Related papers: A Novel Bayes' Theorem for Upper Probabilities
We define the information threshold as the point of maximum curvature in the prior vs. posterior Bayesian curve, both of which are described as a function of the true positive and negative rates of the classification system in question. The…
Bayesian Neural Networks (BNNs) place priors over the parameters in a neural network. Inference in BNNs, however, is difficult; all inference methods for BNNs are approximate. In this work, we empirically compare the quality of predictive…
Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference…
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…
Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…
In this paper, we present new high-probability PAC-Bayes bounds for different types of losses. Firstly, for losses with a bounded range, we recover a strengthened version of Catoni's bound that holds uniformly for all parameter values. This…
We are living in the big data era, as current technologies and networks allow for the easy and routine collection of data sets in different disciplines. Bayesian Statistics offers a flexible modeling approach which is attractive for…
Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…
The Bayesian statistical paradigm uses the language of probability to express uncertainty about the phenomena that generate observed data. Probability distributions thus characterize Bayesian analysis, with the rules of probability used to…
Maximum likelihood fits to data can be done using binned data (histograms) and unbinned data. With binned data, one gets not only the fitted parameters but also a measure of the goodness of fit. With unbinned data, currently, the fitted…
While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…
Bayesian hypothesis tests leverage posterior probabilities, Bayes factors, or credible intervals to inform data-driven decision making. We propose a framework for power curve approximation with such hypothesis tests. We present a fast…
This paper is concerned with a Bayesian approach to testing hypotheses in statistical inverse problems. Based on the posterior distribution $\Pi \left(\cdot |Y = y\right)$, we want to infer whether a feature $\langle\varphi,…
This article explains, and discusses the merits of, three approaches for analyzing the certainty with which statistical results can be extrapolated beyond the data gathered. Sometimes it may be possible to use more than one of these…
We consider a linear regression model, with the parameter of interest a specified linear combination of the regression parameter vector. We suppose that, as a first step, a data-based model selection (e.g. by preliminary hypothesis tests or…
Implementing Bayesian inference is often computationally challenging in applications involving complex models, and sometimes calculating the likelihood itself is difficult. Synthetic likelihood is one approach for carrying out inference…
In 'Theoria motus corporum coelestium in sectionibus conicis solem ambientum' Gauss presents, as a theorem and with emphasis, the rule to update the ratio of probabilities of complementary hypotheses, in the light of an observed event which…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
The inverse relation between mutual information (MI) and Bayesian error is sharpened by deriving finite sequences of upper and lower bounds on MI in terms of the minimum probability of error (MPE) and related Bayesian quantities. The well…
Leveraging algorithmic stability to derive sharp generalization bounds is a classic and powerful approach in learning theory. Since Vapnik and Chervonenkis [1974] first formalized the idea for analyzing SVMs, it has been utilized to study…