Implementation of an MH Algorithm for Linear Regression in R - r

Question

I hope you are well and having a nice day. I am attempting to code an MH algorithm for a multiple linear regression model. I am following a tutorial online for simple linear regression using an MH algorithm and I plan on applying the principles myself to my multiple linear regression model, but I am running into a problem figuring our how to specify prior distributions for the parameters. Below, is the code.
trueA <- 5
trueB <- 0
trueSd <- 10
sampleSize <- 31
# create independent x-values
x <- (-(sampleSize-1)/2):((sampleSize-1)/2)
# create dependent values according to ax + b + N(0,sd)
y <- trueA * x + trueB + rnorm(n=sampleSize,mean=0,sd=trueSd)
likelihood <- function(param){
a = param[1]
b = param[2]
sd = param[3]
pred = a*x + b
singlelikelihoods = dnorm(y, mean = pred, sd = sd, log = T)
sumll = sum(singlelikelihoods)
return(sumll)
}
This is the portion where I am running into problems. In the tutorial, the author now specifies that they define prior distributions for the parameters. In this case, I would like to specify uninformative prior distributions for the slopes, coefficients, and standard deviation. The author says that they used uniform/normal distributions.
I found an example using Poisson regression, which looks like:
LogPriorFunction <- function(param){
beta0 <- param[1]
beta1 <- param[2]
beta0prior <- dnorm(beta0, 0, sqrt(100), log=TRUE)
beta1prior <- dnorm(beta1, 0, sqrt(100), log=TRUE)
return(beta0prior + beta1prior) # Logarithm of prior distributions
}
But I am having trouble adapting it to the simple linear regression. Here is my attempt:
prior <- function(param){
a = param[1]
b = param[2]
sd = param[3]
aprior = dnorm(a, 0, 1000, log=TRUE)
bprior = dnorm(b, 0, 1000, log=TRUE)
sdprior = 1/rgamma(sd, shape = .001, scale = .001)
return(aprior + bprior + sdprior) # Logarithm of prior distributions
}
The rest of the code is:
posterior <- function(param){
return (likelihood(param) + prior(param))
}
proposalfunction <- function(param){
return(rnorm(3,mean = param, sd= c(0.1,0.5,0.3)))
}
run_metropolis_MCMC <- function(startvalue, iterations){
chain = array(dim = c(iterations+1,3))
chain[1,] = startvalue
for (i in 1:iterations){
proposal = proposalfunction(chain[i,])
probab = exp(posterior(proposal) - posterior(chain[i,]))
if (runif(1) < probab){
chain[i+1,] = proposal
}else{
chain[i+1,] = chain[i,]
}
}
return(chain)
}
startvalue = c(4,0,10)
chain = run_metropolis_MCMC(startvalue, 10000)
burnIn = 5000
acceptance = 1-mean(duplicated(chain[-(1:burnIn),]))
Finally, along with specifying the priors, I keep getting the warning message:
Error in if (runif(1) < probab) { : missing value where TRUE/FALSE needed
In addition: Warning message:
In if (runif(1) < probab) { :
the condition has length > 1 and only the first element will be used
I am not sure if this is related to my incorrectly specifying the prior distributions, as the author of the article gets similar results from the MH algorithm as running a simple linear regression model using the lm() function. Any help would with these issues would be greatly appreciated. I look forward to hearing from you. Thank you.
As a reference, here is the link to the article:
https://khayatrayen.github.io/MCMC.html#defining_the_prior
Finally, here is a link to the article from where I tried to emulate the priors, but does Poisson regression and not linear regression:
https://rpubs.com/SaraGarcesCespedes/586440