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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

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.