Related papers: Bayesian Core: The Complete Solution Manual
In this paper, we present two classes of Bayesian approaches to the two-sample problem. Our first class of methods extends the Bayesian t-test to include all parametric models in the exponential family and their conjugate priors. Our second…
This paper presents a Bayesian optimization method with exponential convergence without the need of auxiliary optimization and without the delta-cover sampling. Most Bayesian optimization methods require auxiliary optimization: an…
The past decade has seen an explosion of research in causal mediation analysis. However, most analytic tools developed so far rely on frequentist methods which may not be robust in the case of small sample sizes. In this paper, we propose a…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…
We give a constructive approach for the study of integral representations of classical solutions to Poisson equations under some integrability conditions on data functions.
Existing high-dimensional Bayesian optimization (BO) methods aim to overcome the curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly,…
Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization,…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
We study a regularized variant of the Bayesian Persuasion problem, where the receiver's decision process includes a divergence-based penalty that accounts for deviations from perfect rationality. This modification smooths the underlying…
bde is a user-friendly Python package for Bayesian Deep Ensembles with a particular focus on tabular data. Built on an efficient JAX implementation of the sampling-based inference method Microcanonical Langevin Ensembles (MILE), it provides…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…
This tutorial gives a quick introduction to Variational Bayes (VB), also called Variational Inference or Variational Approximation, from a practical point of view. The paper covers a range of commonly used VB methods and an attempt is made…
This paper introduces a model-free real-time optimization (RTO) framework based on unconstrained Bayesian optimization with embedded constraint control. The main contribution lies in demonstrating how this approach simplifies the black-box…
In this paper we give an outline on the Bayesian Decision Theory.
Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.
Bayesian optimization is an approach to optimizing objective functions that take a long time (minutes or hours) to evaluate. It is best-suited for optimization over continuous domains of less than 20 dimensions, and tolerates stochastic…
Modern machine learning applications should be able to address the intrinsic challenges arising over inference on massive real-world datasets, including scalability and robustness to outliers. Despite the multiple benefits of Bayesian…
Cooking typically involves a plethora of decisions about ingredients and tools that need to be chosen in order to write a good cooking recipe. Cooking can be modelled in an optimization framework, as it involves a search space of…
In this work, I present an automatic system for the evaluation of closed-type exercises in physics at the high school level or in the first year of a degree where physics is a mandatory course. It is expected that this will allow students…
Most of applied statistics involves regression analysis of data. This paper presents a stand-alone and menu-driven software package, Bayesian Regression: Nonparametric and Parametric Models. Currently, this package gives the user a choice…