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We use both Bayesian and neural models to dissect a data set of Chinese learners' pre- and post-interventional responses to two tests measuring their understanding of English prepositions. The results mostly replicate previous findings from…

There is significant growth and interest in the use of synthetic data as an enabler for machine learning in environments where the release of real data is restricted due to privacy or availability constraints. Despite a large number of…

The two key issues of modern Bayesian statistics are: (i) establishing principled approach for distilling statistical prior that is consistent with the given data from an initial believable scientific prior; and (ii) development of a…

A Bayesian network is a graphical model that encodes probabilistic relationships among variables of interest. When used in conjunction with statistical techniques, the graphical model has several advantages for data analysis. One, because…

Statistical analysis is the tool of choice to turn data into information, and then information into empirical knowledge. To be valid, the process that goes from data to knowledge should be supported by detailed, rigorous guidelines, which…

Inferences about hypotheses are ubiquitous in the cognitive sciences. Bayes factors provide one general way to compare different hypotheses by their compatibility with the observed data. Those quantifications can then also be used to choose…

Causal discovery is crucial for understanding complex systems and informing decisions. While observational data can uncover causal relationships under certain assumptions, it often falls short, making active interventions necessary. Current…

Bayesian statistics is an integral part of contemporary applied science. bayesics provides a single framework, unified in syntax and output, for performing the most commonly used statistical procedures, ranging from one- and two-sample…

The Bayes factor, the data-based updating factor of the prior to posterior odds of two hypotheses, is a natural measure of statistical evidence for one hypothesis over the other. We show how Bayes factors can also be used for parameter…

The self-rationalising capabilities of LLMs are appealing because the generated explanations can give insights into the plausibility of the predictions. However, how faithful the explanations are to the predictions is questionable, raising…

Empirical Bayes methods have been around for a long time and have a wide range of applications. These methods provide a way in which historical data can be aggregated to provide estimates of the posterior mean. This thesis revisits some of…

Data-driven approaches have revolutionized scientific research, with machine learning and statistical analysis being commonly used methodologies. Despite their widespread use, these approaches differ significantly in their techniques,…

Forecasting techniques for assessing the power of future experiments to discriminate between theories or discover new laws of nature are of great interest in many areas of science. In this paper, we introduce a Bayesian forecasting method…

We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…

This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…

This chapter offers an accessible introduction to the channel-based approach to Bayesian probability theory. This framework rests on algebraic and logical foundations, inspired by the methodologies of programming language semantics. It…

While observational data are routinely used to estimate causal effects of biomedical treatments, doing so requires special methods to adjust for observed confounding. These methods invariably rely on untestable statistical and causal…

Recent approaches to human concept learning have successfully combined the power of symbolic, infinitely productive rule systems and statistical learning to explain our ability to learn new concepts from just a few examples. The aim of most…

Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a…

Fuzzy data, prevalent in social sciences and other fields, capture uncertainties arising from subjective evaluations and measurement imprecision. Despite significant advancements in fuzzy statistics, a unified inferential regression-based…