Related papers: The anti-Bayesian moment and its passing
The aim of this paper, triggered by some discussions in the astrophysics community raised by astro-ph/0508529, is to introduce the issue of `fits' from a probabilistic perspective (also known as Bayesian), with special attention to the…
The prevailing maximum likelihood estimators for inferring power law models from rank-frequency data are biased. The source of this bias is an inappropriate likelihood function. The correct likelihood function is derived and shown to be…
As suggested by Currie, we apply the probabilistic method to problems regarding pattern avoidance. Using techniques from analytic combinatorics, we calculate asymptotic pattern occurrence statistics and use them in conjunction with the…
Social bias in language - towards genders, ethnicities, ages, and other social groups - poses a problem with ethical impact for many NLP applications. Recent research has shown that machine learning models trained on respective data may not…
Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating…
When statisticians quarrel about hypothesis testing, the debate usually focus on which method is the correct one. The fundamental question of whether we should test hypothesis at all tends to be forgotten. This lack of debate has its roots…
The consistency of posterior distributions in density estimation is at the core of Bayesian statistical theory. Classical work established sufficient conditions, typically combining KL support with complexity bounds on sieves of high prior…
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…
In this paper, we are concerned with attributing meaning to the results of a Bayesian analysis for a problem which is sufficiently complex that we are unable to assert a precise correspondence between the expert probabilistic judgements of…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…
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,…
Bayesian inference provides a rigorous framework to encapsulate our knowledge and uncertainty regarding various physical quantities in a well-defined and self-contained manner. Utilising modern tools, such Bayesian models can be constructed…
This article is a response to recent proposals by Pearl and others for a new approach to personalised treatment decisions, in contrast to the traditional one based on statistical decision theory. We argue that this approach is dangerously…
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
In a recent paper (Phys. Rev. A 105, 042220 (2022)), Daley et al claim that some superdeterministic models are disfavoured against standard quantum mechanics, because such models overfit the statistics of a Bell-type experiment which the…
In the last two decades, Bayesian inference has become commonplace in astronomy. At the same time, the choice of algorithms, terminology, notation, and interpretation of Bayesian inference varies from one sub-field of astronomy to the next,…
This is an invited contribution to the discussion on Professor Deborah Mayo's paper, "On the Birnbaum argument for the strong likelihood principle," to appear in Statistical Science. Mayo clearly demonstrates that statistical methods…
Bayesian inference systems should be able to explain their reasoning to users, translating from numerical to natural language. Previous empirical work has investigated the correspondence between absolute probabilities and linguistic…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…