Related papers: Reference analysis of the signal + background mode…

A novel block prior is proposed for adaptive Bayesian estimation. The prior does not depend on the smoothness of the function or the sample size. It puts sufficient prior mass near the true signal and automatically concentrates on its…

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

Bayesian statistics has two common measures of central tendency of a posterior distribution: posterior means and Maximum A Posteriori (MAP) estimates. In this paper, we discuss a connection between MAP estimates and posterior means. We…

In high-dimensional problems, choosing a prior distribution such that the corresponding posterior has desirable practical and theoretical properties can be challenging. This begs the question: can the data be used to help choose a good…

We review the methods of constructing confidence intervals that account for a priori information about one-sided constraints on the parameter being estimated. We show that the so-called method of sensitivity limit yields a correct solution…

We show how to obtain a Bayesian estimate of the rates or numbers of signal and background events from a set of events when the shapes of the signal and background distributions are known, can be estimated, or approximated; our method works…

We consider a prior for nonparametric Bayesian estimation which uses 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…

The problem of composite hypothesis testing is considered in the context of Bayesian detection of weak target signals in cluttered backgrounds. (A specific example is the detection of sub-pixel targets in multispectral imagery.) In this…

Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown…

We present a procedure for calculating an upper limit on the number of signal events which incorporates the Poisson uncertainty in the background, estimated from control regions of one or two dimensions. For small number of signal events,…

We use rescaled Gaussian processes as prior models for functional parameters in nonparametric statistical models. We show how the rate of contraction of the posterior distributions depends on the scaling factor. In particular, we exhibit…

We propose a method for estimating the posterior distribution of a standard geostatistical model. After choosing the model formulation and specifying a prior, we use normal mixture densities to approximate the posterior distribution. The…

There are intensive efforts searching for new phenomena in many present and future scientific experiments such as LHC at CERN, CLIC, ILC and many others. These new signals are usually rare and frequently contaminated by many different…

The estimation of signal frequency count in the presence of background noise has had much discussion in the recent physics literature, and Mandelkern [1] brings the central issues to the statistical community, leading in turn to extensive…

The martingale posterior framework is a generalization of Bayesian inference where one elicits a sequence of one-step ahead predictive densities instead of the likelihood and prior. Posterior sampling then involves the imputation of unseen…

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

Machine learning models can be improved by adapting them to respect existing background knowledge. In this paper we consider multitask Gaussian processes, with background knowledge in the form of constraints that require a specific sum of…

We consider the standard Neyman-Pearson hypothesis test of a signal-plus-background hypothesis and background-only hypothesis in the presence of uncertainty on the background-only prediction. Surprisingly, this problem has not been…

When choosing between competing symbolic models for a data set, a human will naturally prefer the "simpler" expression or the one which more closely resembles equations previously seen in a similar context. This suggests a non-uniform prior…

This paper studies how imprecision in noisy signals attenuates Bayesian updating toward the prior. This phenomenon is well-known under a normal prior and normal noise, where less precise signals yield posterior means closer to the prior…