Related papers: Bayesian Analysis
In this paper we review the concepts of Bayesian evidence and Bayes factors, also known as log odds ratios, and their application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical…
Physics increasingly uses Bayesian techniques for systematic data analysis and model-to-data comparison. This paper describes how these methods can be implemented to answer questions of relevance to teaching laboratories. It demonstrates…
We review an established Bayesian sampling method called sampling/importance resampling and highlight situations in nuclear theory when it can be particularly useful. To this end we both analyse a toy problem and demonstrate realistic…
This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…
Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model {\it uncertainty} rather than randomness or variability. This thesis is composed of a…
The two statistical methods, namely the frequentist and the Bayesian methods, are both commonly used for probabilistic inference in many scientific situations. However, it is not straightforward to interpret the result of one approach in…
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…
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.…
Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…
A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the…
The idea that the brain is a probabilistic (Bayesian) inference machine, continuously trying to figure out the hidden causes of its inputs, has become very influential in cognitive (neuro)science over recent decades. Here I present a…
The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more…
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…
Bayesian hypothesis testing is investigated when the prior probabilities of the hypotheses, taken as a random vector, are quantized. Nearest neighbor and centroid conditions are derived using mean Bayes risk error as a distortion measure…
A key sticking point of Bayesian analysis is the choice of prior distribution, and there is a vast literature on potential defaults including uniform priors, Jeffreys' priors, reference priors, maximum entropy priors, and weakly informative…
Triggered by a recent interesting New Scientist article on the too frequent incorrect use of probabilistic evidence in courts, I introduce the basic concepts of probabilistic inference with a toy model, and discuss several important issues…
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…
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…
Following a paper in which the fundamental aspects of probabilistic inference were introduced by means of a toy experiment, details of the analysis of simulated long sequences of extractions are shown here. In fact, the striking performance…
We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these…