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This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…

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…

In recent years, Bayesian statistics has gained traction across a wide range of scientific disciplines. This paper explores the growing application of Bayesian methods within the field of linguistics and considers their future potential. A…

In this manuscript, we discuss the substantial importance of Bayesian reasoning in Social Science research. Particularly, we focus on foundational elements to fit models under the Bayesian paradigm. We aim to offer a frame of reference for…

Bayes Factors, the Bayesian tool for hypothesis testing, are receiving increasing attention in the literature. Compared to their frequentist rivals ($p$-values or test statistics), Bayes Factors have the conceptual advantage of providing…

Bayesian hypothesis testing via Bayes factors offers a principled alternative to classical p-value methods in meta-analysis, particularly suited to its cumulative and sequential nature. Unlike commonly reported p-values for standard null…

Statistics comes in two main flavors: frequentist and Bayesian. For historical and technical reasons, frequentist statistics have traditionally dominated empirical data analysis, and certainly remain prevalent in empirical software…

While many studies have previously conducted direct comparisons between results obtained from frequentist and Bayesian models, our research introduces a novel perspective by examining these models in the context of a small dataset…

This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…

Building on a strong foundation of philosophy, theory, methods and computation over the past three decades, Bayesian approaches are now an integral part of the toolkit for most statisticians and data scientists. Whether they are dedicated…

We argue here about the relevance and the ultimate unity of the Bayesian approach in a neutral and agnostic manner. Our main theme is that Bayesian data analysis is an effective tool for handling complex models, as proven by the increasing…

We provide four case studies that use Bayesian machinery to making inductive reasoning. Our main motivation relies in offering several instances where the Bayesian approach to data analysis is exploited at its best to perform complex tasks,…

We present the fundamental ideas underlying statistical hypothesis testing using the frequentist framework. We begin with a simple example that builds up the one-sample t-test from the beginning, explaining important concepts such as the…

Bayesian inference is on the rise, partly because it allows researchers to quantify parameter uncertainty, evaluate evidence for competing hypotheses, incorporate model ambiguity, and seamlessly update knowledge as information accumulates.…

This study examines the application of Bayesian approach in the context of clinical trials, emphasizing their increasing importance in contemporary biomedical research. While conventional frequentist approach provides a foundational basis…

Bayesian hierarchical models are well-suited to analyzing the often noisy data from electroencephalography experiments in cognitive neuroscience: these models provide an intuitive framework to account for structures and correlations in the…

In the case of informative sampling the sampling scheme explicitly or implicitly depends on the response variable. As a result, the sample distribution of response variable can- not be used for making inference about the population. In this…

Frequentist statistical methods, such as hypothesis testing, are standard practice in papers that provide benchmark comparisons. Unfortunately, these methods have often been misused, e.g., without testing for their statistical test…

Experiments in research on memory, language, and in other areas of cognitive science are increasingly being analyzed using Bayesian methods. This has been facilitated by the development of probabilistic programming languages such as Stan,…

The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…