代做MAST90125、代写R编程设计、代做Statistical Learning、R代写代写

日期：2019-09-13 11:15

Assignment 2, Question 1 MAST90125: Bayesian

Statistical Learning

Due: Friday 20 September 2019

There are places in this assignment where R code will be required. Therefore set the random

seed so assignment is reproducible.

set.seed(123456) #Please change random seed to your student id number.

Question One (12 marks)

In generalised linear models, rather than estimating effects from the response data directly, we model through

a link function, η(θ), and assume η(θ)i = x0

iβ. The link function can be determined by re-arranging the

likelihood of interest into the exponential family format,

p(y|θ) = f(y)g(θ)e

a) Re-arrange the Poisson probability mass function into the exponential family format to determine the

canonical link function. The Poisson pmf is

P r(y|λ) = λ

To explore some properties of Metropolis sampling, consider the dataset Warpbreaks.csv, which is on LMS.

This dataset contains information of the number of breaks in a consignment of wool. In addition, Wool type

(A or B) and tension level (L, M or H) was recorded.

b) Fit a Poisson regression to the warpbreak data, with Wool type and tension treated as factors using the

function glm in R. Report co-efficient estimates and the variance-covariance matrix.

c) Fit a Bayesian Poisson regression using Metropolis sampling. Assume flat priors for all coefficients.

Extract the design matrix X from the glm fitted in a). For the proposal distribution, use a Normal

distribution with mean θ

(t−1) and variance-covariance matrix c

2Σˆ where Σ is the variance-covariance

matrix from the glm fit. Consider three candidates for c, 1.6/

of parameters estimated. Run the Metropolis algorithm for 10,000 iterations, and discard the first 5,000.

Report the following:

• Check, using graphs and appropriate statistics, that each chain converges to the same distribution. To

do this, you may find installing the R package coda helpful.

• The proportion of candidate draws that were accepted.

• The effective sample size for each chain.

• What do you think is the best choice for c. Does this match the results stated in class on efficiency and

optimal acceptance rate?

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