Search

Redundant or excessive information can sometimes lead people to lean on it unnecessarily. Certain experimental designs can sometimes bias results in the researcher's favor. And, sometimes, interesting effects are too small to be studied, practically, or are simply zero. We believe a confluence of these factors led to a recent paper (Isaac & Brough, 2014, JCR). This initial paper proposed a new means by which probability judgments can be led astray: the category size bias, by which an individual event coming from a large category is judged more likely to occur than an event coming from a small one. Our work shows that this effect may be due to instructional and mechanical confounds, rather than interesting psychology. We present eleven studies with over ten times the sample size of the original in support of our conclusion: We replicate three of the five original studies and reduce or eliminate the effect by resolving these methodological issues, even significantly reversing the bias in one case (Study 6). Studies 7-8c suggest the remaining two studies are false positives. We conclude with a discussion of the subtleties of instruction wording, the difficulties of correcting the record, and the importance of replication and open science. [ABSTRACT FROM AUTHOR]

This paper presents the results of a study that sheds new light on the shape of indifference curves in the Marschak-Machina triangle. The most important observation, obtained non-parametrically, concerns jumps in indifference curves at the triangle legs towards the triangle origin. These jumps, however, do not appear at the hypotenuse. The pattern observed suggests discontinuity in lottery valuation when the range of lottery outcomes changes and is best explained by decision-making models based on the psychological phenomenon of range dependence (Parducci, 1965; Cohen, 1992; Kontek & Lewandowski, 2018). Models founded on other psychological phenomena, e.g., discontinuity in decision weights (Kahneman & Tversky, 1979), cumulative probability weighting (Tversky & Kahneman, 1992), attention shifting (Birnbaum, 2008), overweighting of salient payoffs (Bordallo, Gennaioli & Shefrin, 2012), and treating stated probabilities as imperfect information (Viscusi, 1989), predict indifference curve shapes that differ from the one obtained in this study. [ABSTRACT FROM AUTHOR]

This paper explored how frames influence people's evaluation of others' probabilistic predictions in light of the outcomes of binary events. Most probabilistic predictions (e.g., "there is a 75% chance that Denver will win the Super Bowl") can be partitioned into two components: A qualitative component that describes the predicted outcome ("Denver will win the Super Bowl"), and a quantitative component that represents the chance of the outcome occurring ("75% chance"). Various logically equivalent variations of a single prediction can be created through different combinations of these components and their logical or numerical complements (e.g., "25% chance that Denver will lose the Super Bowl", "75% chance that Seattle will lose the Super Bowl"). Based on the outcome of the predicted event, these logically equivalent predictions can be categorized into two classes: Congruently framed predictions, in which the qualitative component matches the outcome, and incongruently framed predictions, in which it does not. Although the two classes of predictions are logically equivalent, we hypothesize that people would judge congruently framed predictions to be more accurate. The paper tested this hypothesis in seven experiments and found supporting evidence across a number of domains and experimental manipulations, and even when the congruently framed prediction was logically inferior. It also found that this effect held even for subjects who saw both congruently framed and incongruently framed versions of a prediction and judged the two to be logically equivalent. [ABSTRACT FROM AUTHOR]

Stastny and Lehner (2018) compared the accuracy of forecasts in an intelligence community predictionmarket to comparable forecasts in analysis reports prepared by groups of professional intelligence analysts. To obtain quantitative probabilities from the analysis reports experienced analysts were asked to read the reports and state what probability they thought the reports implied for each forecast question. These were called imputed probabilities. Stastny and Lehner found that the prediction market was more accurate than the imputed probabilities and concluded that this was evidence that the prediction market was more accurate than the analysis reports. In a commentary, Mandel (2019) took exception to this interpretation. In a re-analysis of the data, Mandel found a very strong correlation between readers' personal and imputed probabilities. From this Mandel builds a case that the imputed probabilities are little more than a reflection of the readers' personal views; that they do not fairly reflect the contents of the analysis reports; and therefore, any accuracy results are spurious. This paper argues two points. First, the high correlation between imputed and personal probabilities was not evidence of substantial imputation bias. Rather it was the natural by-product of the fact that the imputed and personal probabilities were both forecasts of the same events. An additional analysis shows a much lower level of imputation bias that is consistent with the original results and interpretation. Second, the focus of Stastny and Lehner (2018) was on the reports as understood by readers. In this context, even if there was substantial imputation bias it would not invalidate accuracy results; it would instead provide a possible causal explanation of those results. [ABSTRACT FROM AUTHOR]

Recent years have seen a large increase in the popularity of Texas hold ’em poker. It is now the most commonly played variant of the game, both in casinos and through online platforms. In this paper, we present a simulation study for games of Texas hold ’em with between two and 23 players. From these simulations, we estimate the probabilities of each player having been dealt the winning hand. These probabilities are calculated conditional on both partial information (that is, the player only having knowledge of his/her cards) and also on fuller information (that is, the true probabilities of each player winning given knowledge of the cards dealt to each player). Where possible, our estimates are compared to exact analytic results and are shown to have converged to three significant figures. With these results, we assess the poker strategies described in two recent pieces of popular culture. In comparing the ideas expressed in Taylor Swift’s song, New Romantics , and the betting patterns employed by James Bond in the 2006 film, Casino Royale , we conclude that Ms Swift demonstrates a greater understanding of the true probabilities of winning a game of Texas hold ’em poker. [ABSTRACT FROM AUTHOR]

This paper summarizes an empirical comparison of the accuracy of forecasts included in analysis reports developed by professional intelligence analysts to comparable forecasts in a prediction market that has broad participation from across an intelligence community. To compare forecast accuracy, 99 event forecasts were extracted from qualitative descriptions found in 41 analysis reports and posted on the prediction market. Quantitative probabilities were imputed from the qualitative forecasts by asking seasoned professional analysts, who did not participate in the prediction market, to read the reports and to infer a quantitative probability based on what was written. These readers were also asked to provide their personal probabilities before and after reading the reports. There were two statistically significant results of particular interest. First, the primary result is that the prediction market forecasts were more accurate than the analysis reports. On average prediction market probabilities were 0.114 closer to ground truth than the analysis report probabilities. Second, in cases where analysts (readers) updated their personal probabilities in a direction opposite to what the reports implied, analysts tended to update their probabilities in the correct direction. This occurred even though, on average, reading the reports did not make readers more accurate. [ABSTRACT FROM AUTHOR]

Brier score decompositions, including those attributed to Murphy and to Yates, provide popular metrics for estimating forecast performance attributes like calibration and discrimination. However, the decompositions are generally limited to situations where forecasters make successive forecast judgments against the same class of substantive event (e.g., rain vs. no rain). They do not readily translate to common situations where: forecasts are weighted unequally; forecasts can be made against a range of heterogeneous topics and events over varying time horizons; forecasts can be updated over time until an event occurs or an event deadline is reached; or outcome alternatives can vary in number and nature (e.g., ordered vs. unordered outcomes) across forecast questions. In this paper, we propose extensions of the Murphy and Yates decompositions to address these features. The extensions involve new analytic expressions for the decompositions of weighted Brier scores, along with proposed resampling methods. We use data from a recent forecasting tournament to illustrate the methods. [ABSTRACT FROM AUTHOR]

When decisions involve opting in or out of competition many decision makers will opt-in even when doing so leads to losses on average. In the current paper, we examine the generality of this effect in risky choices not involving competition. We found that re-framing a sure (certain) zero option as an option to observe the results of the other options without choosing would lead to increased consequential choice (i.e., increased selection of risky options rather than the zero option). Specifically, in two studies we compared the rate of consequential choice in a novel paradigm where decision makers decide to observe or to choose with consequence from a set of risky options (decisions-to-engage) to a full-feedback decisions-from-feedback paradigm where the choice set included a labeled sure zero option. Compared to decisions-from-feedback, participants were more likely to choose from mixed (risky) gambles with consequence (over a zero outcome) in decisions-to-engage. This occurred irrespective of whether doing so was advantageous (i.e., when choice led to monetary gains on average) or disadvantageous (i.e., when choice led to monetary losses on average), and when descriptions of the options outcomes and probabilities were provided (Study 2). These findings provide an important boundary condition for the positive effects of experience on the quality of choice, and suggest that decision makers' preference for agency can sometimes induce poorer choices. [ABSTRACT FROM AUTHOR]

Recently Houdayer and Isono have proved, among other things, that every biexact group $\unicode[STIX]{x1D6E4}$ has the property that for any non-singular strongly ergodic essentially free action $\unicode[STIX]{x1D6E4}\curvearrowright (X,\unicode[STIX]{x1D707})$ on a standard measure space, the group measure space von Neumann algebra $\unicode[STIX]{x1D6E4}\ltimes L^{\infty }(X)$ is full. In this paper, we prove the same property for a wider class of groups, notably including $\text{SL}(3,\mathbb{Z})$. We also prove that for any connected simple Lie group $G$ with finite center, any lattice $\unicode[STIX]{x1D6E4}\leqslant G$, and any closed non-amenable subgroup $H\leqslant G$, the non-singular action $\unicode[STIX]{x1D6E4}\curvearrowright G/H$ is strongly ergodic and the von Neumann factor $\unicode[STIX]{x1D6E4}\ltimes L^{\infty }(G/H)$ is full. [ABSTRACT FROM AUTHOR]

In this paper we introduce probability-preserving convolution algebras on cones of positive semidefinite matrices over one of the division algebras ${\mathbb F} = {\mathbb R}, {\mathbb C}$ or ${\mathbb H}$ which interpolate the convolution algebras of radial bounded Borel measures on a matrix space $M_{p,q}({\mathbb F})$ with $p\geq q$. Radiality in this context means invariance under the action of the unitary group $U_p({\mathbb F})$ from the left. We obtain a continuous series of commutative hypergroups whose characters are given by Bessel functions of matrix argument. Our results generalize well-known structures in the rank-one case, namely the Bessel–Kingman hypergroups on the positive real line, to a higher rank setting. In a second part of the paper we study structures depending only on the matrix spectra. Under the mapping $r\mapsto \text{spec}(r)$, the convolutions on the underlying matrix cone induce a continuous series of hypergroup convolutions on a Weyl chamber of type $B_q$. The characters are now Dunkl-type Bessel functions. These convolution algebras on the Weyl chamber naturally extend the harmonic analysis for Cartan motion groups associated with the Grassmann manifolds $U(p,q)/(U_p\times U_q)$ over ${\mathbb F}$. [ABSTRACT FROM AUTHOR]

In most previous studies of verbal probabilities, participants are asked to translate expressions such as possible and not certain into numeric probability values. This probabilistic translation approach can be contrasted with a novel which-outcome (WO) approach that focuses on the outcomes that people naturally associate with probability terms. The WO approach has revealed that, when given bell-shaped distributions of quantitative outcomes, people tend to associate certainty with minimum (unlikely) outcome magnitudes and possibility with (unlikely) maximal ones. The purpose of the present paper is to test the factors that foster these effects and the conditions in which they apply. Experiment 1 showed that the association of probability term and outcome was related to the association of scalar modifiers (i.e., it is certain that the battery will last at least..., it is possible that the battery will last up to...). Further, we tested whether this pattern was dependent on the frequency (e.g., increasing vs. decreasing distribution) or the nature of the outcomes presented (i.e., categorical vs. continuous). Results showed that despite being slightly affected by the shape of the distribution, participants continue to prefer to associate possible with maximum outcomes and certain with minimum outcomes. The final experiment provided a boundary condition to the effect, showing that it applies to verbal but not numerical probabilities. [ABSTRACT FROM AUTHOR]

Research on forecasting is effectively limited to forecasts that are expressed with clarity; which is to say that the forecasted event must be sufficiently well-defined so that it can be clearly resolved whether or not the event occurred and forecasts certainties are expressed as quantitative probabilities. When forecasts are expressed with clarity, then quantitative measures (scoring rules, calibration, discrimination, etc.) can be used to measure forecast accuracy, which in turn can be used to measure the comparative accuracy of different forecasting methods. Unfortunately most real world forecasts are not expressed clearly. This lack of clarity extends to both the description of the forecast event and to the use of vague language to express forecast certainty. It is thus difficult to assess the accuracy of most real world forecasts, and consequently the accuracy the methods used to generate real world forecasts. This paper addresses this deficiency by presenting an approach to measuring the accuracy of imprecise real world forecasts using the same quantitative metrics routinely used to measure the accuracy of well-defined forecasts. To demonstrate applicability, the inferred probability method is applied to measure the accuracy of forecasts in fourteen documents examining complex political domains. [ABSTRACT FROM AUTHOR]

This paper presents a simple argument against life being the product of design. The argument rests on three points. (1) We can conceive of the debate in terms of likelihoods, in the technical sense – how probable the design hypothesis renders our evidence, versus how probable the competing Darwinian hypothesis renders that evidence. (2) God, as traditionally conceived, had many more options by which to bring about life as we observe it than were available to natural selection. That is, the relevant parameters were, in many cases, far more constrained under natural selection. (3) Utterly mundane features of the world, like that the earth is very old, are actually powerful evidence that the world was not designed, since that outcome was optional on the design hypothesis but nearly inevitable on natural selection. [ABSTRACT FROM PUBLISHER]

The tempting fate effect is that the probability of a fateful outcome is deemed higher following an action that "tempts" the outcome than in the absence of such an action. In this paper we evaluate the hypothesis that the effect is due to an illusion of control induced by a causal framing of the situation. Causal frames require that the action make a difference to an outcome and that the action precedes the outcome. If an illusion of control modulates the reluctance to tempt fate, then actions that make a difference to well-being and that occur prior to the outcome should tempt fate most strongly. In Experiments 1-3 we varied whether the action makes a difference and the temporal order of action and outcome. In Experiment 4 we tested whether an action can tempt fate if all outcomes are negative. The results of all four experiments supported our hypothesis that the tempting fate effect depends on a causal construal that gives rise to a false sense of control. [ABSTRACT FROM AUTHOR]

Let X1 and X2 be two independent and nonnegative random variables with distributions F1 and F2, respectively. This paper proves that if both F1 and F2 are of Weibull type and fulfill certain easily verifiable conditions, then the distribution of the product X1X2, called the product convolution of F1 and F2, belongs to the class 풮* and, hence, is subexponential. [ABSTRACT FROM AUTHOR]

The main problem with the many-worlds theory is that it is not clear how the notion of probability should be understood in a theory in which every possible outcome of a measurement actually occurs. In this paper, I argue for the following theses concerning the many-worlds theory: (1) If probability can be applied at all to measurement outcomes, it must function as a measure of an agent's self-location uncertainty. (2) Such probabilities typically violate reflection. (3) Many-worlds branching does not have sufficient structure to admit self-location probabilities. (4) Decision-theoretic arguments do not solve this problem. [ABSTRACT FROM AUTHOR]

This paper deals with two-species convolution diffusion-competition models of Lotka-Volterra type with delays which describe more accurate information than the Laplacian diffusion-competition models. We first investigate the existence of travelling wave solutions of a class of nonlocal convolution diffusion systems with weak quasimonotonicity or weak exponential quasimonotonicity by a cross-iteration technique and Schauder's fixed point theorem. When the results are applied to the convolution diffusion-competition models with delays, we establish the existence of travelling wave solutions as well as asymptotic behaviour. [ABSTRACT FROM AUTHOR]

In this paper, we consider an insurance company whose surplus (reserve) is modeled by a jump diffusion risk process. The insurance company can invest part of its surplus in n risky assets and purchase proportional reinsurance for claims. Our main goal is to find an optimal investment and proportional reinsurance policy which minimizes the ruin probability. We apply stochastic control theory to solve this problem. We obtain the closed form expression for the minimal ruin probability, optimal investment and proportional reinsurance policy. We find that the minimal ruin probability satisfies the Lundberg equality. We also investigate the effects of the diffusion volatility parameter, the market price of risk and the correlation coefficient on the minimal ruin probability, optimal investment and proportional reinsurance policy through numerical calculations. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a class of reflected backward stochastic differential equations (RBSDEs) corresponding to the subdifferential operator of a lower semi-continuous convex function, driven by Teugels martingales associated with a Lévy process. We show the existence and uniqueness of the solution for RBSDEs by means of the penalization method. As an application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to find a concrete bound for the error involved when approximating the nth Hermite function (in the oscillating range) by an asymptotic formula due to D. Dominici. This bound is then used to study the accuracy of certain approximations to Hermite expansions and to Fourier transforms. A way of estimating an unknown probability density is proposed. [ABSTRACT FROM AUTHOR]

In two recent papers Barry Loewer (2001, 2004) has suggested to interpret probabilities in statistical mechanics as chances in David Lewis's (1994) sense. I first give a precise formulation of this proposal, then raise two fundamental objections, and finally conclude that these can be overcome only at the price of interpreting these probabilities epistemically. [ABSTRACT FROM AUTHOR]

AbstractIn this paper we deduce a universal result about the asymptotic distribution of roots of random polynomials, which can be seen as a complement to an old and famous result of?Erd?s and Turan. More precisely, given a sequence of random polynomials, we show that, under some very general conditions, the roots tend to cluster near the unit circle, and their angles are uniformly distributed. The method we use is deterministic: in particular, we do not assume independence or equidistribution of the coefficients of the polynomial. [ABSTRACT FROM AUTHOR]

One controversy about the existence of so called evolutionary forces such as natural selection and random genetic drift concerns the sense in which such "forces" can be said to interact. In this paper I explain how natural selection and random drift can interact. In particular, I show how population-level probabilities can be derived from individual-level probabilities, and explain the sense in which natural selection and drift are embodied in these population-level probabilities. I argue that whatever causal character the individual-level probabilities have is then shared by the population-level probabilities, and that natural selection and random drift then have that same causal character. Moreover, natural selection and drift can then be viewed as two aspects of probability distributions over frequencies in populations of organisms. My characterization of population-level probabilities is largely neutral about what interpretation of probability is required, allowing my approach to support various positions on biological probabilities, including those which give biological probabilities one or another sort of causal character. [ABSTRACT FROM AUTHOR]

The spontaneous emergence of signaling has already been studied in terms of standard evolutionary dynamics of signaling games. Standard evolutionary dynamics is given by the replicator equations. Thus, it is not clear whether the results for standard evolutionary dynamics depend crucially on the functional form of the replicator equations. In this paper I show that the basic results for the replicator dynamics of signaling games carry over to a number of other evolutionary dynamics. [ABSTRACT FROM AUTHOR]

Since Ramsey, much discussion of the relation between probability and belief has taken for granted that there are degrees of belief, i.e., that there is a real-valued function, B, that characterizes the degree of belief that an agent has in each statement of his language. It is then supposed that B is a probability. It is then often supposed that as the agent accumulates evidence, this function should be updated by conditioning: BE(·) should be B(·∧E)/B(E)). Probability is also important in classical statistics, where it is generally supposed that probabilities are frequencies, and that inference proceeds by controlling error and not by conditioning. I will focus on the tension between these two approaches to probability, and in the main part of the paper show where and when Bayesian conditioning conflicts with error based statistics and how to resolve these conflicts. [ABSTRACT FROM AUTHOR]

In this paper we argue that the emergence of the classical world from the underlying quantum reality involves two elements: self-induced decoherence and macroscopicity. Self-induced decoherence does not require the openness of the system and its interaction with the environment: a single closed system can decohere when its Hamiltonian has continuous spectrum. We show that, if the system is macroscopic enough, after self-induced decoherence it can be described as an ensemble of classical distributions weighted by their corresponding probabilities. We also argue that classicality is an emergent property that arises when the behavior of the system is described from an observational perspective. [ABSTRACT FROM AUTHOR]

In this paper, it is argued that selection and drift might be distinct. This contradicts recent arguments by Brandon (2005) and Matthen and Ariew (2002) that such a distinction "violates sound probabilistic thinking" (Matthen and Ariew 2002, 62). While their arguments might be valid under certain assumptions, they overlook a possible way to make sense of the distinction. Whether selection and drift can be thought of as causally distinct, I argue, depends on the source of probabilities in natural selection. In particular, if the probabilities used in defining fitness values are at least partly a result of abstracting from or ignoring certain features of the environment, then selection and drift might in fact be causally distinct. [ABSTRACT FROM AUTHOR]

In three recent papers, Wayne Myrvold (1996, 2003) and Timothy McGrew (2003) have developed Bayesian accounts of the virtue of unification. In his account, McGrew demonstrates that, ceteris paribus, a hypothesis that unifies its evidence will have a higher posterior probability than a hypothesis that does not. Myrvold, on the other hand, offers a specific measure of unification that can be applied to individual hypotheses. He argues that one must account for this measure in order to calculate correctly the degree of confirmation that a hypothesis receives from its evidence. Using the probability calculus, I prove that the two accounts of unification require the same underlying inequality; thus, McGrew and Myrvold have accounted for unification in fundamentally identical probabilistic terms. I then evaluate five putative counterexamples to this account and show that these examples, far from disqualifying it, serve to clarify our notion of unification by disentangling it from a host of other concepts. [ABSTRACT FROM AUTHOR]

Probability theory is important not least because of its relevance for decision making, which also means: its relevance for the single case. The frequency theory of probability on its own is irrelevant in the single case. However, Howson and Urbach argue that Bayesianism can solve the frequentist's problem: frequentist-probability information is relevant to Bayesians (although to nobody else). The present paper shows that Howson and Urbach's solution cannot work, and indeed that no Bayesian solution can work. There is no way to make frequentist probability relevant. [ABSTRACT FROM AUTHOR]

In this paper, we identify a new and mathematically well-defined sense in which the coherence of a set of hypotheses can be truth-conducive. Our focus is not, as usual, on the probability, but rather on the confirmation of a coherent set and its members. We show that if evidence confirms a hypothesis, confirmation is `transmitted' to any hypotheses that are sufficiently coherent with the former hypothesis, according to some appropriate probabilistic coherence measure such as Olsson's or Fitelson's measure. Our findings have implications for scientific methodology, as they provide a formal rationale for the method of indirect confirmation and the method of confirming theories by confirming their parts. [ABSTRACT FROM AUTHOR]

The most important theories in fundamental physics, quantum mechanics and statistical mechanics, posit objective probabilities or chances. As important as chance is there is little agreement about what it is. The usual "interpretations of probability" give very different accounts of chance and there is disagreement concerning which, if any, is capable of accounting for its role in physics. David Lewis has contributed enormously to improving this situation. In his classic paper "A Subjectivist's Guide to Objective Chance" he described a framework for representing single case objective chances, showed how they are connected to subjective credences, and sketched a novel account what they are within his Humean account of scientific laws. Here I will describe these contributions and add a little to them. [ABSTRACT FROM AUTHOR]

This paper addresses two examples due to Peter Achinstein purporting to show that the positive relevance view of evidence is too strong, that is, that evidence need not raise the probability of what it is evidence for. The first example can work only if it makes a false assumption. The second example fails because what Achinstein claims is evidence is redundant with information we already have. Without these examples Achinstein is left without motivation for his account of evidence, which uses the concept of explanation in addition to that of probability. [ABSTRACT FROM AUTHOR]

This paper is a discussion of David Albert's approach to the foundations of classical statistical menchanics. I point out a respect in which his account makes a stronger claim about the statistical mechanical probabilities than is usually made, and I suggest what might be motivation for this. I outline a less radical approach, which I attribute to Boltzmann, and I give some reasons for thinking that this approach is all we need, and also the most we are likely to get. The issue between the two accounts turns out to be one about the explanatory role probabilities play in statistical mechanics. [ABSTRACT FROM AUTHOR]

Presents additional results on the Richard Jeffrey's earlier paper on the problem of old evidence and new explanation based his solutions. Usage of probability distribution (p) on the algebra from Hypotheses (H) and empirical investigation (E); Formulation of the confirmation of H in terms of inequality and equivalent inequality; Presentation of theorems to identify conditions for confirmations.

The front and back cover matter of the periodical is presented which includes information on submission of research papers in all areas of mathematics such as probability and mathematical physics; and the table of contents for the April 2016 issue.