### sequential

#### how to speed up the M-H MCMC with a large number of parameters updated sequentially

I am confronted with a big problem of speeding up the programming. I have a model which have more than 700 parameters and I need to find their posterior distributions which maximize the log-likelihood function. The following is my code: M = 11 para = matrix(0, M, 771) wt = rnorm(767, 0, 0.25) para[1, ] = c(0.397, 0.013, 1.09, wt, 0.5) trial = rep(1, 771) acc = rep(0, 771) for(t in 1:(M-1)){ T = 10^(14) #the small value of T: T=10^6 para.cur = para[t, ] para.sim = para.cur current = dam.m4.opt(para.cur) for(i in 1:771){ if(i != 771){ para.sim[i] = rnorm(1, para.cur[i], 0.25) }else{ para.sim[i] = abs(rnorm(1, para.cur[i], 0.25)) } propose = dam.m4.opt(para.sim) trial[i] = trial[i] +1 a = (propose - current)/T if(log(runif(1))<a){ para.cur[i] = para.sim[i] current = propose acc[i] = acc[i] + 1 }else{ para.sim[i] = para.cur[i] current = current } } para[t+1, ] = para.cur } M is the number of step of the MCMC chain, dam.opt.m4 is the function to calculate the log-likelihood. There are 771 parameters and I need to update them sequentially. T is the tempering. I am wondering how I can use doParallel to speed up the performance? Because of the large number of parameters, even 11 steps can take 3 three days to run so I desperately to know how I can get faster. I really a appreciate that if anybody can help!

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