Related papers: Bayesian Analysis
In the subjective Bayesian approach uncertainty is described by a prior distribution chosen by the statistician. Fuzzy set theory is another way of representing uncertainty. Here we give a decision theoretic approach which allows a Bayesian…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
This chapter offers an accessible introduction to the channel-based approach to Bayesian probability theory. This framework rests on algebraic and logical foundations, inspired by the methodologies of programming language semantics. It…
Empirical Bayes methods have been around for a long time and have a wide range of applications. These methods provide a way in which historical data can be aggregated to provide estimates of the posterior mean. This thesis revisits some of…
The theory of probability and the quantum theory, the one mathematical and the other physical, are related in that each admits a number of very different interpretations. It has been proposed that the conceptual problems of the quantum…
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…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
In almost every scientific field, an experiment involves collecting data and then analysing it. The analysis stage will often consist in trying to extract some physical parameter and estimating its uncertainty; this is known as Parameter…
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, we adopt a Bayesian point of view for predicting real continuous-time processes. We give two equivalent definitions of a Bayesian predictor and study some properties: admissibility, prediction sufficiency, non-unbiasedness,…
It is well known that a Bayesian probability forecast for all future observations should be a probability measure in order to satisfy a natural condition of coherence. The main topics of this paper are the evolution of the Bayesian…
Realizing the full potential of interconnecting the large amounts of data created in physics experiments, phenomenological models and theory simulations requires robust tools for statistical inference. Here I review a particularly promising…
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 paper focuses on utilizing two different Bayesian methods to deal with a variety of toy problems which occur in data analysis. In particular we implement the Variational Bayesian and Nested Sampling methods to tackle the problems of…
While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures.…
Modern statisticians are often presented with hundreds or thousands of hypothesis testing problems to evaluate at the same time, generated from new scientific technologies such as microarrays, medical and satellite imaging devices, or flow…
Clustering is widely studied in statistics and machine learning, with applications in a variety of fields. As opposed to classical algorithms which return a single clustering solution, Bayesian nonparametric models provide a posterior over…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We ask which distributions over empirical distributions of posteriors beliefs…
The Bayesian posterior probability of the true state is stochastically dominated by that same posterior under the probability law of the true state. This generalizes to notions of "optimism" about posterior probabilities.