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The stochastic sequential assignment problem (SSAP) allocates distinct workers to sequentially arriving tasks with stochastic parameters to maximize the expected total reward. In this paper, the assignment of tasks is performed under the threshold criterion, which seeks a policy that minimizes the probability of the total reward failing to achieve a target value. A Markov-decision-process approach is employed to model the problem, and sufficient conditions for the existence of a deterministic Markov optimal policy are derived, along with fundamental properties of the optimal value function. An algorithm to approximate the optimal value function is presented, and convergence results are established. [ABSTRACT FROM PUBLISHER]

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]

In this paper, we suggest a new class of counting processes, called the Class of Geometric Counting Processes (CGCP), where each member of the counting process in the class has increments described by the geometric distribution. Distinct from the Poisson process, they do not possess the property of independent increments, which usually complicates probabilistic analysis. The suggested CGCP is defined and the dependence structure shared by the members of the class is discussed. As examples of useful applications, we consider stochastic survival models under external shocks. We show that the corresponding survival probabilities under reasonable assumptions can be effectively described by the CGCP without specifying the dependence structure. [ABSTRACT FROM AUTHOR]

The unified multivariate counting process (UMCP), previously studied by the same authors, enables one to describe most of the existing counting processes in terms of its components, thereby providing a comprehensive view for such processes often defined separately and differently. The purpose of this paper is to study a multivariate reward process defined on the UMCP. By examining the probabilistic flow in its state space, various transform results are obtained. The asymptotic behavior, as t→∞, of the expected univariate reward process in a form of a product of components of the multivariate reward process is studied. As an application, a manufacturing system is considered, where the cumulative profit given a preventive maintenance policy is described as a univariate reward process defined on the UMCP. The optimal preventive maintenance policy is derived numerically by maximizing the cumulative profit over the time interval [0, T]. [ABSTRACT FROM AUTHOR]

Solovay proved the arithmetical completeness theorem for the system GL of propositional modal logic of provability. Montagna proved that this completeness does not hold for a natural extension QGL of GL to the predicate modal logic. Let Th(QGL) be the set of all theorems of QGL, Fr(QGL) be the set of all formulas valid in all transitive and conversely well-founded Kripke frames, and let PL(T) be the set of all predicate modal formulas provable in Tfor any arithmetical interpretation. Montagna’s results are described as Th(QGL) ⊊ (Fr(QGL), PL(PA) ⊈ Fr(QGL), and Th(QGL) ⊊ PL(PA).In this paper, we prove the following three theorems: (1) Fr(QGL) ⊈ PL(T) for any Σ1-sound recursively enumerable extension T of I Σ1, (2) PL(T) ⊈ Fr(QGL) for any recursively enumerable A-theory T extending I Σ1, and (3) Th(QGL) ⊊ Fr(QGL) ∩ PL(T) for any recursively enumerable A-theory T extending I Σ2.To prove these theorems, we use iterated consistency assertions and nonstandard models of arithmetic, and we improve Artemov’s lemma which is used to prove Vardanyan’s theorem on the Π02-completeness of PL(T). [ABSTRACT FROM AUTHOR]

Given a rectangle containing uniformly distributed random points, how far are the points from the rectangle’s centre? In this paper we provide closed-form expressions for the cumulative distribution function and probability density function that characterise the distance. An expression for the average distance to the centre of the rectangle is also provided. [ABSTRACT FROM AUTHOR]

We show that a compact group G has finite conjugacy classes, i.e., is an FC-group if and only if its center Z(G) is open if and only if its commutator subgroup G′ is finite. Let d(G) denote the Haar measure of the set of all pairs (x,y) in G×G for which [x,y]=1; this, formally, is the probability that two randomly picked elements commute. We prove that d(G) is always rational and that it is positive if and only if G is an extension of an FC-group by a finite group. This entails that G is abelian by finite. The proofs involve measure theory, transformation groups, Lie theory of arbitrary compact groups, and representation theory of compact groups. Examples and references to the history of the discussion are given at the end of the paper. [ABSTRACT FROM PUBLISHER]

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]

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks. [ABSTRACT FROM AUTHOR]

By the Cameron–Martin theorem, if a function f is in the Dirichlet space D, then B + f has the same a.s. properties as standard Brownian motion, B. In this paper we examine properties of B + f when fD. We start by establishing a general 0-1 law, which in particular implies that for any fixed f, the Hausdorff dimension of the image and the graph of B + f are constants a.s. (This 0-1 law applies to any Lévy process.) Then we show that if the function f is Hölder(1/2), then B + f is intersection equivalent to B. Moreover, B + f has double points a.s. in dimensions d ≤ 3, while in d ≥ 4 it does not. We also give examples of functions which are Hölder with exponent less than 1/2, that yield double points in dimensions greater than 4. Finally, we show that for d ≥ 2, the Hausdorff dimension of the image of B + f is a.s. at least the maximum of 2 and the dimension of the image of f. [ABSTRACT FROM PUBLISHER]

In this paper, we present (in terms of roots) a simple closed-form analysis for evaluating system-length distribution at prearrival epochs of the GI/C-MSP/1 queue. The proposed analysis is based on roots of the associated characteristic equation of the vector-generating function of system-length distribution. We also provide the steady-state system-length distribution at an arbitrary epoch by using the classical argument based on Markov renewal theory. The sojourn-time distribution has also been investigated. The prearrival epoch probabilities have been obtained using the method of roots which is an alternative approach to the matrix-geometric method and the spectral method. Numerical aspects have been tested for a variety of arrival- and service-time distributions and a sample of numerical outputs is presented. The proposed method not only gives an alternative solution to the existing methods, but it is also analytically simple, easy to implement, and computationally efficient. It is hoped that the results obtained will prove beneficial to both theoreticians and practitioners. [ABSTRACT FROM AUTHOR]

In most conventional settings, the events caused by an external shock are initiated at the moments of its occurrence. In this paper, we study the new classes of shock models: (i) When each shock from a nonhomogeneous Poisson processes can trigger a failure of a system not immediately, as in classical extreme shock models, but with delay of some random time. (ii) When each shock from a nonhomogeneous Poisson processes results not in an ‘immediate’ increment of wear, as in classical accumulated wear models, but triggers its own increasing wear process. The wear from different shocks is accumulated and the failure of a system occurs when it reaches a given boundary. We derive the corresponding survival and failure rate functions. Furthermore, we study the limiting behavior of the failure rate function where it is applicable. [ABSTRACT FROM AUTHOR]

This paper proposes a feasible variation of approximate grid-based path-planning methods, which have been replaced with probabilistic methods nowadays, due mainly to their impracticality in high-dimensional spaces. Our aim is to demonstrate that, with an incremental exploration of the CSpace by means of Interpolated walk primitives and ANY-Time algorithms, we can generate – online – high-quality solutions that can be compared with probabilistic methods and can even improve some aspects, such as the completeness. Computational time, path smoothness, path clearance, and path distance are the qualifiers used to evaluate the path planner. These quality factors are critical in robotics. In fact, in both mobile and industrial robots, the computational time is a primary requirement to work online, the clearance gives security to the movements of the robot, and the smoothness can prolong the life of the mechanical components. Our method has been compared to probabilistic path planners, with the feasibility and benefits of our algorithm being proved in terms of the quality factors aforementioned. [ABSTRACT FROM PUBLISHER]

It is known that evidential support, on the Bayesian definition of this notion, is intransitive. According to some, however, the Bayesian definition is too weak to be materially adequate. This paper investigates whether evidential support is transitive on some plausible probabilistic strengthening of that definition. It is shown that the answer is negative. In fact, it will appear that even under conditions under which the Bayesian notion of evidential support is transitive, the most plausible candidate strengthenings are not. [ABSTRACT FROM PUBLISHER]

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]

Configurators have been generally accepted as important tools to elicit customers' needs and find the matches between customers' requirements and company's offerings. With product configurators, product design is reduced to a series of selections of attribute values. However, it has been acknowledged that customers are not patient enough to configure a long list of attributes. Therefore, making every round of configuring process productive and hence reducing the number of inputs from customers are of substantial interest to academic and industry alike. In this paper, we present an efficient product configuration approach by incorporating Shapley value, which is a concept used in game theory, to estimate the usefulness of each attribute in the configurator design. This new method iteratively selects the most relevant attribute that can contribute most in terms of information content from the remaining pool of unspecified attributes. As a result from product providers' perspective, each round of configuration can best narrow down the choices with given amount of time. The selection of the next round query is based on the customer's decision on the previous rounds. The interactive process thus runs in an adaptive manner that different customers will have different query sequences. The probability ranking principle is also exploited to give product recommendation to truncate the configuration process so that customers will not be burdened with trivial selection of attributes. Analytical results and numerical examples are also used to exemplify and demonstrate the viability of the method. [ABSTRACT FROM PUBLISHER]

Collision-free path planning for static robots is a demanding manifold of contemporary robotics research, vastly due to the growing industrial applications. In this paper, a novel ‘visibility map’-based heuristic algorithm is used to generate near-optimal safe path for a three-dimensional congested robot workspace. The final path is obtainable in terms of joint configurations, by considering the Configuration Space of the task space. The developed algorithm has been verified initially by considering representative 2D workspaces, cluttered with different obstacles with regular geometries and then after with the spatial endeavour. A case study reveals the effectiveness of the developed modules of the configuration space mapping, pertaining to a five degrees-of-freedom low payload articulated robot. [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]

Let Cr [0, t] be the function space of the vector-valued continuous paths x : [0, t]→Rr and define Xt : Cr [0; t]→R(n+1)r by Xt (x) = (x(0), x(t1), … , x(tn)), where 0 < t1 < ⋯ < tn = t. In this paper, using a simple formula for the conditional expectations of the functions on Cr [0, t] given Xt , we evaluate the conditional analytic Feynman integral Ean fq [Ft ∣Xt ] of Ft given by (These character(s) cannot be represented in ASCII text), where θ(s, ∙) are the Fourier-Stieltjes transforms of the complex Borel measures on Rr, and provide an inversion formula for Ean fq [Ft ∣Xt ]. Then we present an existence theorem for the solution of an integral equation including the integral equation which is formally equivalent to the Schrödinger differential equation. We show that the solution can be expressed by Ean fq [Ft ∣Xt ] and a probability distribution on Rr when Xt (x) = (x(0), x(t)). [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]

In both modern stochastic analysis and more traditional probability and statistics, one way of characterizing a static or dynamic probability distribution is through its quantile function. This paper is focused on obtaining a direct understanding of this function via the classical approach of establishing and then solving differential equations for the function. We establish ordinary differential equations and power series for the quantile functions of several common distributions. We then develop the partial differential equation for the evolution of the quantile function associated with the solution of a class of stochastic differential equations, by a transformation of the Fokker?Planck equation. We are able to utilize the static formulation to provide elementary time-dependent and equilibrium solutions.Such a direct understanding is important because quantile functions find important uses in the simulation of physical and financial systems. The simplest way of simulating any non-uniform random variable is by applying its quantile function to uniform deviates. Modern methods of Monte?Carlo simulation, techniques based on low-discrepancy sequences and copula methods all call for the use of quantile functions of marginal distributions. We provide web resources for prototype implementations in computer code. These implementations may variously be used directly in live sampling models or in a high-precision benchmarking mode for developing fast rational approximations also for use in simulation. [ABSTRACT FROM AUTHOR]

AbstractLet Sj: d? dfor j= 1, .?.?., Nbe contracting similarities. Also, let (p1,.?.?., pN, p) be a probability vector and let ? be a probability measure on dwith compact support. We show that there exists a unique probability measure ? such that \begin{eqnarray}$$\[ \mu = \sum_{j}p_{j}\mu\circ S_{j}^{-1} \,+\, p\nu. \]$$\end{eqnarray}]The measure ? is called an in-homogenous self-similar measure. In this paper we study the asymptotic behaviour of the Fourier transforms of in-homogenous self-similar measures. Finally, we present a number of applications of our results. In particular, non-linear self-similar measures introduced and investigated by Glickenstein and Strichartz are special cases of in-homogenous self-similar measures, and as an application of our main results we obtain simple proofs of generalizations of Glickenstein and Strichartz's results on the asymptotic behaviour of the Fourier transforms of non-linear self-similar measures. [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]

The modelling of most Global Navigation Satellite System (GNSS) errors/biases and developments of data processing techniques have been improved substantially since the birth of Global Positioning System (GPS), however, there has been much less progress in the improvement of phase multipath mitigation techniques. Multipath therefore remains one of the most important error sources in high precision GNSS positioning. This is because multipath is site-dependent and therefore cannot be eliminated by differencing techniques. Also multipath is highly dependent on satellite-reflector-antenna geometry, which usually causes rapid changes in phase multipath errors especially in Real-Time Kinematic (RTK) applications. Multipath mitigation for static antennas such as those at reference stations can be carried out by site calibration, averaging over long observation times, and through the estimation of the error using filtering based on signal-to-noise ratio (SNR) data. However, multipath mitigation for kinematic antennas is still very difficult today.Nevertheless, much research has been carried out on a particular class of phase multipath mitigation techniques: ones that can be applied within positioning algorithms (rather than incorporated into the receiver tracking loops or antennas). This paper investigates and further develops a number of state-of-the-art techniques in this category. They include phase multipath estimation using SNR data, phase multipath estimation through the use of closely spaced antennas, multipath mitigation stochastic models such as the satellite elevation angle model and SNR-based models (SIGMA-model and our modified SNR-based model), and our own novel ray-tracing method. The techniques are tested with both real and simulated data, the real test datasets have been collected on the Laboratoire Central des Ponts et Chauss?es (LCPC) testbed near Nantes in France, and on the campus of the University of Nottingham during SPACE data collection experiments. [ABSTRACT FROM AUTHOR]

In this paper we estimate the number of habitable planets in our Galaxy over cosmological time scales. This number can be derived from the planet formation rate (PFR) of Earth-like planets and the convolution of this value with the probability of being habitable. The PFR is calculated from the star formation rate (SFR) with the help of a so-called Goldilocks problem. The probability that an Earth-like planet is in the habitable zone (HZ) is estimated with the help of our Earth system model. In order to calculate the HZ an integrated system approach is used, taking into account a variety of climatological, biogeochemical, and geodynamical processes. Habitability is linked to the photosynthetic activity on the planetary surface. We find that habitability strongly depends on the age of the stellar system and the characteristics of a virtual Earth-like planet. There was a maximum number of habitable planets around the time of the Earth’s origin and interstellar panspermia was most probable at that time. Furthermore, we discuss our results in the framework of the so-called principle of mediocrity. [ABSTRACT FROM PUBLISHER]

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.

A recent paper published in this journal (Poole & Kuhn, 1973) has reported that ‘a relatively large family appeared to be no impediment to the educational achievements of middle-class children’. This finding, however, is based upon an analysis which fell into a relatively unknown statistical trap. Poole & Kuhn are only the latest in a long line of victims of this trap and some of their predecessors are reviewed below. [ABSTRACT FROM PUBLISHER]

It is well established that, in general, pregnancies at advanced maternal ages or of advanced birth order are at greater risk of aborting spontaneously. It does not follow that each individual woman, as she proceeds through her reproductive life, becomes steadily more prone to abort. The present paper attempts to analyse evidence on how individual women's abortion probabilities vary during their reproductive lives. Statistical examination of the data suggests that:1. A spontaneous abortion in a given birth rank is more likely than a live birth in the same rank to be followed by a further pregnancy. Abortion-prone women have more pregnancies than other women.2. There is no significant overall tendency for spontaneous abortions to appear early or late in sibships even when account is taken of the reproductive compensation reported above.3. Pathological examination of spontaneously aborted fetuses suggests that more (perhaps many more) than 10% of spontaneous abortions (e.g. those associated with trisomy and maternal isoimmunization) are causally associated with advanced maternal age or birth order.4. The mean maternal age of spontaneously aborted fetuses which fail to grow in culture is higher than that of fetuses which are successfully cultured.One would infer:A. (from suggestions 1 and 2 above) that reproductive compensation (rather than a real birth order effect) is a major reason why abortion rates are higher at higher maternal ages and higher birth ranks;B. (from suggestions 2 and 3 above) that there must be another group of abortions, roughly equal in number, which are causally associated with low maternal age or early birth order.Little is known about this second group of reproductive casualties (those associated with low birth order or maternal age), but it is suggested that some have CNS malformations. I have made similar suggestions in regard to stillbirth and neonatal death. [ABSTRACT FROM PUBLISHER]

Son preference is strong in Vietnam, according to attitudinal surveys and studies of contraceptive prevalence and birth hazards. These techniques assume a single model is valid for all families, but it is more plausible that son preference is found for some, but not all, families. Heterogeneous preferences may be addressed with a mixture model. This paper specifies and estimates a two-Weibull regression model, applied to the interval between the second and third births. The data come from the Vietnam Living Standards Survey of 1992–93. Applying information criteria, graphs, and martingale-based residuals, the two-Weibull model is found to fit better than a one-Weibull model. Roughly half of parents have son preference and, curiously, a propensity for fewer children. The other group has more children, no son preference, and is colourless in the sense that the birth interval is difficult to predict on the basis of the regressors used. [ABSTRACT FROM PUBLISHER]

Reported information on the duration of post-partum amenorrhoea usually shows considerable number preference, particularly at 6-monthly intervals. This paper presents a technique for smoothing such amenorrhoea data using a modified exponential curve. An attempt has also been made to estimate the average number of months a mother is expected to remain amenorrhoeic. [ABSTRACT FROM PUBLISHER]

This paper examines the patterns of timing of births of women using data from the Canadian Fertility Survey of 1984. Semi-Markovian schemes are applied to the maternity histories of the 5315 sample women in their reproductive ages in order to measure the intensity and timing of childbearing. Age-and-duration-specific transition probabilities are found to have substantially changed for the more recent birth cohorts compared to the older cohorts. [ABSTRACT FROM PUBLISHER]

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.

The rising number of military conflicts worldwide cause an increase in the influx of asylum seekers to Western Europe, Austria included. The Austrian Interior Ministry predicts that the number of asylum seekers in 2014 will reach 26 000 people compared to 17 500 in 2013, an increase of almost 50 %. This rising tendency will in all probability continue. Asylum seekers from Russia (Chechnia) are the second largest group of refugees. Asylum seekers left their home countries when they turned into devouring Chronos who eats his children. Having fled from perdition they find themselves vulnerable in a foreign language-cultural matrix. This is difficult to cope with to highly traumatized people. Psychotherapy in their mother tongue or one that is familiar to them constitutes emergency support and is of utmost importance for this group. This paper will focus on the preliminary results of the 'Mobile Psychotherapie für sozial Bedürftige in Niederösterreich” project, conducted in Lower Austria, in which the author participates as a psychotherapist. The aims are to evaluate in the mid-treatment phase what helps the patients who participated in this project and why and how it helped. The evaluation is done with the help of Client Change Interview (Elliott), 5 patients take part in this qualitative research. Results are reflected using psychoanalytic approach with the focus on the process and psychotherapeutic relationship. [ABSTRACT FROM AUTHOR]