UP TO 15 % DISCOUNT

Get Your Assignment Completed At Lower Prices

Plagiarism Free Solutions
100% Original Work
24*7 Online Assistance
Native PhD Experts
Hire a Writer Now
ST2195 Programming For Data Science Report, SUSS, Singapore: The Markov Chain Monte Carlo algorithm, in particular the Metropolis-Hastings algorithm
University Singapore University of Social Science (SUSS)
Subject ST2195 Programming For Data Science Report
Posted on: 7th Feb 2024

ST2195 Programming For Data Science Report: The Markov Chain Monte Carlo algorithm, in particular the Metropolis-Hastings algorithm

Part 1 In this part, you are asked to work with the Markov Chain Monte Carlo algorithm, in particular the Metropolis-Hastings algorithm. The aim is to simulate random numbers for the distribution with the probability density function given below

ST2195 Coursework Project
where x takes values in the real line and |x| denotes the absolute value of x. More specifically, you are asked to generate x0, x1, . . . , xN values and store them using the following version of the Metropolis-Hastings algorithm (also known as random walk Metropolis) that consists of the steps below:

Stuck with a lot of homework assignments and feeling stressed ? Take professional academic assistance & Get 100% Plagiarism free papers

Random walk Metropolis
Step 1 Set up an initial value x0 as well as a positive integer N and a positive real number s.
Step 2 Repeat the following procedure for i = 1, . . . , N :
• Simulate a random number x∗ from the Normal distribution with mean xi−1 and standard deviation s.
• Compute the ratio
ST2195 Coursework Project
• Generate a random number u from the uniform distribution between 0 and 1.
• If u < r (x∗, xi−1), set xi = x∗, else set xi = xi−1.

(a) Apply the random walk Metropolis algorithm using N = 10000 and s = 1. Use the generated samples (x1, . . . xN ) to construct a histogram and a kernel density plot in the same figure. Note that these provide estimates of f (x). Overlay a graph of f (x) on this figure to visualize the quality of these estimates. Also, report the sample mean and standard deviation of the generated samples (Note: these are also known as the Monte Carlo estimates of the mean and standard deviation respectively).

Practical tip: To avoid numerical errors, it is better to use the equivalent criterion log u < log r (x∗, xi−1) = log f (x∗) − log f (xi−1) instead of u < r (x∗, xi−1).

Buy Custom Answer of This Assessment & Raise Your Grades

Get Help By Expert

Are you a Singapore University of Social Science (SUSS) student grappling with the ST2195 Coursework Project? Ease your academic journey with our expert Assignment Helper and specialized Case Study Writing Help. Pay for assistance and conquer the complexities of the Markov Chain Monte Carlo algorithm effortlessly.

Categories:-
Tags:-
Answer
No Need To Pay Extra
  • Turnitin Report

    $10.00
  • Proofreading and Editing

    $9.00
    Per Page
  • Consultation with Expert

    $35.00
    Per Hour
  • Live Session 1-on-1

    $40.00
    Per 30 min.
  • Quality Check

    $25.00
  • Total
    Free

New Special Offer

Get 30% Off

UP TO 15 % DISCOUNT

Get Your Assignment Completed At Lower Prices

Plagiarism Free Solutions
100% Original Work
24*7 Online Assistance
Native PhD Experts
Hire a Writer Now
My Assignment Help SG Services
My Assignment Help SG

Rated 4.9/5 Based on 22945 Singaporean Students