Update Conjugate_prior_and_RSTAN_MCMC.R

Conjugate_prior_and_RSTAN_MCMC.R → Conjugate_prior_approach.R

@@ -36,78 +36,3 @@ conj <- bayesLMConjugate(y~x,data,n.samples,beta.prior.mean,beta.prior.precision
 print(c(mean(conj$p.beta.tauSq.samples[,1]),sd((conj$p.beta.tauSq.samples[,1]))))
 print(c(mean(conj$p.beta.tauSq.samples[,2]),sd((conj$p.beta.tauSq.samples[,2]))))
 print(c(mean(sqrt(conj$p.beta.tauSq.samples[,3])),sd((sqrt(conj$p.beta.tauSq.samples[,3])))))
-
-## For clarity, MCMC approach in R. Require RSTAN
-## "0.7071068" corresponds to sqrt(0.5) (square root of the variance 0.5). Change it if prior 
-## precision matrix is changed. "b" in prior sigma is converted to rate rather than scale (1/scale)
-## to match the conjugate approach package.
-
-library(ggplot2)
-library(rstan)
-
-mymodel <- "
-data {
-int n;
-vector[n] y;
-vector[n] x;
-}
-parameters{
-real alpha;
-real beta;
-real<lower=0> sigma;
-}
-model {
-sigma ~ inv_gamma(0.5,1/0.5);
-beta ~ normal(0,sigma/0.7071068);
-alpha ~ normal(1,sigma/0.7071068);
-y ~ normal(beta + x * alpha, sigma);
-}
-"
-
-## Algorithm is NUTS as in PyMC3.
-results <- stan(model_code = mymodel, data=list(n=14,x=x,y=y),iter=10000,chain=4,algorithm="NUTS")
-
-beta_stan <- extract(results,pars="beta")
-alpha_stan <- extract(results,pars="alpha")
-sigma_stan <- extract(results,pars="sigma")
-
-beta <- beta_stan$beta
-alpha <- alpha_stan$alpha
-sigma <- sigma_stan$sigma
-
-## Check if same outputs than conjugate approach
-print(c(mean(beta),sd(beta)))
-print(c(mean(alpha),sd(alpha)))
-print(c(mean(sigma),sd(sigma)))
-
-## Below is the Bayesian inference to compute posterior S
-## Truncated Cauchy prior
-trunc <- function(loc, scale, a, b, sz) {
-  ua = atan((a - loc)/scale)/pi + 0.5
-  ub = atan((b - loc)/scale)/pi + 0.5
-  U <- runif(n = sz,ua,ub)
-  rvs <<- loc + scale * tan(pi*(U-0.5))}
-pri <- trunc(2.5,3,1/Inf,Inf,20000)
-
-quantile(pri,probs=c(0.05,0.95))
-
-model_T = alpha*pri + beta + rnorm(n=20000,0,sd = sigma)
-
-## PlioMIP temp
-t = 0.8
-stdt = 1
-
-#
-#t = -2.2
-#stdt = 0.4
-
-gaussobs <- rnorm(n=800000,t,stdt)
-quantile(gaussobs,probs=c(0.05,0.95))
-
-weight <- dnorm(model_T,t,stdt)
-weight <- weight/sum(weight)
-
-posterior <- sample(size = 1000000,x = pri,prob=weight,replace=TRUE)
-quantile(posterior,probs=c(0.05,0.95))
-median(posterior)
-hist(posterior)

[David Jones]

Key_Similarities_Between_a_Research_Essay_and_a_Research_Paper_2.pdf