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About 10,000 papers for “Bayesian probability”

Bayesian Probability

Herman Bruyninckx · 2002

This document introduces the foundations of Bayesian probability theory. The emphasis is on understanding why Bayesian probability theory works, and on realizing that the theory relies, on the one hand, on a very limited number of fundamental properties for information processing, and, on the other hand, on a number of application-dependent and arbitrary choices for decision making. 1 What is Bayesian probability theory? Bayesian probability, is one of the major theoretical and practical frameworks for reasoning and decision making under uncertainty. The historical roots of this theory lie in the late 18th, early 19th century, with Thomas Bayes [2] and Pierre-Simon de Laplace [6]. It was “forgotten ” for a long time, and began to be re-appreciated in different application domains, during various periods of the 20th century. Hence, Bayesian probability was never developed as one single, homogeneous piece of scientific activity. So, it should come as no surprise that its concepts, methods and solution practices became known under various names: • the Bayesian approach to uncertainty reasoning. • Bayesianism.

Cited by 0

Bayesian Probability Theory

Wolfgang von der Linden, V. Dose, U. von Toussaint · Cambridge University Press eBooks · 2014

From the basics to the forefront of modern research, this book presents all aspects of probability theory, statistics and data analysis from a Bayesian perspective for physicists and engineers. The book presents the roots, applications and numerical implementation of probability theory, and covers advanced topics such as maximum entropy distributions, stochastic processes, parameter estimation, model selection, hypothesis testing and experimental design. In addition, it explores state-of-the art numerical techniques required to solve demanding real-world problems. The book is ideal for students and researchers in physical sciences and engineering.

Cited by 105

Vagueness and Bayesian probability

Nic Wilson · IEEE Transactions on Fuzzy Systems · 1994

This paper is a response to Michael Laviolette and John W. Seaman Jr.'s ( ibid. vol.2, no.1, p.4 (1994)) position paper "The efficacy of fuzzy representations of uncertainty," which criticizes fuzzy representations of uncertainty, and suggests that Bayesian probability can do better. The commenter argues that the author's make some misleading comments about Bayesian probability, and he briefly discusses the problem of giving a satisfactory interpretation of membership functions.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Cited by 9

Bayesian posterior probability parameters.

Coral Diaz-Recio Lorenzo (17343251), Tasnim Patel (11309979), Eve-Julie Arsenault-Pernet (17343254) et al. · Figshare · 2023

&lt;div&gt;&lt;p&gt;Hydrothermal vents are extreme environments, where abundant communities of copepods with contrasting life history traits co-exist along hydrothermal gradients. Here, we discuss how these traits may contribute to the observed differences in molecular diversity and population genetic structure. Samples were collected from vent locations across the globe including active ridges and back-arc basins and compared to existing deep-sea hydrothermal vent and shallow water data, covering a total of 22 vents and 3 non-vent sites. A total of 806 sequences of mtDNA from the &lt;i&gt;Cox1&lt;/i&gt; gene were used to reconstruct the phylogeny, haplotypic relationship and demography within vent endemic copepods (Dirivultidae, &lt;i&gt;Stygiopontius&lt;/i&gt; spp.) and non-vent-endemic copepods (Ameiridae, Miraciidae and Laophontidae). A species complex within &lt;i&gt;Stygiopontius lauensis&lt;/i&gt; was studied across five pacific back-arc basins at eight hydrothermal vent fields, with cryptic species being restricted to the basins they were sampled from. Copepod populations from the Lau, North Fiji and Woodlark basins are undergoing demographic expansion, possibly linked to an increase in hydrothermal activity in the last 10 kya. Highly structured populations of &lt;i&gt;Amphiascus&lt;/i&gt; aff. &lt;i&gt;varians&lt;/i&gt; 2 were also observed from the Lau to the Woodlark basins with populations also undergoing expansion. Less abundant harpacticoids exhibit little to no population structure and stable populations. This study suggests that similarities in genetic structure and demography may arise in vent-associated copepods despite having different life history traits. As structured meta-populations may be at risk of local extinction should major anthropogenic impacts, such as deep-sea mining, occur, we highlight the importance of incorporating a trait-based approach to investigate patterns of genetic connectivity and demography, particularly regarding area-based management tools and environmental management plans.&lt;/p&gt;&lt;/div&gt;

Cited by 0Open access

Probability and Bayesian Modeling

Jim Albert, Jingchen Hu · 2019

Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.

Cited by 43

ON BAYESIAN LOGICAL PROBABILITY

Melvin R. Novick · ETS Research Bulletin Series · 1964

ABSTRACT In a recent paper (Edwards, Lindman, and Savage, 1963), psychologists have been urged to adopt a Bayesian personal probability approach to statistical inference. The purpose of this paper is to suggest that a Bayesian logical probability approach may be superior to the personal probability approach. The concepts of frequency, personal and logical probability are defined and the characteristics and advantages of Bayesian approaches are discussed. It is shown that a theory of personal probability is dependent upon utility or preference theory. The problem of Bayes postulate is described and it is shown that an explication of the concept of logical probability is dependent upon the solution of this problem. Some work of Novick and Hall directed toward the solution of this problem is discussed. Finally, an attempt is made to integrate the concepts of personal and frequency probability within the framework of the theory of logical probability.

Cited by 8Open access

Probability and Bayesian Modeling

Subir Ghosh · Technometrics · 2020

Probability and Bayesian Modeling is a book on classical probability (Chapters 1–6) in understanding probability and probability distributions by using simulation based approximations and the R pro...

Cited by 11Open access

Illustration of Bayesian probability approach.

Amrita X. Sarkar (242591), Eric A. Sobie (242595) · Figshare · 2015

&lt;p&gt;(&lt;b&gt;A&lt;/b&gt;) Distributions of G&lt;sub&gt;Na&lt;/sub&gt; with different constraints. From left to right, histograms show G&lt;sub&gt;Na&lt;/sub&gt; values in the complete data set; given that APD is in a particular range (from 295–298 ms, representing 10% of the samples); given that APD and V&lt;sub&gt;rest&lt;/sub&gt; (−84.96 to −85.02 mV) are in particular ranges; given that APD, V&lt;sub&gt;rest&lt;/sub&gt;, and V&lt;sub&gt;peak&lt;/sub&gt; (37.05 to 37.81 mV) are in particular ranges. (&lt;b&gt;B&lt;/b&gt;) Distributions of G&lt;sub&gt;Ca&lt;/sub&gt;, given the same constraints as in (&lt;b&gt;A&lt;/b&gt;).&lt;/p&gt;

Cited by 0Open access

Bayesian Probability in Quantum Mechanics

Rüdiger Schack · 2007

Abstract This paper reviews arguments for the claim that all probabilities arising in quantum mechanics are Bayesian degrees of belief. The starting point is the observation that there is a one-to-one map from quantum states to points on the probability simplex. Bayes’s rule remains valid in quantum theory, provided it is kept in mind that the outcomes of quantum measurements have no preassigned values. The probabilities of quantum measurement outcomes depend explicitly on a quantum prior whose general form will be discussed. Similar to the classical case, the quantum de Finetti theorem simplifies the analysis of repeated quantum trials if the prior is exchangeable. The Bayesian approach to quantum theory described here solves the problem of the ‘collapse of the wave function’. It also provides almost trivial explanations of a number of phenomena in quantum information theory, including the no-cloning theorem and quantum teleportation.

Cited by 0