Related papers: Empirical Bayes Method for Boltzmann Machines

In this study, we introduce a novel methodological framework called Bayesian Penalized Empirical Likelihood (BPEL), designed to address the computational challenges inherent in empirical likelihood (EL) approaches. Our approach has two…

We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove…

Empirical analysis serves as an important complement to theoretical analysis for studying practical Bayesian optimization. Often empirical insights expose strengths and weaknesses inaccessible to theoretical analysis. We define two metrics…

One of the main goals of mathematical modeling in systems medicine related to medical applications is to obtain patient-specific parameterizations and model predictions. In clinical practice, however, the number of available measurements…

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…

Likelihood functions evaluated using particle filters are typically noisy, computationally expensive, and non-differentiable due to Monte Carlo variability. These characteristics make conventional optimization methods difficult to apply…

Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…

Empirical Bayes (EB) improves the accuracy of simultaneous inference "by learning from the experience of others" (Efron, 2012). Classical EB theory focuses on latent variables that are iid draws from a fitted prior (Efron, 2019). Modern…

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…

Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…

This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…

Purpose: Machine learning is broadly used for clinical data analysis. Before training a model, a machine learning algorithm must be selected. Also, the values of one or more model parameters termed hyper-parameters must be set. Selecting…

There are many advantages to use probability method for nonlinear system identification, such as the noises and outliers in the data set do not affect the probability models significantly; the input features can be extracted in probability…

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…

Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…

When dealing with Bayesian inference the choice of the prior often remains a debatable question. Empirical Bayes methods offer a data-driven solution to this problem by estimating the prior itself from an ensemble of data. In the…

We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…

The block maxima method is one of the most popular approaches for extreme value analysis with independent and identically distributed observations in the domain of attraction of an extreme value distribution. The lack of a rigorous study on…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

Identifying leading measurement units from a large collection is a common inference task in various domains of large-scale inference. Testing approaches, which measure evidence against a null hypothesis rather than effect magnitude, tend to…