DE4MH

This repo contains the codes, images, report and slides for the project of the course - MTH516A: Non-Parametric Inference at IIT Kanpur during the academic year 2022-2023.

Project Members

• Arkajyoti Bhattacharjee
• Nitin Garg
• Suchismita Roy

Project Title

Nonparametric Kernel Density Estimation for the Metropolis-Hastings Algorithm [Report] [Slides]

Abstract

In this report, we discuss how the rejection step of the Metropolis-Hastings algorithm affects kernel density estimation. We elaborate on the theory developed by [1] by providing extensive proofs and explore applications exhibiting their efficiency in various problems.

Table of Content

Section	Topic
1	Introduction 1.1 Notations
2	An Overview of Kernel Density Estimation 2.1 Measures of Discrepeancy 2.1.1 Independent Data 2.1.2 Time Series Data 2.2 Bandwidth Selection
3	The Metropolis-Hastings Algorithm
4	KDE for the M-H algorithm 4.1 Bandwidth Selection for the MH 4.1.1 Plug-in Method 4.1.2 Bump killing
5	Applications 5.1 Problem 1 5.2 Problem 2 5.3 Problem 3

Primary Reference

[1]. Sköld, M., & Roberts, G. O. (2003). Density estimation for the Metropolis–Hastings algorithm. Scandinavian journal of statistics, 30(4), 699-718.