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Bayesian_mPWP_with_RSTAN.R

+## 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.
+## Priors on the parameters can be freely changed just as when using PyMC3. Please refer to
+## RSTAN for a list of possible prior distributions.
+
+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)
\ No newline at end of file

[David Jones]

Five_Steps_to_Writing_a_Top_Notch_Research_1.pdf