progress in the study of Bayesian reasoning will depend on continued research that honestly, vigorously, and consistently engages across these different theoretical accounts rather than staying “siloed” within one particular perspective. The process of science requires an understanding of competing points of view, with the ultimate goal being integration. (shrink)

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector,” a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine's activation that (...) required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4-year-olds were found. We suggest that children's causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base rate of certain events occurring. Four-year-olds, but not 3-year-olds were able to make this inference. (shrink)

Modelling data in applied areas particularly in reliability engineering is a prominent research topic. Statistical models play a vital role in modelling reliability data and are useful for further decision-making policies. In this paper, we study a new class of distributions with one additional shape parameter, called a new generalized exponential-X family. Some of its properties are taken into account. The maximum likelihood approach is adopted to obtain the estimates of the model parameters. For assessing the performance of these (...) estimators, a comprehensive Monte Carlo simulation study is carried out. The usefulness of the proposed family is demonstrated by means of a real-life application representing the failure times of electronic components. The fitted results show that the new generalized exponential-X family provides a close fit to data. Finally, considering the failure times data, the Bayesian analysis and performance of Gibbs sampling are discussed. The diagnostics measures such as the Raftery–Lewis, Geweke, and Gelman–Rubin are applied to check the convergence of the algorithm. (shrink)

Some authors claim that minimal models have limited epistemic value (Fumagalli, 2016; Grüne-Yanoff, 2009a). Others defend the epistemic benefits of modelling by invoking the role of robustness analysis for hypothesis confirmation (see, e.g., Levins, 1966; Kuorikoski et al., 2010) but such arguments find much resistance (see, e.g., Odenbaugh & Alexandrova, 2011). In this paper, we offer a Bayesian rationalization and defence of the view that robustness analysis can play a confirmatory role, and thereby shed light on the potential (...) of minimal models for hypothesis confirmation. We illustrate our argument by reference to a case study from macroeconomics. At the same time, we also show that there are cases in which robustness analysis is detrimental to confirmation. We characterize these cases and link them to recent investigations on evidential variety (Landes, 2020b, 2021; Osimani and Landes, forthcoming). We conclude that robustness analysis over minimal models can confirm, but its confirmatory value depends on concrete circumstances. (shrink)

The concept of non-arbitrage plays an essential role in finance theory. Under certain regularity conditions, the Fundamental Theorem of Asset Pricing states that, in non-arbitrage markets, prices of financial instruments are martingale processes. In this theoretical framework, the analysis of the statistical distributions of financial assets can assist in understanding how participants behave in the markets, and may or may not engender arbitrage conditions. Assuming an underlying Variance Gamma statistical model, this study aims to test, using the FBST - Full (...) Bayesian Significance Test, if there is a relevant price difference between essentially the same financial asset traded at two distinct locations. Specifically, we investigate and compare the behavior of call options on the BOVESPA Index traded at (a) the Equities Segment and (b) the Derivatives Segment of BM&FBovespa. Our results seem to point out significant statistical differences. To what extent this evidence is actually the expression of perennial arbitrage opportunities is still an open question. (shrink)

In earlier work I argued that using ‘vague probabilities’ did not ground any argument for significantly adjusting Bayesian decision theory. In this note I show that my earlier arguments don’t carry across smoothly to game theory. Allowing agents to have vague probabilities over possible outcomes dramatically increases the range of possible Nash equilibria in certain games, and hence arguably (but only arguably) increases the range of possible rational action.

A key role in inference is played by randomization, which has been extensively used in clinical trials designs. Randomization is primarily intended to prevent the source of bias in treatment allocation by producing comparable groups. In the frequentist framework of inference, randomization allows also for the use of probability theory to express the likelihood of chance as a source for the difference of end outcome. In the Bayesian framework, its role is more nuanced. The Bayesian analysis of clinical (...) trials can afford a valid rationale for selective controls, pointing out a more limited role for randomization than it is generally accorded. This paper is aimed to offer a view of randomization from the perspective of both frequentist and Bayesian statistics and discussing the role of randomization also in theoretical decision models. (shrink)

This essay is an attempt to gain better insight into Russell's positive account of inductive inference. I contend that Russell's postulates play only a supporting role in his overall account. At the center of Russell's positive view is a probabilistic, Bayesian model of inductive inference. Indeed, Russell and Maxwell actually held very similar Bayesian views. But the Bayesian component of Russell's view in Human Knowledge is sparse and easily overlooked. Maxwell was not aware of it when (...) he developed his own view, and I believe he was never fully aware of the extent to which Russell's account anticipates his own. The primary focus of this paper will be the explication of the Bayesian component of the Russell-Maxwell view, and the way in which it undermines judgment empiricism. (shrink)

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector”, a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine’s activation that (...) required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4- year-olds were found. We suggest that children’s causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base-rate of certain events occurring. Fouryear-olds, but not 3-year-olds were able to make this inference. (shrink)

If sensory organs encode environment, this code must be decoded to perception. The currently dominant theory of perception – predictive coding – assumes a “Bayesian decoder,” a probability function, which will present an optimal guess, given previous encodings of the environment – old codes testing new codes. Such a process would delay perception noticeably. This is inconsistent with the perception of music, which for several reasons must be direct.

Languages show substantial variability between their speakers, but it is currently unclear how the structure of the communicative network contributes to the patterning of this variability. While previous studies have highlighted the role of network structure in language change, the specific aspects of network structure that shape language variability remain largely unknown. To address this gap, we developed a Bayesian agent‐based model of language evolution, contrasting between two distinct scenarios: language change and language emergence. By isolating the relative effects (...) of specific global network metrics across thousands of simulations, we show that global characteristics of network structure play a critical role in shaping interindividual variation in language, while intraindividual variation is relatively unaffected. We effectively challenge the long‐held belief that size and density are the main network structural factors influencing language variation, and show that path length and clustering coefficient are the main factors driving interindividual variation. In particular, we show that variation is more likely to occur in populations where individuals are not well‐connected to each other. Additionally, variation is more likely to emerge in populations that are structured in small communities. Our study provides potentially important insights into the theoretical mechanisms underlying language variation. (shrink)

In the last 25 years, the concept of information has played a crucial role in communication theory, so much so that the terms information theory and communication theory are sometimes used almost interchangeably. It seems to us, however, that the notion of information is also destined to render valuable services to the student of induction and probability, of learning and reinforcement, of semantic meaning and deductive inference, as~well as of scientific method in general. The present volume is an attempt to (...) illustrate some of these uses of information concepts. In 'On Semantic Information' Hintikka summarizes some of his and his associates' recent work on information and induction, and comments briefly on its philosophical suggestions. Jamison surveys from the sub jectivistic point of view some recent results in 'Bayesian Information Usage'. Rosenkrantz analyzes the information obtained by experimen tation from the Bayesian and Neyman-Pearson standpoints, and also from the standpoint of entropy and related concepts. The much-debated principle of total evidence prompts Hilpinen to examine the problem of measuring the information yield of observations in his paper 'On the Information Provided by Observations'. Pietarinen addresses himself to the more general task of evaluating the systematizing power of hypotheses and theories, a task which quickly leads him to information concepts. Domotor develops a qualitative theory of information and entropy. His paper gives what is probably the first axiomatization of a general qualitative theory of information adequate to guarantee a numerical representation of the standard sort. (shrink)

Objective Bayesian epistemology invokes three norms: the strengths of our beliefs should be probabilities, they should be calibrated to our evidence of physical probabilities, and they should otherwise equivocate sufficiently between the basic propositions that we can express. The three norms are sometimes explicated by appealing to the maximum entropy principle, which says that a belief function should be a probability function, from all those that are calibrated to evidence, that has maximum entropy. However, the three norms of objective (...) Bayesianism are usually justified in different ways. In this paper we show that the three norms can all be subsumed under a single justification in terms of minimising worst-case expected loss. This, in turn, is equivalent to maximising a generalised notion of entropy. We suggest that requiring language invariance, in addition to minimising worst-case expected loss, motivates maximisation of standard entropy as opposed to maximisation of other instances of generalised entropy. Our argument also provides a qualified justification for updating degrees of belief by Bayesian conditionalisation. However, conditional probabilities play a less central part in the objective Bayesian account than they do under the subjective view of Bayesianism, leading to a reduced role for Bayes’ Theorem. (shrink)

So-called “traditional epistemology” and “Bayesian epistemology” share a word, but it may often seem that the enterprises hardly share a subject matter. They differ in their central concepts. They differ in their main concerns. They differ in their main theoretical moves. And they often differ in their methodology. However, in the last decade or so, there have been a number of attempts to build bridges between the two epistemologies. Indeed, many would say that there is just one branch of (...) philosophy here—epistemology. There is a common subject matter after all. In this paper, we begin by playing the role of a “bad cop,” emphasizing many apparent points of disconnection, and even conflict, between the approaches to epistemology. We then switch role, playing a “good cop” who insists that the approaches are engaged in common projects after all. We look at various ways in which the gaps between them have been bridged, and we consider the prospects for bridging them further. We conclude that this is an exciting time for epistemology, as the two traditions can learn, and have started learning, from each other. (shrink)

I present a puzzle about the epistemic role beliefs about experts' beliefs play in a rational agent's system of beliefs. It is shown that accepting the claim that an expert's degree of belief in a proposition, A, screens off the evidential support another proposition, B, gives to A in case the expert knows and is certain about whether B is true, leads in some cases to highly unintuitive conclusions. I suggest a solution to the puzzle according to which evidential (...) screening off is rejected, but show that the price of this solution is either giving up on the mere idea of deferring to expert's opinion or giving up on Bayesian conditionalization. (shrink)

Constructing an intuitive theory from data confronts learners with a “chicken‐and‐egg” problem: The laws can only be expressed in terms of the theory's core concepts, but these concepts are only meaningful in terms of the role they play in the theory's laws; how can a learner discover appropriate concepts and laws simultaneously, knowing neither to begin with? We explore how children can solve this chicken‐and‐egg problem in the domain of magnetism, drawing on perspectives from computational modeling and behavioral experiments. (...) We present 4‐ and 5‐year‐olds with two different simplified magnet‐learning tasks. Children appropriately constrain their beliefs to two hypotheses following ambiguous but informative evidence. Following a critical intervention, they learn the correct theory. In the second study, children infer the correct number of categories given no information about the possible causal laws. Children's hypotheses in these tasks are explained as rational inferences within a Bayesian computational framework. (shrink)

A widespread assumption in the contemporary discussion of probabilistic models of cognition, often attributed to the Bayesian program, is that inference is optimal when the observer's priors match the true priors in the world—the actual “statistics of the environment.” But in fact the idea of a “true” prior plays no role in traditional Bayesian philosophy, which regards probability as a quantification of belief, not an objective characteristic of the world. In this paper I discuss the significance of the (...) traditional Bayesian epistemic view of probability and its mismatch with the more objectivist assumptions about probability that are widely held in contemporary cognitive science. I then introduce a novel mathematical framework, the observer lattice, that aims to clarify this issue while avoiding philosophically tendentious assumptions. The mathematical argument shows that even if we assume that “ground truth” probabilities actually do exist, there is no objective way to tell what they are. Different observers, conditioning on different information, will inevitably have different probability estimates, and there is no general procedure to determine which one is right. The argument sheds light on the use of probabilistic models in cognitive science, and in particular on what exactly it means for the mind to be “tuned” to its environment. (shrink)

People are adept at inferring novel causal relations, even from only a few observations. Prior knowledge about the probability of encountering causal relations of various types and the nature of the mechanisms relating causes and effects plays a crucial role in these inferences. We test a formal account of how this knowledge can be used and acquired, based on analyzing causal induction as Bayesian inference. Five studies explored the predictions of this account with adults and 4-year-olds, using tasks in (...) which participants learned about the causal properties of a set of objects. The studies varied the two factors that our Bayesian approach predicted should be relevant to causal induction: the prior probability with which causal relations exist, and the assumption of a deterministic or a probabilistic relation between cause and effect. Adults’ judgments (Experiments 1, 2, and 4) were in close correspondence with the quantitative predictions of the model, and children’s judgments (Experiments 3 and 5) agreed qualitatively with this account. (shrink)

Intonation plays an integral role in comprehending spoken language. Listeners can rapidly integrate intonational information to predictively map a given pitch accent onto the speaker's likely referential intentions. We use mouse tracking to investigate two questions: (a) how listeners draw predictive inferences based on information from intonation? and (b) how listeners adapt their online interpretation of intonational cues when these are reliable or unreliable? We formulate a novel Bayesian model of rational predictive cue integration and explore predictions derived under (...) a concrete linking hypothesis relating a quantitative notion of evidential strength of a cue to the moment in time, relative to the unfolding speech signal, at which mouse trajectories turn towards the eventually selected option. In order to capture rational belief updates after concrete observations of a speaker's behavior, we formulate and explore an extension of this model that includes the listener's hierarchical beliefs about the speaker's likely production behavior. Our results are compatible with the assumption that listeners rapidly and rationally integrate all available intonational information, that they expect reliable intonational information initially, and that they adapt these initial expectations gradually during exposition to unreliable input. All materials, data, and scripts can be retrieved here: https://osf.io/dnbuk/. (shrink)

Recent years have seen a surge in online collaboration between experts and amateurs on scientific research. In this article, we analyse the epistemological implications of these crowdsourced projects, with a focus on Zooniverse, the world’s largest citizen science web portal. We use quantitative methods to evaluate the platform’s success in producing large volumes of observation statements and high impact scientific discoveries relative to more conventional means of data processing. Through empirical evidence, Bayesian reasoning, and conceptual analysis, we show how (...) information and communication technologies enhance the reliability, scalability, and connectivity of crowdsourced e-research, giving online citizen science projects powerful epistemic advantages over more traditional modes of scientific investigation. These results highlight the essential role played by technologically mediated social interaction in contemporary knowledge production. We conclude by calling for an explicitly sociotechnical turn in the philosophy of science that combines insights from statistics and logic to analyse the latest developments in scientific research. (shrink)

Probabilistic Relational Models (PRMs) are a framework for compactly representing uncertainties (actually probabilities). They result from the combination of Bayesian Networks (BNs), Object-Oriented languages, and relational models. They are specifically designed for their efficient construction, maintenance and exploitation for very large scale problems, where BNs are known to perform poorly. Actually, in large-scale problems, it is often the case that BNs result from the combination of patterns (small BN fragments) repeated many times. PRMs exploit this feature by defining these (...) patterns only once (the so-called PRM’s classes) and using them through multiple instances, as prescribed by the Object-Oriented paradigm. This design induces low construction and maintenance costs. In addition, by exploiting the classes’ structures, PRM’s state-of-the-art inference algorithm “Structured Variable Elimination” (SVE) significantly outperforms BN’s classical inference algorithms (e.g., Variable Elimination, VE; Local Conditioning, LC). SVE is actually an extension of VE that simply exploits classes to avoid redundant computations. In this article, we show that SVE can be enhanced using LC. Although LC is often thought as being outperformed by VE-like algorithms in BNs, we do think that it should play an important role for PRMs because its features are very well suited for best exploiting PRM classes. In this article, relying on Faÿ and Jaffray’s works, we show how LC can be used in conjunction with VE and deduce an extension of SVE that outperforms it for large-scale problems. Numerical experiments highlight the practical efficiency of our algorithm. (shrink)

Epistemologists often appeal to the idea that a normative theory must provide useful, usable, guidance to argue for one normative epistemology over another. I argue that this is a mistake. Guidance considerations have no role to play in theory choice in epistemology. I show how this has implications for debates about the possibility and scope of epistemic dilemmas, the legitimacy of idealisation in Bayesian epistemology, uniqueness versus permissivism, sharp versus mushy credences, and internalism versus externalism.

Contrary to common views that philosophy is extraneous to cognitive science, this paper argues that philosophy has a crucial role to play in cognitive science with respect to generality and normativity. General questions include the nature of theories and explanations, the role of computer simulation in cognitive theorizing, and the relations among the different fields of cognitive science. Normative questions include whether human thinking should be Bayesian, whether decision making should maximize expected utility, and how norms should be (...) established. These kinds of general and normative questions make philosophical reflection an important part of progress in cognitive science. Philosophy operates best, however, not with a priori reasoning or conceptual analysis, but rather with empirically informed reflection on a wide range of findings in cognitive science. (shrink)

Defenders of Inference to the Best Explanation claim that explanatory factors should play an important role in empirical inference. They disagree, however, about how exactly to formulate this role. In particular, they disagree about whether to formulate IBE as an inference rule for full beliefs or for degrees of belief, as well as how a rule for degrees of belief should relate to Bayesianism. In this essay I advance a new argument against non-Bayesian versions of IBE. My argument (...) focuses on cases in which we are concerned with multiple levels of explanation of some phenomenon. I show that in many such cases, following IBE as an inference rule for full beliefs leads to deductively inconsistent beliefs, and following IBE as a non-Bayesian updating rule for degrees of belief leads to probabilistically incoherent degrees of belief. (shrink)

This paper proposes a framework for representing in Bayesian terms the idea that analogical arguments of various degrees of strength may provide inductive support to yet untested scientific hypotheses. On this account, contextual information plays a crucial role in determining whether, and to what extent, a given similarity or dissimilarity between source and target may confirm an empirical hypothesis over a rival one. In addition to showing confirmation by analogy compatible with the adoption of a Bayesian standpoint, the (...) proposal outlined in this paper reveals a close agreement between the fulfillment of Hesse’s (Models and analogies in science, University of Notre Dame Press, 1963) criteria for analogical arguments capable of inductive support and the attribution of confirmatory power by the lights of Bayesian confirmation theory. In this sense, the Bayesian representation not only enriches a framework, Hesse’s, of enduring relevance for understanding scientific activity, but may offer something akin to a proof of concept of it. (shrink)

Abductive reasoning is central to reconstructing the past in the geosciences. This paper outlines the nature of the abductive method and restates it in Bayesian terms. Evidence plays a key role in this working method and, in particular, traces of the past are important in this explanatory framework. Traces, whether singularly or as groups, are interpreted within the context of the event for which they have evidential claims. Traces are not considered as independent entities but rather as inter-related pieces (...) of information concerning the likelihood of specific events. Exemplification of the use of such traces is provided by dissecting an example of their use in the environmental reconstruction of mountain climate. (shrink)

Norms—that is, specifications of what we ought to do—play a critical role in the study of informal argumentation, as they do in studies of judgment, decision-making and reasoning more generally. Specifically, they guide a recurring theme: are people rational? Though rules and standards have been central to the study of reasoning, and behavior more generally, there has been little discussion within psychology about why (or indeed if) they should be considered normative despite the considerable philosophical literature that bears on (...) this topic. In the current paper, we ask what makes something a norm, with consideration both of norms in general and a specific example: norms for informal argumentation. We conclude that it is both possible and desirable to invoke norms for rational argument, and that a Bayesian approach provides solid normative principles with which to do so. (shrink)

The major competing statistical paradigms share a common remarkable but unremarked thread: in many of their inferential applications, different probability interpretations are combined. How this plays out in different theories of inference depends on the type of question asked. We distinguish four question types: confirmation, evidence, decision, and prediction. We show that Bayesian confirmation theory mixes what are intuitively “subjective” and “objective” interpretations of probability, whereas the likelihood-based account of evidence melds three conceptions of what constitutes an “objective” probability.

This paper considers a special case of belief updating—when an agent learns testimonial data, or in other words, the beliefs of others on some issue. The interest in this case is twofold: (1) the linear averaging method for updating on testimony is somewhat popular in epistemology circles, and it is important to assess its normative acceptability, and (2) this facilitates a more general investigation of what it means/requires for an updating method to have a suitable Bayesian representation (taken here (...) as the normative standard). The paper initially defends linear averaging against Bayesian-compatibility concerns raised by Bradley (Soc Choice Welf 29:609-632, 2007), as well as problems associated with multiple testimony updates. The resolution of these issues, however, requires an extremely nuanced interpretation of the parameters of the linear averaging model—the so-called weights of respect. We go on to propose a role that the parameters of any 'shortcut' updating function should play, by way of minimal interpretation of these parameters. The class of updating functions that is consistent with this role, however, excludes linear averaging, at least in its standard form. (shrink)

The aim of this study is to justify the belief that there are biological normative mechanisms that fulfill non-trivial causal roles in the explanations (as formulated by researchers) of actions and behaviors present in specific systems. One example of such mechanisms is the predictive mechanisms described and explained by predictive processing (hereinafter PP), which (1) guide actions and (2) shape causal transitions between states that have specific content and fulfillment conditions (e.g. mental states). Therefore, I am guided by a specific (...) theoretical goal associated with the need to indicate those conditions that should be met by the non-trivial theory of normative mechanisms and the specific models proposed by PP supporters. In this work, I use classical philosophical methods, such as conceptual analysis and critical reflection. I also analyze selected studies in the field of cognitive science, cognitive psychology, neurology, information theory and biology in terms of the methodology, argumentation and language used, in accordance with their theoretical importance for the issues discussed in this study. In this sense, the research presented here is interdisciplinary. My research framework is informed by the mechanistic model of explanation, which defines the necessary and sufficient conditions for explaining a given phenomenon. The research methods I chose are therefore related to the problems that I intend to solve. In the introductory chapter, “The concept of predictive processing”, I discuss the nature of PP as well as its main assumptions and theses. I also highlight the key concepts and distinctions for this research framework. Many authors argue that PP is a contemporary version of Kantianism and is exposed to objections similar to those made against the approach of Immanuel Kant. I discuss this thesis and show that it is only in a very general sense that the PP framework is neo-Kantian. Here we are not dealing with transcendental deduction nor with the application of transcendental arguments. I argue that PP is based on reverse engineering and abduction inferences. In the second part of this chapter, I respond to the objection formulated by Dan Zahavi, who directly accuses this research framework of anti-realistic consequences. I demonstrate that the position of internalism, present in the so-called conservative PP, does not imply anti-realism, and that, due to the explanatory role played in it by structural representations directed at real patterns, it is justified to claim that PP is realistic. In this way, I show that PP is a non-trivial research framework, having its subject, specific methods and its own epistemic status. Finally, I discuss positions classified as the socalled radical PP. In the chapter “Predictive processing as a Bayesian explanatory model” I justify the thesis according to which PP offers Bayesian modeling. Many researchers claim that the brain is an implemented statistical probabilistic network that is an approximation of the Bayesian 7 rule. In practice, this means that all cognitive processes are to apply Bayes' rule and can be described in terms of probability distributions. Such a solution arouses objections among many researchers and is the subject of wide criticism. The purpose of this chapter is to justify the thesis that Bayesian PP is a non-trivial research framework. For this purpose, I argue that it explains certain phenomena not only at the computational level described by David Marr, but also at the level of algorithms and implementation. Later in this chapter I demonstrate that PP is normative modeling. Proponents of the use of Bayesian models in psychology or decision theory argue that they are normative because they allow the formulation of formal rules of action that show what needs to be done to make a given action optimal. Critics of this approach emphasize that such thinking about the normativity of Bayesian modeling is unjustified and that science should shift from prescriptive to descriptive positions. In a polemic with Shira Elqayam and Jonathan Evans (2011), I show that the division they propose into prescriptivism and Bayesian descriptivism is apparent, because, as I argue, there are two forms of prescriptivism, i.e. the weak and the strong. I argue that the weak version is epistemic and can lead to anti-realism, while the strong version is ontic and allows one to justify realism in relation to Bayesian models. I argue that a weak version of prescriptivism is valid for PP. It allows us to adopt anti-realism in relation to PP. In practice, this means that you can explain phenomena using Bayes' rule. This does not, however, imply that they are Bayesian in nature. However, the full justification of realism in relation to the Bayesian PP presupposes the adoption of strong prescriptivism. This position assumes that phenomena are explained by Bayesian rule because they are Bayesian as such. If they are Bayesian in nature, then they should be explained using Bayesian modeling. This thesis will be substantiated in the chapters “Normative functions and mechanisms in the context of predictive processing” and “Normative mechanisms and actions in predictive processing”. In the chapter “The Free Energy Principle in predictive processing”, I discuss the Free Energy Principle (hereinafter FEP) formulated by Karl Friston and some of its implications. According to this principle, all biological systems (defined in terms of Markov blankets) minimize the free energy of their internal states in order to maintain homeostasis. Some researchers believe that PP is a special case of applying this principle to cognition, and that predictive mechanisms are homeostatic mechanisms that minimize free energy. The discussion of FEP is important due to the fact that some authors consider it to be important for explanatory purposes and normative. If this is the case, then FEP turns out to be crucial in explaining normative predictive mechanisms and, in general, any normative biological mechanisms. To define the explanatory possibilities of this principle, I refer to the discussion of its supporters on the issue they define as the problem of continuity and discontinuity between life and mind. A critical analysis of this discussion and the additional arguments I have formulated have allowed me to revise the explanatory ambitions of FEP. I also reject the belief that this principle is necessary to explain the nature of predictive mechanisms. I argue that the principle formulated and defended by Friston is an important research heuristic for PP analysis. 8 In the chapter “Normative functions and mechanisms in predictive processing”, I start my analyzes by formulating an answer to the question about the normative nature of homeostatic mechanisms. I demonstrate that predictive mechanisms are not homeostatic. I defend the view that a full explanation of normative mechanisms presupposes an explanation of normative functions. I discuss the most important proposals for understanding the normativity of a function, both from a systemic and teleosemantic perspective. I conclude that the non-trivial concept of a function must meet two requirements which I define as explanatory and normative. I show that none of the theories I have invoked satisfactorily meets both of these requirements. Instead, I propose a model of normativity based on Bickhard's account, but supplemented by a mechanistic perspective. I argue that a function is normative when: (1) it allows one to explain the dysfunction of a given mechanism; (2) it contributes to the maintenance of the organism's stability by shaping and limiting possible relations, processes and behaviors of a given system; and when (3) (according to the representational and predictive functions) it enables explaining the attribution of logical values of certain representations / predictions. In such an approach, a mechanism is normative when it performs certain normative functions and when it is constitutive for a specific action or behavior, despite the fact that for some reason it cannot realize it either currently or in the long-term. Such an understanding of the normativity of mechanisms presupposes the acceptance of the epistemic hypothesis. I argue that this hypothesis is not cognitively satisfactory, and therefore the ontic hypothesis should be justified, which is directly related to adopting the position of ontic prescriptivism. For this reason, referring to the mechanistic theory of scientific explanations, I formulate an ontical interpretation of the concept of a normative mechanism. According to this approach, a mechanism or a function is normative when they perform such and such causal roles in explaining certain actions and behaviors. With regard to the normative properties of predictive mechanisms and functions, this means that they are the causes of specific actions an organism carries out in the environment. In this way, I justify the necessity of accepting the ontic hypothesis and rejecting the epistemic hypothesis. The fifth chapter, “Normative mechanisms and actions in predictive processing”, is devoted to the dark room problem and the related exploration-exploitation trade-off. A dark room is the state that an agent could be in if it minimized the sum of all potential prediction errors. I demonstrate that, in accordance with the basic assumption of PP about the need for continuous and long-term minimization of prediction errors, such a state should be desirable for the agent. Is it really so? Many authors believe it is not. I argue that the test of the value of PP is the possibility of a non-trivial solution of this problem, which can be reduced to the choice between active and uncertainty-increasing exploration and safe and easily predictable exploitation. I show that the solution proposed by PP supporters present in the literature does not enable a fully satisfactory explanation of this dilemma. Then I defend the position according to which the full explanation of the normative mechanisms, and, subsequently, the solution to the dilemma of exploration and exploitation, involves reference to the existence of constraints present in the environment. The constraints 9 include elements of the environment that make a given mechanism not only causal but also normative. They are therefore key to explaining the predictive mechanisms. They do not only play the role of the context in which the mechanism is implemented, but, above all, are its constitutive component. I argue that the full explanation of the role of constraints in normative predictive mechanisms presupposes the integration of individual models of specific cognitive phenomena, because only the mechanistic integration of PP with other models allows for a non-trivial explanation of the nature of normative predictive mechanisms that would have a strong explanatory value. The explanatory monism present in many approaches to PP makes it impossible to solve the problem of the dark room. Later in this chapter, I argue that the Bayesian PP is normative not because it enables the formulation of such and such rules of action, but because the predictive mechanisms themselves are normative. They are normative because they condition the choice of such and such actions by agents. In this way, I justify the hypothesis that normative mechanisms make it possible to explain the phenomenon of agent motivation, which is crucial for solving the dark room problem. In the last part of the chapter, I formulate the hypothesis of distributed normativity, which assumes that the normative nature of certain mechanisms, functions or objects is determined by the relations into which these mechanisms, functions or objects enter. This means that what is normative (in the primary sense) is the relational structure that constitutes the normativity of specific items included in it. I suggest that this hypothesis opens up many areas of research and makes it possible to rethink many problems. In the “Conclusion”, I summarize the results of my research and indicate further research perspectives. (shrink)

This paper aims to reconcile (i) the intuitively plausible view that a higher degree of coherence among independent pieces of evidence makes the hypothesis they support more probable, and (ii) the negative results in Bayesian epistemology to the effect that there is no probabilistic measure of coherence such that a higher degree of coherence among independent pieces of evidence makes the hypothesis they support more probable. I consider a simple model in which the negative result appears in a stark (...) form: the prior probability of the hypothesis and the individual vertical relations between each piece of evidence and the hypothesis completely determine the conditional probability of the hypothesis given the total evidence, leaving no room for the lateral relation (such as coherence) among the pieces of evidence to play any role. Despite this negative result, the model also reveals that a higher degree of coherence is indirectly associated with a higher conditional probability of the hypothesis because a higher degree of coherence indicates stronger individual supports. This analysis explains why coherence appears truth-conducive but in such a way that it defeats the idea of coherentism since the lateral relation (such as coherence) plays no independent role in the confirmation of the hypothesis. (shrink)

Heinz Von Forester characterizes the objects “known” by an autopoietic system as eigen-solutions, that is, as discrete, separable, stable and composable states of the interaction of the system with its environment. Previous articles have presented the FBST, Full Bayesian Significance Test, as a mathematical formalism specifically designed to access the support for sharp statistical hypotheses, and have shown that these hypotheses correspond, from a constructivist perspective, to systemic eigen-solutions in the practice of science. In this article several issues related (...) to the role played by language in the emergence of eigen-solutions are analyzed. The last sections also explore possible connections with the semiotic theory of Charles Sanders Peirce. (shrink)