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Abstract This paper presents results of computer simulations for a number of different probabilistic versions of inference to the best explanation (IBE), which are distinguished by the probabilistic measures used to identify the best explanation. Simulation results are presented which include cases involving ignorance of a catch-all hypothesis, uncertainty regarding the prior probability distribution over the remaining hypotheses, initial elimination of implausible hypotheses, and variations in the number of pieces of evidence taken into consideration. The results show that at least some versions of IBE perform very well in a wide range of cases. In particular, the results for all approaches remain very similar (or improve in some cases) when just the two hypotheses with the highest prior probabilities are retained and the rest are eliminated from consideration. Highlights • Probabilistic models of Inference to the Best Explanation (IBE) are proposed. • Realistic aspects include elimination of implausible hypotheses and uncertainty. • Computer simulations are used to implement and evaluate these models. • Results demonstrate the effectiveness of IBE as a mode of inference. [ABSTRACT FROM AUTHOR]

Starting with Dempster's seminal work, several approaches to statistical inference based on belief functions have been proposed. Some of these approaches can be seen as implementing some form of prior-free Bayesian inference, while some others put the emphasis on long-run frequency properties and are more related to classical frequentist methods. This paper focusses on the latter class of techniques, which have been developed independently and had not been put in perspective until now. Existing definitions for frequency-calibrated belief functions as well as corresponding construction methods are reviewed, and some new notions and techniques are introduced. The connections with other frequentist notions such as confidence distributions and confidence curves are also explored. The different construction techniques are illustrated on simple inference problems, with a focus on interpretation and implementation issues. [ABSTRACT FROM AUTHOR]

The majority of Bayesian networks learning and inference algorithms rely on the assumption that all random variables are discrete, which is not necessarily the case in real-world problems. In situations where some variables are continuous, a trade-off between the expressive power of the model and the computational complexity of inference has to be done: on one hand, conditional Gaussian models are computationally efficient but they lack expressive power; on the other hand, mixtures of exponentials (MTE), basis functions (MTBF) or polynomials (MOP) are expressive but this comes at the expense of tractability. In this paper, we introduce an alternative model called a ctdBN that lies in between. It is composed of a “discrete” Bayesian network (BN) combined with a set of univariate conditional truncated densities modeling the uncertainty over the continuous random variables given their discrete counterpart resulting from a discretization process. We prove that ctdBNs can approximate (arbitrarily well) any Lipschitz mixed probability distribution. They can therefore be exploited in many practical situations. An efficient inference algorithm is also provided and its computational complexity justifies theoretically why inference computation times in ctdBNs are very close to those in discrete BNs. Experiments confirm the tractability of the model and highlight its expressive power, notably by comparing it with BNs on classification problems and with MTEs and MOPs on marginal distributions estimations. [ABSTRACT FROM AUTHOR]

In this paper we present an approach for scaling up Bayesian learning using variational methods by exploiting distributed computing clusters managed by modern big data processing tools like Apache Spark or Apache Flink, which efficiently support iterative map-reduce operations. Our approach is defined as a distributed projected natural gradient ascent algorithm, has excellent convergence properties, and covers a wide range of conjugate exponential family models. We evaluate the proposed algorithm on three real-world datasets from different domains (the Pubmed abstracts dataset, a GPS trajectory dataset, and a financial dataset) and using several models (LDA, factor analysis, mixture of Gaussians and linear regression models). Our approach compares favorably to stochastic variational inference and streaming variational Bayes, two of the main current proposals for scaling up variational methods. For the scalability analysis, we evaluate our approach over a network with more than one billion nodes and approx. 75 % latent variables using a computer cluster with 128 processing units (AWS). The proposed methods are released as part of an open-source toolbox for scalable probabilistic machine learning ( http://www.amidsttoolbox.com ) Masegosa et al. (2017) [29] . [ABSTRACT FROM AUTHOR]

Reconstruction of the tridimensional geometry of a visual scene using the binocular disparity information is an important issue in computer vision and mobile robotics, which can be formulated as a Bayesian inference problem. However, computation of the full disparity distribution with an advanced Bayesian model is usually an intractable problem, and proves computationally challenging even with a simple model. In this paper, we show how probabilistic hardware using distributed memory and alternate representation of data as stochastic bitstreams can solve that problem with high performance and energy efficiency. We put forward a way to express discrete probability distributions using stochastic data representations and perform Bayesian fusion using those representations, and show how that approach can be applied to diparity computation. We evaluate the system using a simulated stochastic implementation and discuss possible hardware implementations of such architectures and their potential for sensorimotor processing and robotics. [ABSTRACT FROM AUTHOR]

Living organisms survive and multiply even though they have uncertain and incomplete information about their environment and imperfect models to predict the consequences of their actions. Bayesian models have been proposed to face this challenge. Indeed, Bayesian inference is a way to do optimal reasoning when only uncertain and incomplete information is available. Various perceptive, sensory-motor, and cognitive functions have been successfully modeled this way. However, the biological mechanisms allowing animals and humans to represent and to compute probability distributions are not known. It has been proposed that neurons and assemblies of neurons could be the appropriate scale to search for clues to probabilistic reasoning. In contrast, in this paper, we propose that interacting populations of macromolecules and diffusible messengers can perform probabilistic computation. This suggests that probabilistic reasoning, based on cellular signaling pathways, is a fundamental skill of living organisms available to the simplest unicellular organisms as well as the most complex brains. [ABSTRACT FROM AUTHOR]

Abstract: We develop a global sensitivity analysis to measure the robustness of the Bayesian estimators with respect to a class of prior distributions. This class arises when we consider multiplicative contamination of a base prior distribution. A similar structure was presented by van der Linde [12]. Some particular specifications for this multiplicative contamination class coincide with well known families of skewed distributions. In this paper, we explore the skew-normal multiplicative contamination class for the prior distribution of the location parameter of a normal model. Results of a Bayesian conjugation and expressions for some measures of distance between posterior means and posterior variance are obtained. We also elaborate on the behavior of the posterior means and of the posterior variances through a simulation study. [Copyright &y& Elsevier]