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This paper introduces a computational framework for reasoning in Bayesian belief networks that derives significant advantages from focused inference and relevance reasoning. This framework is based on d -separation and other simple and…

We define the notion of compiling a Bayesian network with evidence and provide a specific approach for evidence-based compilation, which makes use of logical processing. The approach is practical and advantageous in a number of application…

The likelihood ratio (LR) measures the relative weight of forensic data regarding two hypotheses. Several levels of uncertainty arise if frequentist methods are chosen for its assessment: the assumed population model only approximates the…

We look at the distribution of the Bayesian evidence for mock realizations of supernova and baryon acoustic oscillation data. The ratios of Bayesian evidences of different models are often used to perform model selection. The significance…

Bayesian inference has theoretical attractions as a principled framework for reasoning about beliefs. However, the motivations of Bayesian inference which claim it to be the only 'rational' kind of reasoning do not apply in practice. They…

Although researchers have found evidence contextual bias in forensic science, the discussion of contextual bias is currently qualitative. We formalize years of empirical research and extend this research by showing quantitatively how biases…

The basic idea of importance sampling is to use independent samples from a proposal measure in order to approximate expectations with respect to a target measure. It is key to understand how many samples are required in order to guarantee…

Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…

Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…

This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…

Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a…

Artificial Intelligence (AI), and in particular, the explainability thereof, has gained phenomenal attention over the last few years. Whilst we usually do not question the decision-making process of these systems in situations where only…

One of the main problems of importance sampling in Bayesian networks is representation of the importance function, which should ideally be as close as possible to the posterior joint distribution. Typically, we represent an importance…

For more than a century, fingerprints have been used with considerable success to identify criminals or verify the identity of individuals. The categorical conclusion scheme used by fingerprint examiners, and more generally the inference…

This paper studies the role played by identification in the Bayesian analysis of statistical and econometric models. First, for unidentified models we demonstrate that there are situations where the introduction of a non-degenerate prior…

This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…

We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…

The use of profiling evidence in criminal trials is a longstanding controversy in legal epistemology and evidence law theory. Many scholars, even when they oppose its use at trial, still assume that profiling evidence can be probative of…

This paper is concerned with the epistemic question of confirming a hypothesis -- the guilt of a defendant -- by way of testimony heard by a juror over the course of an American-style criminal trial. In it, I attempt to settle a dispute…

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal…