Related papers: Confidence intervals with maximal average power
We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…
In recent years the ultrahigh dimensional linear regression problem has attracted enormous attentions from the research community. Under the sparsity assumption most of the published work is devoted to the selection and estimation of the…
Consider a statistical problem where a set of parameters are of interest to a researcher. Then multiple confidence intervals can be constructed to infer the set of parameters simultaneously. The constructed multiple confidence intervals are…
Bayesian estimation is increasingly popular for performing model based inference to support policymaking. These data are often collected from surveys under informative sampling designs where subject inclusion probabilities are designed to…
We propose a framework for general Bayesian inference. We argue that a valid update of a prior belief distribution to a posterior can be made for parameters which are connected to observations through a loss function rather than the…
Bayesian hypothesis testing and minimax hypothesis testing represent extreme instances of detection in which the prior probabilities of the hypotheses are either completely and precisely known, or are completely unknown. Group minimax, also…
Two semimetrics on probability distributions are proposed, given as the sum of differences of expectations of analytic functions evaluated at spatial or frequency locations (i.e, features). The features are chosen so as to maximize the…
We consider the nonparametric regression problem with multiple predictors and an additive error, where the regression function is assumed to be coordinatewise nondecreasing. We propose a Bayesian approach to make an inference on the…
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 power prior and its variations have been proven to be a useful class of informative priors in Bayesian inference due to their flexibility in incorporating the historical information by raising the likelihood of the historical data to a…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
Motivated by parametric models for which the likelihood is analytically unavailable, numerically unstable, or prohibitively expensive to compute or optimize, we develop a prior- and likelihood-free framework for fully probabilistic…
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…
This paper explores the intrinsic connections between the Bayesian false discovery rate (FDR) control procedures and their counterpart of frequentist procedures. We attempt to offer a unified view of FDR control within and beyond the…
We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…
To assess whether there is some signal in a big database, aggregate tests for the global null hypothesis of no effect are routinely applied in practice before more specialized analysis is carried out. Although a plethora of aggregate tests…
This paper presents a general and efficient framework for probabilistic inference and learning from arbitrary uncertain information. It exploits the calculation properties of finite mixture models, conjugate families and factorization. Both…
There are over 55 different ways to construct a confidence respectively credible interval (CI) for the binomial proportion. Methods to compare them are necessary to decide which should be used in practice. The interval score has been…
We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible…
Bayesian hypothesis testing is investigated when the prior probabilities of the hypotheses, taken as a random vector, are quantized. Nearest neighbor and centroid conditions are derived using mean Bayes risk error as a distortion measure…