Exercise 5.12 (Control brains)

# Load packages
library(bayesrules)
library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.4     ✔ readr     2.1.5
## ✔ forcats   1.0.0     ✔ stringr   1.5.1
## ✔ ggplot2   3.5.1     ✔ tibble    3.2.1
## ✔ lubridate 1.9.3     ✔ tidyr     1.3.1
## ✔ purrr     1.0.2     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

#a)sujetos de control a los que no se les ha diagnosticado una conmoción cerebral
#Load the data
data(football)
no_concussion_subjects <- football %>%
  filter(group == "fb_no_concuss")
#tamaño de la muestra 
n<-nrow(no_concussion_subjects)
n

## [1] 25

#volumen medio del hipocampo de la muestra
y_bar<-no_concussion_subjects %>%
  summarize(mean(volume))
y_bar

##   mean(volume)
## 1       6.4592

#ggplot
ggplot(no_concussion_subjects, aes(x = volume)) + 
  geom_density()

#b)summarize_normal_normal()
summarize_normal_normal(mean = 6.5, sd = 0.4, sigma = 0.5,y_bar =  6.4592, n = 25)

##       model   mean   mode         var         sd
## 1     prior 6.5000 6.5000 0.160000000 0.40000000
## 2 posterior 6.4616 6.4616 0.009411765 0.09701425

#c)Plot the prior pdf, likelihood function, and posterior pdf of μ
#Plot the prior 
plot_normal(mean = 6.5, sd = 0.4)

#plot likelihood
plot_normal_likelihood(y = no_concussion_subjects$volume, sigma = 0.5)

#plot_normal_normal (prior pdf, likelihood function, and posterior)
plot_normal_normal(mean = 6.5, sd = 0.4, sigma = 0.5,y_bar = 6.4592, n = 25)