Meten is weten

library(dplyr)
library(ggplot2)
library(sjPlot)
library(sjmisc)

p_grid                   <- seq(from=0 , to=1   , length.out=100)
prior                    <- dbinom(60, size=100 , prob=p_grid)
likelihood               <- dbinom(50, size=100 , prob=p_grid)
unstd.posterior          <- likelihood * prior
posterior                <- unstd.posterior / sum(unstd.posterior)
bayesdata                <- as.data.frame(cbind(p_grid, prior, likelihood, unstd.posterior, posterior))
ggplot(bayesdata, aes(x=p_grid))+
  geom_area(aes(y=prior, fill="Prior"),alpha=0.5)+
  geom_area(aes(y=likelihood, fill="Likelihood"),alpha=0.5)+
  geom_area(aes(y=unstd.posterior, fill="Unstandardized Posterior"),alpha=0.5)+
  geom_area(aes(y=posterior,fill="Posterior"),alpha=0.5)+
  scale_fill_manual(values=c("seagreen","red","orange","brown"))+
  ggtitle("Posterior Probability given Prior and Likelihood")+
  xlab("Probability") + ylab("Posterior Probability")+
  guides(fill=guide_legend(title="Bayesian Analysis"))+
  theme_bw()

nth(prior, 50)
nth(likelihood, 50)
nth(posterior, 50)

prior_est<-bayesdata %>%
  slice(which.max(prior))%>%dplyr::select(p_grid)
like_est<-bayesdata %>%
  slice(which.max(likelihood))%>%dplyr::select(p_grid)
post_est<-bayesdata %>%
  slice(which.max(posterior))%>%dplyr::select(p_grid)
ggplot(bayesdata, aes(x=p_grid))+
  geom_area(aes(y=prior, fill="Prior"),alpha=0.5)+
  geom_vline(xintercept = prior_est[[1]], color="orange", lty=2) +
  geom_area(aes(y=likelihood, fill="Likelihood"),alpha=0.5)+
  geom_vline(xintercept = like_est[[1]], color="seagreen", lty=2) +
  geom_area(aes(y=unstd.posterior, fill="Unstandardized Posterior"),alpha=0.5)+
  geom_area(aes(y=posterior,fill="Posterior"),alpha=0.5)+
  geom_vline(xintercept = post_est[[1]], color="red", lty=2) +
  scale_fill_manual(values=c("seagreen","red","orange","brown"))+
  ggtitle("Posterior Probability given Prior and Likelihood")+
  xlab("Probability") + ylab("Posterior Probability")+
  guides(fill=guide_legend(title="Bayesian Analysis"))+
  xlim(0.4,0.7)+
  theme_bw()


set.seed(11454)
plot(density(rbinom(100,1,0.5454545)))
hist(rbinom(100,1,0.5454545))

hist(rbinom(100,100,0.5454545),breaks=10)
hist(rbinom(1000,100,0.5454545),breaks=30)
hist(rbinom(100,1000,0.5454545),breaks=10)

p_grid                   <- seq(from=0 , to=1   , length.out=1000)
prior                    <- dbinom(600, size=1000 , prob=p_grid)
likelihood               <- dbinom(500, size=1000 , prob=p_grid)
unstd.posterior          <- likelihood * prior
posterior                <- unstd.posterior / sum(unstd.posterior)
bayesdata                <- as.data.frame(cbind(p_grid, prior, likelihood, unstd.posterior, posterior))

prior_est<-bayesdata %>%
  slice(which.max(prior))%>%dplyr::select(p_grid)
like_est<-bayesdata %>%
  slice(which.max(likelihood))%>%dplyr::select(p_grid)
post_est<-bayesdata %>%
  slice(which.max(posterior))%>%dplyr::select(p_grid)

ggplot(bayesdata, aes(x=p_grid))+
  geom_area(aes(y=prior, fill="Prior"),alpha=0.5)+
  geom_vline(xintercept = prior_est[[1]], color="orange", lty=2) +
  geom_area(aes(y=likelihood, fill="Likelihood"),alpha=0.5)+
  geom_vline(xintercept = like_est[[1]], color="seagreen", lty=2) +
  geom_area(aes(y=unstd.posterior, fill="Unstandardized Posterior"),alpha=0.5)+
  geom_area(aes(y=posterior,fill="Posterior"),alpha=0.5)+
  geom_vline(xintercept = post_est[[1]], color="red", lty=2) +
  scale_fill_manual(values=c("seagreen","red","orange","brown"))+
  ggtitle("Posterior Probability given Prior and Likelihood")+
  xlab("Probability") + ylab("Posterior Probability")+
  guides(fill=guide_legend(title="Bayesian Analysis"))+
  xlim(0.4,0.7)+
  theme_bw()