Related papers: Reference analysis of the signal + background mode…
We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. We exhibit a prior on intensities which both leads to a computationally feasible method and enjoys…
In this present work, we discuss the Bayesian inference for the bivariate pseudo-exponential distribution. Initially, we assume independent gamma priors and then pseudo-gamma priors for the pseudo-exponential parameters. We are primarily…
We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of…
Approximate Bayesian computation is a statistical framework that uses numerical simulations to calibrate and compare models. Instead of computing likelihood functions, Approximate Bayesian computation relies on numerical simulations, which…
Approximate learning machines have become popular in the era of small devices, including quantised, factorised, hashed, or otherwise compressed predictors, and the quest to explain and guarantee good generalisation abilities for such…
Bayesian analysis of data from the general linear mixed model is challenging because any nontrivial prior leads to an intractable posterior density. However, if a conditionally conjugate prior density is adopted, then there is a simple…
Reference analysis produces objective Bayesian inference, in the sense that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a…
The Poisson model is frequently employed to describe count data, but in a Bayesian context it leads to an analytically intractable posterior probability distribution. In this work, we analyze a variational Gaussian approximation to the…
We study the identifiability of parameters and falsifiability of predictions under the process of model expansion in a Bayesian setting. Identifiability is represented by the closeness of the posterior to the prior distribution and…
The problem of detecting new signals in the presence of an unknown background is ubiquitous in scientific discoveries and is especially prominent in the physical sciences. Most solutions proposed thus far to address the problem focus on…
We revisit the problem of simultaneously testing the means of $n$ independent normal observations under sparsity. We take a Bayesian approach to this problem by introducing a scale-mixture prior known as the normal-beta prime (NBP) prior.…
Uncertainty quantification in reinforcement learning can greatly improve exploration and robustness. Approximate Bayesian approaches have recently been popularized to quantify uncertainty in model-free algorithms. However, so far the focus…
We consider priors for several nonparametric Bayesian models which use finite random series with a random number of terms. The prior is constructed through distributions on the number of basis functions and the associated coefficients. We…
Large-scale randomized experiments, sometimes called A/B tests, are increasingly prevalent in many industries. Though such experiments are often analyzed via frequentist $t$-tests, arguably such analyses are deficient: $p$-values are hard…
Scientific knowledge expands by observing the world, hypothesizing some theories about it, and testing them against collected data. When those theories take the form of statistical models, statistical analyses are involved in the process of…
The analysis of count data is commonly done using Poisson models. Negative binomial models are a straightforward and readily motivated generalization for the case of overdispersed data, i.e., when the observed variance is greater than…
We produce approximation bounds on a semidefinite programming relaxation for sparse principal component analysis. These bounds control approximation ratios for tractable statistics in hypothesis testing problems where data points are…
By exploiting the well-known observation that size-biasing or zero-biasing an infinitely divisible random variable may be achieved by adding an independent increment, combined with tools from Stein's method for compound Poisson and Gaussian…
Bayesian methods are increasingly applied in these days in the theory and practice of statistics. Any Bayesian inference depends on a likelihood and a prior. Ideally one would like to elicit a prior from related sources of information or…
We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a "penalized divergence" of the prior, which measures the ability of the prior distribution to propose a nonnegligible…