We want to estimate a single unknown parameter in a certain model. Assume that in R we have defined a function log-post to calculate the log of the unnormalized posterior density as a function of 0. This function and the data y being analysed are not shown in the code extract below. The posterior density is p(0|y). Consider the following R code: nm = 10000 theta vector (length=nm) S = 0.4 theta = 2 log-post = log-post (thetao) for (i in 1: nm) { thetal theta + s*rnorm (1) log-post1= log-post (thetal) if(log (runi f(1)) < log-post1-log-post0){ theta0 thetal log-postolog.post1 } theta[i] theta } quantile (theta, probs-c (0.5, 0.025, 0.975)) An explanation in words is all that is needed for this question. (a) What is the name of the algorithm that the code is carrying out? (b) Explain what the command thetal = theta + s*rnorm (1) is doing in the context of the algorithm. (c) When the code has run, what will the vector the ta contain? (d) In statistical terms, what will the last line of code output? Suppose that the data y was a sample from an exponential distribution with parameter 0. The code below follows from the preceding code. v = rexp (length(theta), rate-theta) mean (v>5 & v<10) (e) When this code has run, what will v contain? (f) What will the last line of code output (in statistical terms)?
We want to estimate a single unknown parameter in a certain model. Assume that in R we have defined a function log-post to calculate the log of the unnormalized posterior density as a function of 0. This function and the data y being analysed are not shown in the code extract below. The posterior density is p(0|y). Consider the following R code: nm = 10000 theta vector (length=nm) S = 0.4 theta = 2 log-post = log-post (thetao) for (i in 1: nm) { thetal theta + s*rnorm (1) log-post1= log-post (thetal) if(log (runi f(1)) < log-post1-log-post0){ theta0 thetal log-postolog.post1 } theta[i] theta } quantile (theta, probs-c (0.5, 0.025, 0.975)) An explanation in words is all that is needed for this question. (a) What is the name of the algorithm that the code is carrying out? (b) Explain what the command thetal = theta + s*rnorm (1) is doing in the context of the algorithm. (c) When the code has run, what will the vector the ta contain? (d) In statistical terms, what will the last line of code output? Suppose that the data y was a sample from an exponential distribution with parameter 0. The code below follows from the preceding code. v = rexp (length(theta), rate-theta) mean (v>5 & v<10) (e) When this code has run, what will v contain? (f) What will the last line of code output (in statistical terms)?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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answer all parts please
![We want to estimate a single unknown parameter in a certain model. Assume that in R we
have defined a function log-post to calculate the log of the unnormalized posterior density as
a function of 0. This function and the data y being analysed are not shown in the code extract
below. The posterior density is p(0|y). Consider the following R code:
nm = 10000
theta vector (length=nm)
S = 0.4
theta = 2
log-post = log-post (thetao)
for (i in 1: nm) {
thetal theta + s*rnorm (1)
log-post1= log-post (thetal)
if(log (runi f(1)) < log-post1-log-post0){
theta0
thetal
log-postolog.post1
}
theta[i] theta
}
quantile (theta, probs-c (0.5, 0.025, 0.975))
An explanation in words is all that is needed for this question.
(a) What is the name of the algorithm that the code is carrying out?
(b) Explain what the command thetal = theta + s*rnorm (1) is doing in the context
of the algorithm.
(c) When the code has run, what will the vector the ta contain?
(d) In statistical terms, what will the last line of code output?
Suppose that the data y was a sample from an exponential distribution with parameter 0. The
code below follows from the preceding code.
v = rexp (length(theta), rate-theta)
mean (v>5 & v<10)
(e) When this code has run, what will v contain?
(f) What will the last line of code output (in statistical terms)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbed59e22-0eed-48e4-8876-1179a1046437%2Fa47704e7-cbb4-4cb6-85c9-aa93bf207526%2Fm0yurko_processed.png&w=3840&q=75)
Transcribed Image Text:We want to estimate a single unknown parameter in a certain model. Assume that in R we
have defined a function log-post to calculate the log of the unnormalized posterior density as
a function of 0. This function and the data y being analysed are not shown in the code extract
below. The posterior density is p(0|y). Consider the following R code:
nm = 10000
theta vector (length=nm)
S = 0.4
theta = 2
log-post = log-post (thetao)
for (i in 1: nm) {
thetal theta + s*rnorm (1)
log-post1= log-post (thetal)
if(log (runi f(1)) < log-post1-log-post0){
theta0
thetal
log-postolog.post1
}
theta[i] theta
}
quantile (theta, probs-c (0.5, 0.025, 0.975))
An explanation in words is all that is needed for this question.
(a) What is the name of the algorithm that the code is carrying out?
(b) Explain what the command thetal = theta + s*rnorm (1) is doing in the context
of the algorithm.
(c) When the code has run, what will the vector the ta contain?
(d) In statistical terms, what will the last line of code output?
Suppose that the data y was a sample from an exponential distribution with parameter 0. The
code below follows from the preceding code.
v = rexp (length(theta), rate-theta)
mean (v>5 & v<10)
(e) When this code has run, what will v contain?
(f) What will the last line of code output (in statistical terms)?
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