Related papers: Tutorial on Bayesian Functional Regression Using S…
Bayesian neural network posterior distributions have a great number of modes that correspond to the same network function. The abundance of such modes can make it difficult for approximate inference methods to do their job. Recent work has…
Recent years have witnessed an upsurge of interest in employing flexible machine learning models for instrumental variable (IV) regression, but the development of uncertainty quantification methodology is still lacking. In this work we…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
This paper proposes a new formulation of functional Gaussian Process regression in manifolds, based on an Empirical Bayes approach, in the spatiotemporal random field context. We apply the machinery of tight Gaussian measures in separable…
We provide a new flexible framework for inference with the instrumental variable model. Rather than using linear specifications, functions characterizing the effects of instruments and other explanatory variables are estimated using machine…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
We consider the problems of hypothesis testing and model comparison under a flexible Bayesian linear regression model whose formulation is closely connected with the linear mixed effect model and the parametric models for SNP set analysis…
Accurate epidemic forecasting is critical for effective public health interventions. This study compares Bayesian and Frequentist estimation frameworks within deterministic compartmental epidemic models, focusing on nonlinear least squares…
We present a Bayesian inference scheme for scaled Brownian motion, and investigate its performance on synthetic data for parameter estimation and model selection in a combined inference with fractional Brownian motion. We include the…
Functional data are ubiquitous in scientific modeling. For instance, quantities of interest are modeled as functions of time, space, energy, density, etc. Uncertainty quantification methods for computer models with functional response have…
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…
We consider the functional regression model with multivariate response and functional predictors. Compared to fitting each individual response variable separately, taking advantage of the correlation between the response variables can…
We develop a unifying framework for Bayesian nonparametric regression to study the rates of contraction with respect to the integrated $L_2$-distance without assuming the regression function space to be uniformly bounded. The framework is…
We propose a doubly robust approach to characterizing treatment effect heterogeneity in observational studies. We develop a frequentist inferential procedure that utilizes posterior distributions for both the propensity score and outcome…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
Methods utilizing instrumental variables have been a fundamental statistical approach to estimation in the presence of unmeasured confounding, usually occurring in non-randomized observational data common to fields such as economics and…
A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone…
This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…
Due to developments in instruments and computers, functional observations are increasingly popular. However, effective methodologies for flexibly estimating the underlying trends with valid uncertainty quantification for a sequence of…
Neuroradiologists and neurosurgeons increasingly opt to use functional magnetic resonance imaging (fMRI) to map functionally relevant brain regions for noninvasive presurgical planning and intraoperative neuronavigation. This application…