Use the Metropolis-Hastings algorithm to generate a MCMC sample from the univariate distribution with PDF function: p(x) 1 • exp(- (x - 10)2. -+2. exp(- (т — 25)2 , TE (-00, 00). 12.6 7 20 10

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Create a R code
Use the Metropolis-Hastings algorithm to generate a MCMC sample from the univariate distribution with PDF function:
10)2,
-) +2. exp(-
1
(x -
(x - 25)2
p(x)
• Jexp(-
7
,T E (-00, 00).
12.6
WE
20
10
20
30
40
50
Use g(a|u) ~ N(µ, o) with calibration parameter o > 0, as proposal distribution.
Verify your sample, via histograms, traceplots/meanplots and autocorrelation charts. Record your solution MCMC sample as
my_sample_MCMC.
Include a set.seed(xxxx) line, before coding the algorithm. Your answer should include a histogram of the solution MCMC sample, with the
target density superimposed. The parameter o should be calibrated, to insure good mixing, as well as acceptable autocorrelation. Include the
associated traceplots/meanplots and autocorrelation charts.
Transcribed Image Text:Use the Metropolis-Hastings algorithm to generate a MCMC sample from the univariate distribution with PDF function: 10)2, -) +2. exp(- 1 (x - (x - 25)2 p(x) • Jexp(- 7 ,T E (-00, 00). 12.6 WE 20 10 20 30 40 50 Use g(a|u) ~ N(µ, o) with calibration parameter o > 0, as proposal distribution. Verify your sample, via histograms, traceplots/meanplots and autocorrelation charts. Record your solution MCMC sample as my_sample_MCMC. Include a set.seed(xxxx) line, before coding the algorithm. Your answer should include a histogram of the solution MCMC sample, with the target density superimposed. The parameter o should be calibrated, to insure good mixing, as well as acceptable autocorrelation. Include the associated traceplots/meanplots and autocorrelation charts.
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