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Conjugate_priors_Bayes.R

+## Library: In particular, spBayes is used for the conjugate problem
+
+library(coda)
+library(magic)
+library(abind)
+library(Formula)
+library(Matrix)
+library(spBayes)
+library(extraDistr)
+
+## PlioMIP1 + 2 ensemble
+x <- c(3.2, 3.4, 4.05, 2.8, 4.1, 3.2, 3.3, 3.1,
+       3.37, 2.6,4.50, 2.29,5.3,4.3)
+
+y <- c(1.0256042, 1.3337059, 1.9900227, 1.1576538, 2.1806774, 1.151104, 1.9331722, 1.445343,
+       2.14, 0.9211941,2.1174774, 1.3736095,3.4950447,2.94250999999997)
+
+model_data <- data.frame(y,x)
+
+## p defines number of parameters (2: Intercept and Slope)
+n <- nrow(model_data)
+p <- 2
+n.samples <- 10000
+
+beta.prior.mean <- c(0,1)
+
+beta.prior.precision <- 1*diag(p)
+
+## Emulate the original Cauchy prior with some specific parameters of InvGamma
+prior.shape <- 0.5
+prior.rate <- 0.5
+
+bmod <- bayesLMConjugate(y ~ x, data=model_data, n.samples,beta.prior.mean, beta.prior.precision, prior.shape, prior.rate)
+beta <- as.vector(bmod$p.beta.tauSq.samples[,1])
+alpha <- as.vector(bmod$p.beta.tauSq.samples[,2])
+sigma <- as.vector(bmod$p.beta.tauSq.samples[,3])
+
+hist(beta)
+hist(alpha)
+hist(sigma)
+
+write.csv(beta, file="intercept_conj.csv")
+write.csv(alpha, file="slope_conj.csv")
+write.csv(sigma,file="sigma_conj.csv")
+
+## 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,100000)
+
+quantile(pri,probs=c(0.05,0.95))
+
+model_T = alpha*pri + beta + rnorm(n=100000,0,sd = sigma)
+
+## PlioMIP temp
+t = 0.8
+stdt = 1
+
+gaussobs <- rnorm(n=8000000,t,stdt)
+quantile(gaussobs,probs=c(0.05,0.95))
+
+weight <- dnorm(model_T,t,stdt)
+weight <- weight/sum(weight)
+
+posterior <- sample(size = 10000,x = pri,prob=weight)
+quantile(posterior,probs=c(0.05,0.95))
+median(posterior)
+hist(posterior)
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