lab_week_05.Rmd

---
title: "EEEB UN3005/GR5005  \nLab - Week 05 - 24 and 26 February 2020"
author: "USE YOUR NAME HERE"
output: pdf_document
fontsize: 12pt
---

```{r setup, include = FALSE}

knitr::opts_chunk$set(echo = TRUE)

library(rethinking)
```


# Statistical Distributions and Summary Statistics


## Exercise 1: Grid Approximation, Our Old Friend

Imagine that the globe tossing example from the *Statistical Rethinking* text and class resulted in 8 water observations out of 15 globe tosses.

With this set of data, use grid approximation (with 101 grid points) to construct the posterior for *p* (the probability of water). Assume a flat prior.

Plot the posterior distribution.

```{r}

```


## Exercise 2: Sampling From a Grid-Approximate Posterior

Now generate 10,000 samples from the posterior distribution of *p*. Call these samples `post.samples`. Visualize `post.samples` using the `dens()` function. 

For your own understanding, re-run your sampling and plotting code multiple times to observe the effects of sampling variation.

```{r}

```


## Exercise 3: Summarizing Samples

Return the mean, median, and mode (using `chainmode()`) of `post.samples`. Then calculate the 80%, 90%, and 99% highest posterior density intervals of `post.samples`.

```{r}

```


## Exercise 4: Model Predictions

Using `post.samples`, generate 10,000 simulated model predictions (you can call these `preds`) for a binomial trial of size 15. Visualize the model predictions using the `simplehist()` function. 

Based on these posterior predictions, what is the probability of observing 8 waters in 15 globe tosses?

```{r}

```


## Exercise 5: More Model Predictions

Using the *same* posterior samples (i.e., `post.samples`), generate 10,000 posterior predictions for a binomial trial of size 9.

Using these new predictions, calculate the posterior probability of observing 8 waters in 9 tosses.

```{r}

```