Flexible Bayesian Regression Modelling

Yanan Fan, David Nott, Mike S. Smith, Jean-Luc Dortet-Bernadet

• Publisher: Academic Press
• Year: 2019
• Print ISBN: 9780128158623
• eBook ISBN: 9780128158630
• Topic: Economics
• Subtopic: Business Mathematics
• Index: Economics

Flexible Bayesian Regression Modeling is a step-by-step guide to the Bayesian revolution in regression modeling, for use in advanced econometric and statistical analysis where datasets are characterized by complexity, multiplicity, and large sample sizes, necessitating the need for considerable flexibility in modeling techniques. It reviews three forms of flexibility: methods which provide flexibility in their error distribution; methods which model non-central parts of the distribution (such as quantile regression); and finally models that allow the mean function to be flexible (such as spline models). Each chapter discusses the key aspects of fitting a regression model. R programs accompany the methods.This book is particularly relevant to non-specialist practitioners with intermediate mathematical training seeking to apply Bayesian approaches in economics, biology, finance, engineering and medicine.- Introduces powerful new nonparametric Bayesian regression techniques to classically trained practitioners- Focuses on approaches offering both superior power and methodological flexibility- Supplemented with instructive and relevant R programs within the text- Covers linear regression, nonlinear regression and quantile regression techniques- Provides diverse disciplinary case studies for correlation and optimization problems drawn from Bayesian analysis 'in the wild'

Chapter 1

Bayesian quantile regression with the asymmetric Laplace distribution

J.-L. Dortet-Bernadet^a; Y. Fan^b; T. Rodrigues^{c a}Institut de Recherche Mathématique Avancée, UMR 7501 CNRS, Université de Strasbourg, Strasbourg, France
^bSchool of Mathematics and Statistics, University of New South Wales, Sydney, NSW, Australia
^cDepartamento de Estatistica, Universidade de Brasilia, Brasília, Brazil

Abstract

We give in this chapter an overview of the use of the asymmetric Laplace distribution for Bayesian quantile regression. We describe linear and nonlinear models in this context and provide R code and instructions for their use. We give several examples, including additive models, and present some postprocessing procedures able to correct known potential limitations of the asymmetric Laplace approach.

Keywords

quantile regression; asymmetric Laplace distribution; postprocess; additive models

Chapter Outline

• 1.1 Introduction
• 1.2 The asymmetric Laplace distribution for quantile regression
  • 1.2.1 A simple and efficient sampler
  • 1.2.2 Quantile curve fitting
  • 1.2.3 Additive models
• 1.3 On coverage probabilities
• 1.4 Postprocessing for multiple fittings
• 1.5 Final remarks and conclusion
• References

1.1 Introduction

Following the seminal work by Koenker and Bassett [15] quantile regression has been recognised in recent years as a robust statistical procedure that offers a powerful alternative to ordinary mean regression. This type of regression has proven its interest and its effectiveness in...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Contributors
• Preface
• Chapter 1: Bayesian quantile regression with the asymmetric Laplace distribution
• Chapter 2: A vignette on model-based quantile regression: analysing excess zero response
• Chapter 3: Bayesian nonparametric density regression for ordinal responses
• Chapter 4: Bayesian nonparametric methods for financial and macroeconomic time series analysis
• Chapter 5: Bayesian mixed binary-continuous copula regression with an application to childhood undernutrition
• Chapter 6: Nonstandard flexible regression via variational Bayes
• Chapter 7: Scalable Bayesian variable selection regression models for count data
• Chapter 8: Bayesian spectral analysis regression
• Chapter 9: Flexible regression modelling under shape constraints
• Index