Statistical Thinkking 2023_v1.Rmd

---
title: "Statistical Thinking 2023"
author: "LAC"
date: "2023-01-11"
output:
  pdf_document: default
  html_document:
    df_print: paged
  rmarkdown::pdf_document:
    fig_caption: yes
    number_sections: yes
header-includes:
- \usepackage[margin=1in]{geometry} 
- \usepackage{amsmath,amsthm,amssymb,amsfonts}
- \usepackage{relsize}
- \usepackage{lscape}
- \usepackage{enumerate}
- \usepackage{enumitem}
- \usepackage{setspace}
- \usepackage{tikz}
- \usepackage{bm}
- \usepackage{bbm}
- \usepackage[utf8]{inputenc}
- \usepackage{mathtools, nccmath}
- \usepackage{fancyhdr}
- \usepackage{float}
- \usepackage{longtable}
- \usepackage{threeparttable}
- \usepackage[linesnumbered,vlined,ruled,commentsnumbered]{algorithm2e}
- \floatplacement{figure}{H}
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- \setlength{\parskip}{1em}
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- \rhead{Statistical Thinking 2023}
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urlcolor: blue
---

```{r setup, include=FALSE, cache = FALSE}
require("knitr")

## setting working directory
opts_chunk$set(echo = FALSE, warning=FALSE, message = FALSE)

library(ggplot2)
library(tidyverse)
library(dplyr)
library(kableExtra)

# The palette with black - Used in Graphs with :
cbp1 <- c("#999999", "#E69F00", "#56B4E9", "#009E73",
          "#F0E442", "#0072B2", "#D55E00", "#CC79A7")
cbp2 <- c("#000000", "#E69F00", "#56B4E9", "#009E73",
          "#F0E442", "#0072B2", "#D55E00", "#CC79A7")
cbp3 <- c("#FFDB6D", "#C4961A", "#F4EDCA", "#D16103", 
          "#C3D7A4", "#52854C", "#4E84C4", "#293352")
```

\section{Lecture 1}

\pagebreak

\section{Lecture 2}

A new model has born

\begin{align*}
  W\sim Binomial(N, p) \label{eq:1a} \test{ with }p\sum U(0,1)
\end{align*}

\subsection{Simulation of a Bayesian Experiment}

```{r}
# definegrid
p_grid <-seq(from=0,to=1,length.out=20)

# defineprior
#prior <-rep(1,20)
prior <-ifelse(p_grid<0.5,0,1)

# computelikelihoodateachvalueingrid
likelihood <-dbinom(6,size=9,prob=p_grid)

# computeproductoflikelihoodandprior
unstd.posterior <-likelihood*prior

# standardizetheposterior,soitsumsto1
posterior <-unstd.posterior/sum(unstd.posterior)
```


```{r, cache=FALSE}
plot( p_grid,posterior,type="b",
xlab="probability ofwater",ylab="posteriorprobability")
mtext( "20points")
```