Related papers: The False Dilemma: Bayesian vs. Frequentist
Hypothesis testing and model choice are quintessential questions for statistical inference and while the Bayesian paradigm seems ideally suited for answering these questions, it faces difficulties of its own ranging from prior modelling to…
After some general remarks about the interrelation between philosophical and statistical thinking, the discussion centres largely on significance tests. These are defined as the calculation of $p$-values rather than as formal procedures for…
These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…
The problematic relationship between science and philosophy has, since the beginning of modernity, divided the world into two separate domains: nature and human. Some of today's schools of philosophy and epistemological inquiry have…
Accurate epidemic forecasting is critical for effective public health interventions. This study compares Bayesian and Frequentist estimation frameworks within deterministic compartmental epidemic models, focusing on nonlinear least squares…
Predicting the future state of a system has always been a natural motivation for science and practical applications. Such a topic, beyond its obvious technical and societal relevance, is also interesting from a conceptual point of view.…
It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings…
Experiments on decision making under uncertainty are known to display a classical pattern of risk aversion and risk seeking referred to as "fourfold pattern" (or "reflection effect") , but recent experiments varying the speed and order of…
We propose a semester-long Bayesian statistics course for undergraduate students with calculus and probability background. We cultivate students' Bayesian thinking with Bayesian methods applied to real data problems. We leverage modern…
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper we show that, despite being prescribed by a fundamental…
In this paper the Bayesian analysis is applied to assign a probability density to the value of a quantity having a definite sign. This analysis is logically consistent with the results, positive or negative, of repeated measurements.…
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,…
Background: Confirmation bias is the tendency to acquire or evaluate new information in a way that is consistent with one's preexisting beliefs. It is omnipresent in psychology, economics, and even scientific practices. Prior theoretical…
While philosophy of science is the study of problems of knowledge concerning science in general, there also exists - or should exist - a '' philosophy in science'' directed at finding out in what ways our actual scientific knowledge may…
Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes…
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…
Neural Networks (NNs) have provided state-of-the-art results for many challenging machine learning tasks such as detection, regression and classification across the domains of computer vision, speech recognition and natural language…
In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that…
Contemporary machine learning methods will try to approach the Bayes error, as it is the lowest possible error any model can achieve. This paper postulates that any decision is composed of not one but two Bayesian decisions and that…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…