Bayesian Approaches to Shrinkage and Sparse Estimation

12/22/2021
by   Dimitris Korobilis, et al.
0

In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference is the norm in several fields of applied econometric work. The purpose of this paper is to introduce the reader to the world of Bayesian model determination, by surveying modern shrinkage and variable selection algorithms and methodologies. Bayesian inference is a natural probabilistic framework for quantifying uncertainty and learning about model parameters, and this feature is particularly important for inference in modern models of high dimensions and increased complexity. We begin with a linear regression setting in order to introduce various classes of priors that lead to shrinkage/sparse estimators of comparable value to popular penalized likelihood estimators (e.g. ridge, lasso). We explore various methods of exact and approximate inference, and discuss their pros and cons. Finally, we explore how priors developed for the simple regression setting can be extended in a straightforward way to various classes of interesting econometric models. In particular, the following case-studies are considered, that demonstrate application of Bayesian shrinkage and variable selection strategies to popular econometric contexts: i) vector autoregressive models; ii) factor models; iii) time-varying parameter regressions; iv) confounder selection in treatment effects models; and v) quantile regression models. A MATLAB package and an accompanying technical manual allow the reader to replicate many of the algorithms described in this review.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/09/2018

On variance estimation for Bayesian variable selection

Consider the problem of high dimensional variable selection for the Gaus...
research
07/25/2022

Sparse Bayesian State-Space and Time-Varying Parameter Models

In this chapter, we review variance selection for time-varying parameter...
research
07/18/2021

Decoupling Shrinkage and Selection for the Bayesian Quantile Regression

This paper extends the idea of decoupling shrinkage and sparsity for con...
research
02/17/2021

Variational Inference for Shrinkage Priors: The R package vir

We present vir, an R package for variational inference with shrinkage pr...
research
12/09/2019

Semiparametric Regression for Dual Population Mortality

Parameter shrinkage applied optimally can always reduce error and projec...
research
09/03/2015

Bayesian Masking: Sparse Bayesian Estimation with Weaker Shrinkage Bias

A common strategy for sparse linear regression is to introduce regulariz...
research
07/10/2023

Predicting milk traits from spectral data using Bayesian probabilistic partial least squares regression

High-dimensional spectral data – routinely generated in dairy production...

Please sign up or login with your details

Forgot password? Click here to reset