Bayesian Confirmation Theory

When an empirical prediction E of hypothesis H is observed to be true, such observation is said to confirm, i.e., support (although not prove) the truth of the hypothesis. But why? What justifies the claim that such evidence supports the hypothesis? The widely accepted answer is that it is justified by induction. More specifically, it is commonly held that the following argument: (1) If H then E; (2) E; (3) Therefore, (probably) H—here referred to as ‘hypothetico-deductive con-firmation argument’—is inductively strong. Yet this argument looks nothing like an inductive generalisation, i.e., it doesn’t seem inductive in the term's traditional, enumerative sense. If anything, it has the form of the fallacy of affirming the consequent. This paper aims to solve this puzzle. True, in recent decades, ‘in-duction’ has been sometimes used more broadly to encompass any non-deductive, i.e., ampliative, argument. Applying Bayesian confirmation theory has famously demonstrated that hypothetico-deductive confirmation is indeed inductive in this broader, ampliative sense. Nonetheless, it will be argued here that, despite appearance, hypothetico-deductive confirmation can also be recast as a strong enumerative induction. Hence, by being enumeratively inductive, the scientific method of hypothetico-deductive confirmation is justified through this traditional, more restrictive type of induction rather than merely by ampliative induction.

ABSTRACTThe paper discusses the role of George L.S. Shackle in fostering an unconventional approach to individual decision making. Up until the early 1970s Shackle was the single critic of the probabilistic approach to decision making who proposed an alternative formal corpus for dealing with uncertainty. The main aim of the paper is to analyse Shackle's non‐probabilistic conceptualization of individual decisions under uncertainty from a specific viewpoint, namely that of a possible connection between his theory and one of the most interesting recent approaches to decision under uncertainty, the so‐called non‐additive probability approach of Gilboa and Schmeidler. The paper shows that these developments in modern decision theory take Shackle's issue seriously and confirm that the reliance of strict Bayesian theory on probabilistic judgements based on point‐probability estimates, a reliance that Shackle intended to oppose, is untenable. Non‐additive decision theory also provi...

The problem of evil presents the most prominent argument against the existence of God. The basic idea of the problem of evil is simple enough for anyone to understand, but there's still some philosophical work to be done regarding it-some general work about epistemology and some specific work about God and evil. The problem of evil once took the form of an argument claiming a logical incompatibility between the existence of God and the existence of evil; such arguments are widely agreed to fail.  But soon after, a variety of evidential or probabilistic arguments arrived. Such arguments typically involve a theological premise, one according to which some sort of evil would be strong evidence against the existence of God,  and an empirical premise, one according to which that sort of evil obtains. Given these two premises (and sometimes other background assumptions), the arguments conclude that God's existence is improbable, perhaps highly improbable. A prominent response to such arguments goes by the name "skeptical theism."  Although authors advocating this approach have taken a  As acknowledged by Rowe , fn. , Alston , , and many others, due largely to work by Plantinga (esp. , ch. , and , ch. ; see also , ff.).  Unless otherwise noted, we use the term 'God' in a fairly loose, minimal way. Our arguments are consistent with, but do not presuppose, the traditional conception of God as omniscient, omnipotent, and omnibenevolent. For these purposes, take the hypothesis that God exists to be the hypothesis that an extremely knowledgeable, extremely powerful, extremely benevolent being exists.  This is, as many have pointed out, an inapt label, since one can endorse the skeptical component of skeptical theism without being a theist at all.

The paper discusses the role of George L.S. Shackle in fostering an unconventional approach to individual decision making. Up until the early 1970s Shackle was the single critic of the probabilistic approach to decision making who proposed an alternative formal corpus for dealing with uncertainty. The main aim of the paper is to analyse Shackle's non-probabilistic conceptualization of individual decisions under uncertainty from a specific viewpoint, namely that of a possible connection between his theory and one of the most interesting recent approaches to decision under uncertainty, the so-called non-additive probability approach of Gilboa and Schmeidler. The paper shows that these developments in modern decision theory take Shackle's issue seriously and confirm that the reliance of strict Bayesian theory on probabilistic judgements based on point-probability estimates, a reliance that Shackle intended to oppose, is untenable. Non-additive decision theory also provides a usage of non-additive probability distributions in choice that is an alternative to Shackle's approach of using a qualitative notion of probability, such as potential surprise.

This note argues that a representation of the epistemic state of the individual through a non-additive measure provides a novel account of Keynes's view of probability theory proposed in his Treatise on Probability. The paper shows, first, that Keynes's "nonnumerical probabilities" can be interpreted in terms of decisional weights and distorsions of the probability priors. Second, that the degree of non-additivity of the probability measure can account for the confidence in the assessment without any reference to a second order probability. And, third, that the criterion for decision making under uncertainty derived in the non-additive literature incorporates a measure of the degree of confidence in the probability assessment. The paper emphasises the Keynesian derivation of Ellsberg's analysis: the parallel between Keynes and Ellsberg is deemed to be significant since Ellsberg's insights represent the main starting point of the modern developments of decision theory under uncertainty and ambiguity.

The computer package WinBUGS is introduced. We first give a brief introduction to Bayesian theory and its implementation using Markov chain Monte Carlo (MCMC) algorithms. We then present three case studies showing how WinBUGS can be used when classical theory is difficult to implement. The first example uses data on white storks from Baden Württemberg, Germany, to demonstrate the use of mark-recapture models to estimate survival, and also how to cope with unexplained variance through random effects. Recent advances in methodology and also the WinBUGS software allow us to introduce (i) a flexible way of incorporating covariates using spline smoothing and (ii) a method to deal with missing values in covariates. The second example shows how to estimate population density while accounting for detectability, using distance sampling methods applied to a test dataset collected on a known population of wooden stakes. Finally, the third case study involves the use of state-space models of wildlife population dynamics to make inferences about density dependence in a North American duck species. Reversible Jump MCMC is used to calculate the probability of various candidate models. For all examples, data and WinBUGS code are provided.

Fingerprinting is a common technique for indoor positioning using short range Radio Frequency (RF) technologies such as Wireless Location Area Network (WLAN) and Bluetooth (BT). It works in two phases: The first phase is a data training phase in which a radio map for the targeted area is generated in advance, while the second phase is the real-time location determination phase using the radio map. Considering the work amount for generating the radio map, only a few samples of the Radio Signal Strength Indicator (RSSI ...

En esta charla, se ofrece una caracterización del problema de la inducción como un problema asociado al razonamiento científico. Se describe su formulación clásica por parte de Hume y una versión constructiva como parte del proyecto de la teoría de la confirmación. Se examinan brevemente las contribuciones de la epistemología bayesiana a este proyecto

Moral conflicts are the situations which emerge as a response to deal with conflicting obligations or duties. An interesting case arises when an agent thinks that two obligations A and B are equally important, but yet fails to choose one obligation over the other. Despite the fact that the systematic study and the resolution of moral conflicts finds prominence in our linguistic discourse, standard deontic logic when used to represent moral conflicts, implies the impossibility of moral conflicts. This presents a conundrum for appropriate logic to address these moral conflicts. We frequently believe that there is a close connection between tolerating inconsistencies and conflicting moral obligations. In paraconsistent logics, we tolerate inconsistencies by treating them to be both true and false. In this paper, we analyze Graham Priest’s paraconsistent logic LP, and extend our examination to the deontic extension of LP known as DLP. We illustrate our work, with a classic example from ...

In this paper, we report the experimental results of Machine Translation models conducted by a NECTEC team (Team-ID: NECTEC) for the WAT-2021 Myanmar-English translation task (Nakazawa et al., 2021). Basically, our models are based on neural methods for both directions of English-Myanmar and Myanmar-English language pairs. Most of the existing Neural Machine Translation (NMT) models mainly focus on the conversion of sequential data and do not directly use syntactic information. However, we conduct multisource neural machine translation (NMT) models using the multilingual corpora such as string data corpus, tree data corpus, or POS-tagged data corpus. The multisource translation is an approach to exploit multiple inputs (e.g. in two different formats) to increase translation accuracy. The RNN-based encoder-decoder model with attention mechanism and transformer architectures have been carried out for our experiment. The experimental results showed that the proposed models of RNNbased architecture outperform the baseline model for the English-to-Myanmar translation task, and the multi-source and sharedmulti-source transformer models yield better translation results than the baseline.

In this paper, the Bayesian Theory is used to formulate the Inverse Problem (IP) of the EEG/MEG. This formulation offers a comparison framework for the wide range of inverse methods available and allows us to address the problem of model uncertainty that arises when dealing with different solutions for a single data. In this case, each model is defined by the set of assumptions of the inverse method used, as well as by the functional dependence between the data and the Primary Current Density (PCD) inside the brain. The key point is that the Bayesian Theory not only provides for posterior estimates of the parameters of interest (the PCD) for a given model, but also gives the possibility of finding posterior expected utilities unconditional on the models assumed. In the present work, this is achieved by considering a third level of inference that has been systematically omitted by previous Bayesian formulations of the IP. This level is known as Bayesian model averaging (BMA). The new approach is illustrated in the case of considering different anatomical constraints for solving the IP of the EEG in the frequency domain. This methodology allows us to address two of the main problems that affect linear inverse solutions (LIS): (a) the existence of ghost sources and (b) the tendency to underestimate deep activity. Both simulated and real experimental data are used to demonstrate the capabilities of the BMA approach, and some of the results are compared with the solutions obtained using the popular lowresolution electromagnetic tomography (LORETA) and its anatomically constraint version (cLORETA).

In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional interpretation of quantifiers in crucial ways, and show that Field's approach is closely related to the usual objectual semantics. One of Field's quantifier rules, however, must be significantly modified to be adapted to nonmonotonic conditional semantics. And this modification suggests, in turn, an alternative quantifier rule for probabilistic semantics.

The aim of this paper is to evaluate the best mode of transport in relation to the transport quality perceived by users. To this aim, we have found a framework to aggregate data and information coming from multiple information sources, often characterized by a high level of uncertainty. The proposed method is a hybrid approach based on two different theories: the Analytical Hierarchy Process (Saaty, 1980) and the Evidence-or Dempster-Shafer-Theory(Dempster 1967; 1968; Shafer, 1976). First, we have carried out a survey to investigate the users' point of view about the quality of transport, expressed through fifteen criteria, representative of the transport quality. Within the survey, the users were asked to rank the chosen criteria. Due to the complexity of the transport problem, we have used the Analytical Hierarchy Process to decompose the problem in different levels. Because of the decomposition, we have obtained priority vectors, which we have taken as basic probability assignments for application of the Dempster-Shafer Theory (DST). The DST is used to fuse different users' opinions and to take into account Uncertainty embedded in human judgment. The results show which alternatives users consider the best in relation to analyzed criteria.

This paper explores alternative axiomatizations of subjective expected utility theory for decision makers with direct preferences over actions; including a general subjective expected utility representation with actiondependent utility, and separately additive representations. In the context of the state-space formulation of agency theory the results of this paper constitute axiomatic foundations of the agent's behavior. ¤ My thinking on the issues discussed in this paper was inspired and stimulated by conversations with Steven Matthews, for which I am deeply grateful. I also bene…ted from Steve's comments on an earlier version of this paper. I am particularly grateful to Larry Epstein and Peter Wakker for their insightful comments and suggestions and to John Quiggin for calling my attention to some of the references. Suggetions of Simon Grant, Matthew Jackson, Mark Machina, and Zvi Safra help improve the exposition. 1 See Hart and Holmstrom (1987) and Chambers and Quiggin (2000).

This paper examines the indeterminacy of the representations of beliefs by subjective probabilities in non-expected utility theories of decision making under uncertainty. These theories include the rankdependent utility models, probabilistically sophisticated choice and probabilistic sophistication based on event exchangeability.

The aim of this paper is to argue for a revised and precisified version of the infamous Verifiability Criterion for the meaningfulness of declarative sentences. The argument is based on independently plausible premises concerning probabilistic confirmation and meaning as context-change potential, it is shown to be logically valid, and its ramifications for potential applications of the criterion are being discussed. Although the paper is not historical but systematic, the criterion thus vindicated will resemble the original one(s) in some important ways. At the same time, it will also be more modest insofar as meaningfulness will turn out to be relativized linguistically and probabilistically, and different choices of the linguistic and probabilistic parameters may lead to different verdicts on meaningfulness.

Consider an odd-sized jury, which determines a majority verdict between two equiprobable states of Nature. If each juror independently receives a binary signal identifying the correct state with identical probability p, then the probability of a correct verdict tends to one as the jury size tends to infinity (Marquis de Condorcet in Essai sur l'application de l'analyseà la probabilité des décisions renduesà la pluralité des voix, Imprim. Royale,

Term-modal logic uses modal operators that are indexed with terms of the language, which allows for quantification over these operators. Term-modal deontic logics (TMDL) can capture reasoning with rules, directed, and undirected obligations. Using the rich language of TMDL, we identify different types of deontic conflicts between directed obligations and describe reasoning in the face of these conflicts. We develop several monotonic logics in the TMDL family and show that none is capable of capturing all plausible deontic principles, while also being conflict-tolerant. To remedy this we develop several non-monotonic extensions in the format of adaptive logics. We end by isolating one of these, TMDL m , and commenting on it.

The linear discriminant analysis (LDA) is a linear classifier which has proven to be powerful and competitive compared to the main state-of-the-art classifiers. However, the LDA algorithm assumes the sample vectors of each class are generated from underlying multivariate normal distributions of common covariance matrix with different means (i.e., homoscedastic data). This assumption has restricted the use of LDA considerably. Over the years, authors have defined several extensions to the basic formulation of LDA. One such method is the heteroscedastic LDA (HLDA) which is proposed to address the heteroscedasticity problem. Another method is the nonparametric DA (NDA) where the normality assumption is relaxed. In this paper, we propose a novel Bayesian logistic discriminant (BLD) model which can address both normality and heteroscedasticity problems. The normality assumption is relaxed by approximating the underlying distribution of each class with a mixture of Gaussians. Hence, the proposed BLD provides more flexibility and better classification performances than the LDA, HLDA and NDA. A subclass and multinomial versions of the BLD are proposed. The posterior distribution of the BLD model is elegantly approximated by a tractable Gaussian form using variational transformation and Jensen's inequality, allowing a straightforward computation of the weights. An extensive comparison of the BLD to the LDA, support vector machine (SVM), HLDA, NDA and subclass discriminant analysis (SDA), performed on artificial and real data sets, has shown the advantages and superiority of our proposed method. In particular, the experiments on face recognition have clearly shown a significant improvement of the proposed BLD over the LDA.

Probabilistic syntactic parsing has made rapid progress, but is reaching a performance ceiling. More semantic resources need to be included. We exploit a number of semantic resources to improve parsing accuracy of a dependency parser. We compare semantic lexica on this task, then we extend the back-off chain by punishing underspecified decisions. Further, a simple distributional semantics approach is tested. Selectional restrictions are employed to boost interpretations that are semantically plausible. We also show that self-training can improve parsing even without needing a re-ranker, as we can rely on a sufficiently good estimation of parsing accuracy. Parsing large amounts of data and using it in self-training allows us to learn world knowledge from the distribution of syntactic relation. We show that the performance of the parser considerably improves due to our extensions.

It should be kept in mind that this relationship is strictly speaking a three-place one, involving a given background of knowledge and assumptions, often denote as K. Such a term will be omitted from our notation for simple reasons of convenience, as it is unconsequential for our discussion.

ABSTRACTThe paper discusses the role of George L.S. Shackle in fostering an unconventional approach to individual decision making. Up until the early 1970s Shackle was the single critic of the probabilistic approach to decision making who proposed an alternative formal corpus for dealing with uncertainty. The main aim of the paper is to analyse Shackle's non‐probabilistic conceptualization of individual decisions under uncertainty from a specific viewpoint, namely that of a possible connection between his theory and one of the most interesting recent approaches to decision under uncertainty, the so‐called non‐additive probability approach of Gilboa and Schmeidler. The paper shows that these developments in modern decision theory take Shackle's issue seriously and confirm that the reliance of strict Bayesian theory on probabilistic judgements based on point‐probability estimates, a reliance that Shackle intended to oppose, is untenable. Non‐additive decision theory also provi...

The World Health Organization (WHO) announced phasing out artemisinin as a single drug therapy for oral treatment of malaria from the market and has started advising prescription of Artemisin Combination Therapies (ACTs) in 2010. The objective of this work is to study the ACTs practice pattern by the doctors and selling pattern by the chemist in Varanasi city market. A Bayesian approach is used to perform agreement analysis between doctors and chemists drug practice in this regard. It has been found that the agreement level between doctors and chemist towards ACTs is higher in case of pregnant mothers in comparison to the other population.

The impact of the decision maker features on decision making process sometimes contradicts with the traditional theories. Modeling a decision making model it should be noted that it is primarily a behavioral model and behavior is influenced by ambiguity. Decision making is a behavioral process highly conditioned by the primary motives beliefs of a DM. In this paper we consider an imprecise hierarchical decision-making model where the first and the second level are described by interval probabilities. This method associates with the construction of a non-additive measure as a lower prevision and uses this capacity in Choquet integral for constructing a utility function. This method uses combined state of nature and decision maker's state which allows distinguishing the ambiguity and ambiguity attitude. We provide an experiment showing application of the suggested analysis.

If you love someone, is it good to believe better of her than epistemic norms allow? The partiality view says that it is: love, on this view, issues norms of belief that clash with epistemic norms. The partiality view is supposedly supported by an analogy between beliefs and actions, by the phenomenology of love, and by the idea that love commits us to the loved one's good character. I argue that the partiality view is false, and defend what I call the epistemic view. On the epistemic view, love also issues norms of belief. But these say simply (and perhaps surprisingly) that you should adhere to epistemic norms in forming and maintaining beliefs about loved ones. I offer two arguments for the epistemic view. The first appeals to the emotional responses of love, which, when sensitive to what the loved one is really like, can make love great and be morally transformative. The second is a new argument for why caring for a loved one requires true beliefs about him. We see that there may be some boundaries, such as stuffy traditions, that love is right to defy, but that epistemic boundaries are not among them.

Deontic conflicts pose an important challenge to deontic logicians. The standard account —standard deontic logic, SDL— is not apt for addressing this challenge since it trivializes conflicts. Two main stratagems for gaining conflict-tolerance have been proposed: to weaken SDL in various ways, and to contextualize the reign of SDL to consistent subsets of the premise set. The latter began with the work of van Fraassen and has been further developed by Horty. In this paper we characterize this second approach in general terms. We also study three basic ways to contextualize SDL and supplement each of these with a dynamic proof theory in the framework of adaptive logics.

Alongside science and law, argumentation is also of central importance in everyday life. But what characterizes a good argument? This question has occupied philosophers and psychologists for centuries. The theory of Bayesian argumentation is particularly suitable for clarifying it, because it allows us to take into account in a natural way the role of uncertainty, which is central to much argumentation. Moreover, it offers the possibility of measuring the strength of an argument in probabilistic terms. One way to do this, implicit in much work, is to identify the strength of an argument with the degree to which the premises of the argument confirm the conclusion. We criticize this prima facie plausible proposal and suggest instead that the strength of an argument has something to do with how much the premises and the conclusion of the argument cohere with each other. This leads to a new probabilistic measure whose properties we examine in more detail.

Orte of the challenges Kuhn's work poses to philosophy of science concems the insight that theory-choice and, accordingly, theory-change is governed by a more complex and subtle procedure than anticipated. In particular, this procedure is claimed to inevitably and justifiedly leave room for individual preferences so that theory-choice fails to be determined unambiguously by criteria with epistemic bearing. This methodological uncertainty can be labeled as Kuhn-underdetermination. Unlike Duhem-Quine underdetermination, it does not require empirical equivalence but rather refers to a situation in which alternative theories have their strengths and faults in different areas and in different respects so that no clear overall picture emerges. Overarching methodological theories can be construed as attempts to overcome the limits set by Kuhn underdetermination. In this perspective, theories like Lakatosianism and Bayesianism provide mies for epistemic judgments that are intended to make a clear evaluation of the credentials of rivaling scientific theories possible. The two methodological theories are supposed to serve as guidelines for methodological judgment or at least to explain with hindsight why a particular theory was picked. However, an closer scrutiny the two methodological theories founder in this tack of accounting for theory choice decisions. The criteria of excellence they specify are kable to uncertainties of the saure sort as the more traditional virtues they are intended to replace. The paper proposes an alternative picture: methodological theories suggest general maxims and mies that guide the confirmation process rather than provide criteria for specific theorychoice decisions. Methodological theories serve to connect and unify such maxims and rules. Traditionally, lists of methodological virtues are drawn up ad hoc. One could easily add further criteria or delete others. By contrast, methodological theories provide a coherent approach to appreciating scientific theories and comparing their explanatory achievements. And they give a rationale for why these rules rather than others deserve to be preferred.

This note argues that a representation of the epistemic state of the individual through a non-additive measure provides a novel account of Keynes's view of probability theory proposed in his Treatise on Probability. The paper shows, first, that Keynes's "nonnumerical probabilities" can be interpreted in terms of decisional weights and distorsions of the probability priors. Second, that the degree of non-additivity of the probability measure can account for the confidence in the assessment without any reference to a second order probability. And, third, that the criterion for decision making under uncertainty derived in the non-additive literature incorporates a measure of the degree of confidence in the probability assessment. The paper emphasises the Keynesian derivation of Ellsberg's analysis: the parallel between Keynes and Ellsberg is deemed to be significant since Ellsberg's insights represent the main starting point of the modern developments of decision theory under uncertainty and ambiguity.

This work relies on a probabilistic framework to search for suitable grasping regions on objects. In this approach, the object model is acquired based on occupancy grid representation that deals with the sensor uncertainty allowing later the decomposition of the object global shape into components. Through mixture distribution-based representation we achieve the object segmentation where the outputs are the point cloud clustering. Each object component is matched to a geometrical primitive. The advantage of representing object components into geometrical primitives is due to the simplification and approximation of the shape that facilitates the search for suitable object region for grasping given a context. Human demonstrations of predefined grasp are recorded and then overlaid on the object surface given by the probabilistic volumetric map to find the contact points of stable grasps. By observing the human choice during the object grasping, we perform the learning phase. Bayesian theory is used to identify a potential object region for grasping in a specific context when the artificial system faces a new object that is taken as a familiar object due to the primitives approximation into known components.

In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process' behaviour to be partly unknown. Then we use Walley's theory of coherent lower previsions, a generalisation of the Bayesian theory to imprecision, to derive the rule to update beliefs under incompleteness that logically follows from our assumptions, and that we call conservative inference rule. This rule has some remarkable properties: it is an abstract rule to update beliefs that can be applied in any situation or domain; it gives us the opportunity to be neither too optimistic nor too pessimistic about the incompleteness process, which is a necessary condition to draw reliable while strong enough conclusions; and it is a coherent rule, in the sense that it cannot lead to inconsistencies. We give examples to show how the new rule can be ap...

Imprecise probability models and their applications This special issue of the International Journal of Approximate Reasoning (IJAR) grew out of the 5th International Symposium on Imprecise Probabilities and Their Applications (ISIPTA'07), held in the beautiful city of Prague, Czech Republic, in July 2007 (http://www.sipta.org/isipta07). The symposium was organized by Gert de Cooman, Jiřina Vejnarová, and Marco Zaffalon. The term imprecise probabilities is used to refer to a number of approaches that allow for a more general and flexible modeling of uncertainty or chance by giving up the restriction to sharp and additive numerical probabilities. These approaches may be characterised from many different philosophical standpoints and many different types of mathematical calculus. ISIPTA meetings are a primary forum for presenting and discussing new advances in imprecise probabilities. Previous meetings were held in Ghent (Belgium) in 1999, in Cornell (USA) in 2001, in Lugano (Switzerland) in 2003, and in Pittsburgh (USA) in 2005. Here, we continue the good tradition of basing a special issue of the International Journal of Approximate Reasoning on the ISIPTA meetings. The meeting in Prague started with a series of tutorials devoted to different aspects of imprecise probabilities, that were presented by Scott Ferson, George Klir, Enrique Miranda and Teddy Seidenfeld. It also benefited from invited talks by Terrence Fine and Glenn Shafer. After a rather selective reviewing process, 48 papers were included in the proceedings of the conference, and we had the pleasure, and the burden, to select eight of them for this special issue. In our selection we have tried to encompass the variety mentioned above, both from the theoretical and from the applied point of view; there are nonetheless many other papers that would have also deserved to be included in this special issue. We begin with three papers concerned with results in the context of generalised Bayesian learning. The first of these, authored by Kriegler, presents a so-to-say open version of Bayes' rule, dropping the implicit closed world assumption that one of the considered models has to be the true model producing the data. Technically this is achieved by extending the parameter space to the space of all models and then contracting it again. The methodology is illustrated in the context of auto-regressive processes. The paper by Piatti, Zaffalon, Trojani and Hutter investigates the problem of learning about a categorical random variable. It is well known that, in this context, an initial state of prior ignorance is not compatible with learning. The authors consider then an alternative approach, called near ignorance, which resembles ignorance in many respects but seems at the same time to allow for learning. To which extent this is really the case is established in this paper. The paper by Pelessoni and Vicig is concerned with a structure-free version of Williams' notion of coherence of a number of conditional lower previsions. The authors study this notion and compare it with other approaches to consistency in the literature, such as Walley's notion of coherence or the notion of centered convexity. All these approaches arise in the extension of the subjective probability approach of de Finetti to take into account imprecision. Next, the paper by Fierens contributes to the frequentist branch of imprecise probability, initiated by T.L. Fine and colleagues, where sets of measures are interpreted from the frequentist point of view, leading to so-called chaotic models. By introducing real-valued test functions, Fierens extends the concept of chaotic models to real-valued variables, investigates their properties and illustrates the basic ideas with data on exchange rates in Argentina. The third part of the issue is devoted to the problem of decision making with imprecise probabilities. We have two papers on this. The one by Hable is concerned with decision making under imprecise sample (and prior) information. He derives a necessary and sufficient condition for the existence of a least favorable model, which allows to reduce the complex decision problem to an easier solvable classical decision problem. Next, Troffaes investigates the approximation of loss functions and credal sets by finitary ones, and bounds the effects of such an approximation. He considers a decision problem where the available information is modeled by an arbitrary (not necessarily convex nor closed) set of probabilities and a state-independent utility function. We conclude the issue with two different applications of imprecise probability models of general methodological interest. The paper by Antonucci, Brühlmann, Piatti and Zaffalon presents a credal network for risk evaluation in case of intrusion of

A new trend in deep learning, represented by Mutual Information Neural Estimation (MINE) and Information Noise Contrast Estimation (InfoNCE), is emerging. In this trend, similarity functions and Estimated Mutual Information (EMI) are used as learning and objective functions. Coincidentally, EMI is essentially the same as Semantic Mutual information (SeMI) proposed by the author 30 years ago. This paper first reviews the evolutionary histories of semantic information measures and learning functions. Then, it briefly introduces the author’s semantic information G theory with the rate-fidelity function R(G) (G denotes SeMI, and R(G) extends R(D)) and its applications to multi-label learning, the maximum Mutual Information (MI) classification, and mixture models. Then it discusses how we should understand the relationship between SeMI and Shannon’s MI, two generalized entropies (fuzzy entropy and coverage entropy), Autoencoders, Gibbs distributions, and partition functions from the perspective of the R(G) function or the G theory. An
important conclusion is that mixture models and Restricted Boltzmann Machines converge because SeMI is maximized, and Shannon’s MI is minimized, making information efficiency G/R close to 1. A potential opportunity is to simplify deep learning by using Gaussian channel mixture models for pre-training deep neural networks’ latent layers without considering gradients. It also discusses how the SeMI measure is used as the reward function (reflecting purposiveness) for reinforcement learning. The G theory helps interpret deep learning but is far from enough. combining semantic information theory and deep learning will accelerate their development.

Advisory system for operators of complex industrial processes has been developed and improved by an international team of scientists and people from industry since 2000. Main purpose of the advisory system is to help operator set up manually adjustable parameters of an industrial process, with the aim to reach required production quality. Industrial process is taken for a stochastic process and input signals of its control system are taken for random variables. Based on Bayesian probability theory, a software toolbox was created for handling mixtures of probability density functions describing behavior of the process. Advisory system was tested and pilot application was installed on rolling mills producing metal strips. During the tests, an idea emerged to exploit verified probabilistic approach for complicated diagnostic tasks too. This diagnostics is intended for recognition of process malfunction which cannot be easily revealed by analysis of particular single signals only but analysis in multidimensional data space must be involved instead. Main principle of the advanced diagnostic method consists in finding a representation of process behavior in a short history by a mixture of probability density functions called historical mixture. Process behavior in the latest time period is represented by actual mixture. Difference between historical and actual mixtures is evaluated by calculation of Kullback-Leibler divergence. Mixtures and divergences are calculated repeatedly in time and a big change in the divergence value can be used as a source of alarm for non-standard process behavior.

Tacking by conjunction is a well-known problem for Bayesian confirmation theory. In the first section, disadvantages of existing Bayesian solution proposals to this problem are pointed out and an alternative solution proposal is presented: that of genuine confirmation (GC). In the second section, the notion of GC is briefly recapitulated and three versions of GC are distinguished: full (qualitative) GC, partial (qualitative) GC and quantitative GC. In the third section, the application of partial GC to pure postfacto speculations is explained. In the fourth section it is demonstrated that full GC is a necessary condition for Bayesian convergence to certainty based on the accumulation of conditionally independent pieces of evidence. It is found that whenever a hypothesis is equivalent to a disjunction of more fine-grained hypotheses conveying different probabilities to the evidence, then conditional independence of the evidence fails. This failure occurs typically for unspecific negations of hypotheses. A refined version of the convergence to certainty theorem that overcomes this difficulty is developed in the final section.

The Problem of Old Evidence (POE) states that Bayesian confirmation theory cannot explain why a theory H can be confirmed by a piece of evidence E already known. Different dimensions of POE have been highlighted. Here, I consider the dynamic and static dimension. In the former, we want to explain how the discovery that H accounts for E confirms H. In the latter, we want to understand why E is and will be a reason to prefer H over its competitors. The aim of the paper is twofold. Firstly, I stress that two recent solutions to the dynamic dimension, recently proposed by Eva and Hartmann, can be read in terms of Inference to the Best Explanation (IBE). On this basis, I gauge the weaknesses and strengths of the two models by showing that the two authors endorse a particular formulation of IBE, and that it is still unsure if it is the one descriptively used. Moreover, I contend that, while one condition of their first model is not expression of this formulation, the only condition of their second model is. Secondly, I focus on the static dimension of POE which, now, has to be expressed in IBE terms. To solve it, I rely on the counterfactual approach, and on a version of IBE in which explanatory considerations help to evaluate the terms in Bayes' theorem. However, it turns out that the problems of the counterfactual approach recur even when it is used to solve the static POE in IBE terms.

A yearlong study was conducted to determine factors that affect the abundance and distribution of lysogens and free viruses at fresh-, brackish-, and saltwater stations in Newport Bay, CA. The viral and bacterial abundance were highest in the freshwater (average 1.1 Â 10 8 and 1.1 Â 10 7 mL À1 , respectively) and lowest in the marine water (average 0.4 Â 10 8 and 0.5 Â 10 7 mL À1 , respectively). Bacterial and viral counts were also several times higher during the summer than in winter. Approximately, 35% of the 141 samples were inducible in the presence of mitomycin C. The highest percentage of inducible lysogens was observed in marine waters (42%), while the lowest percentage was observed in the warmer freshwater (23%). A statistical model for the joint occurrence of lysogens and free viruses was formulated and estimated using Bayesian techniques to understand the key environmental determinants of viruses and lysogens. Our results support the existence of significant heterogeneity between the saltwater and freshwater sites. A parsimonious model that combines the two saltwater sites performs best among the specifications that were considered. Bacteria and water temperature were significant determinants of virus counts, whereas lysogen relationships are unclear. Importantly, conditional on the covariates, viruses and lysogen fractions exhibit robust negative correlation.

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.

The three biggest advances in fungal molecular phylogenetics in the last few years have been (1) the huge expansion in data sets, (2) the development of nonribosomal loci for phylogenetic analysis, and (3) the use of increasingly sophisticated types of analyses. In addition, advances in parallel computing hold great promise for dramatic increases in speed of analysis. These changes have had, or will have, a direct impact on mycorrhizal ecology through the use of sequence-based identification and an indirect impact through the conclusions drawn from such studies. One problem in the field has been the accidental addition of erroneous sequences to the public databases through a variety of means, including polymerase change reaction contamination. We discuss several examples, suggest ways to identify errors, and argue the case for third-party annotations of sequences. Multiple studies have produced compelling evidence that the ectomycorrhizal habit has developed convergently in multiple...

1. Mark-recapture models are valuable for assessing diverse demographic and behavioural parameters, yet the precision of traditional estimates is often constrained by sparse empirical data. Bayesian inference explicitly recognizes estimation uncertainty, and hierarchical Bayes has proven particularly useful for dealing with sparseness by combining information across data sets. 2. We developed a general hierarchical Bayesian multi-state mark-recapture model, tested its performance on simulated data sets and applied it to real ecological data on stopovers by migratory birds. 3. Our hierarchical model performed well in terms of both precision and accuracy of parameters when tested with simulated data of varying quality (sample size, capture and survivorship probabilities). It also provided more precise and accurate parameter estimates than a non-hierarchical model when data were sparse. 4. A specific version of the model, designed for estimation of daily transience and departure of migratory birds at a mid-route stopover, was applied to 11 years of autumn migration data from Atlantic Canada. Hierarchical estimates of departure and transience were more precise than those derived from parallel non-hierarchical and frequentist methods, and indicated that inter-annual variability in parameters suggested by these other methods was largely due to sampling error. 5. Synthesis and applications. Estimates of demographic parameters, often derived from markrecapture studies, provide the basis for evaluating the status of species at risk, for developing conservation and management strategies and for evaluating the results of current protocols. The hierarchical Bayesian multi-state mark-recapture model presented here permits partitioning of complex parameter variation across space or time, and the simultaneous analysis of multiple data sets results in a marked increase in the precision of estimates derived from sparse capture data. Its structural flexibility should make it a valuable tool for conservation ecologists and wildlife managers.

In this paper, I argue that it is typical of many scientific reasoning processes that they involve the integrated use of inductive and deductive steps. I moreover illustrate with examples from the sciences that the distinction between induction and deduction is context-dependentan inference treated in one context as deductive may in a different context may be treated as inductive-and that their integration leads to interesting forms of dynamics. The main example concerns Clausius' derivation of Carnot's theorem from an inconsistent set of premises. Although this reasoning process involves no other inference rules than those validated by Classical Logic, it nevertheless exhibits many of the characteristics traditionally associated with inductive reasoning processes. Finally, I show how the integrated use of induction and deduction can be explicated in terms of adaptive logics, and illustrate this with adaptive logics for three main types of scientific reasoning: an inconsistency-adaptive logic, a logic of induction, and a logic of abduction.

This paper offers an incomplete survey of recent results on inconsistency-adaptive logics (disregarding results on other adaptive logics). Much at-tention is paid to the so-called standard format, because it provides most of the required metatheory for adaptive logics that are ...

A prerequisite to the design of future Advanced Driver Assistance Systems for cars is a sensing system providing all the information required for high-level driving assistance tasks. Carsense is a European project whose purpose is to develop such a new sensing system. It will combine different sensors (laser, radar and video) and will rely on the fusion of the information coming from these sensors in order to achieve better accuracy, robustness and an increase of the information content. This paper demonstrates the interest of using probabilistic reasoning techniques to address this challenging multi-sensor data fusion problem. The approach used is called Bayesian Programming. It is a general approach based on an implementation of the Bayesian theory. It was introduced first to design robot control programs but its scope of application is much broader and it can be used whenever one has to deal with problems involving uncertain or incomplete knowledge.

An on-demand single-photon source is a key requirement for scaling many optical quantum technologies. A promising approach to realize an on-demand single-photon source is to multiplex an array of heralded single-photon sources using an active optical switching network. However, the performance of multiplexed sources is degraded by photon loss in the optical components and the non-unit detection efficiency of the heralding detectors. We provide a theoretical description of a general multiplexed single-photon source with lossy components and derive expressions for the output probabilities of single-photon emission and multi-photon contamination. We apply these expressions to three specific multiplexing source architectures and consider their tradeoffs in design and performance. To assess the effect of lossy components on near-and long-term experimental goals, we simulate the multiplexed sources when used for many-photon state generation under various amounts of component loss. We find that with a multiplexed source composed of switches with ∼ 0.2 − 0.4 dB loss and high efficiency number-resolving detectors, a single-photon source capable of efficiently producing 20-40 photon states with low multi-photon contamination is possible, offering the possibility of unlocking new classes of experiments and technologies.

In his recent paper in the Journal of Economic Methodology, Tobias Henschen puts forth a manipulationist definition of macroeconomic causality that strives for adequacy. As the notion of 'adequacy' remains underdeveloped in that paper, in this study we offer a discussion of what it means for a definition of causality to be adequate to macroeconomics. One of the meanings of adequacy is that the definition of causality describes the types of relations for which macroeconomic causal models stand for. On this understanding of adequacy, we take issue with Henschen's claim. We argue that his manipulationist definition is only applicable to a sample of causal models used by macroeconomists. There are other sets of macroeconomic causal models to which probabilistic and mechanistic definitions seem more adequate. We show relevant examples to support this claim and conclude that a moderate causal pluralism is an adequate stance with respect to macroeconomic causal models.