Adding week 05 lecture and lab

lab/lab_week_05.Rmd

@@ -0,0 +1,71 @@
+---
+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}
+
+```

lecture/lecture_week_04.R

@@ -1,67 +1,74 @@
 
 
-# Demonstrate grid approximation of the posterior for a globe tossing problem
-# with 6 water observations out of 9 globe tosses
+# Demonstrate grid approximation of the posterior for a 
+# globe tossing problem with 6 water observations out of 
+# 9 globe tosses
 
-#==============================================================================
+#==========================================================
 
 
 # 1) Define the grid to be used to compute the posterior
 
 # In this case, let's say we choose 20 grid points
-# Since the parameter of interest (proportion of water on the globe) is
-# bounded by 0 and 1, our grid should have those limits as well
+# Since the parameter of interest (proportion of water on 
+# the globe) is bounded by 0 and 1, our grid should have 
+# those limits as well
 p_grid <- seq(from = 0, to = 1, length.out = 20)
 
 p_grid
 
-#==============================================================================
+#==========================================================
 
 
-# 2) Compute/define the value of the prior at each parameter value on the grid
+# 2) Compute/define the value of the prior at each 
+# parameter value on the grid
 
 # In this case, simply choose a flat prior
 prior <- rep(1, 20)
 
 # You could visualize this prior
 plot(p_grid, prior, pch = 19, type = "b")
 
-#==============================================================================
+#==========================================================
 
 
-# 3) Compute the likelihood at each parameter value on the grid
+# 3) Compute the likelihood at each parameter value on 
+# the grid
 
-# This requires the use of a likelihood function applied to the observed data,
-# evaluated at each potential parameter value on the grid
+# This requires the use of a likelihood function applied 
+# to the observed data, evaluated at each potential 
+# parameter value on the grid
 likelihood <- dbinom(6, size = 9, prob = p_grid)
 
 # You could also visualize the likelihood
 plot(p_grid, likelihood, pch = 19, type = "b")
 
-#==============================================================================
+#==========================================================
 
 
-# 4) Compute the unstandardized posterior at each parameter value on the grid
+# 4) Compute the unstandardized posterior at each 
+# parameter value on the grid
 
-# The unstandardized posterior is simply the product of the likelihood and 
-# prior
+# The unstandardized posterior is simply the product of 
+# the likelihood and prior
 unstd.posterior <- likelihood * prior
 
 # Again, could visualize
 plot(p_grid, unstd.posterior, pch = 19, type = "b")
 
-# Note that this unstandardized posterior is not a proper probability 
-# distribution since it does not add to 1
+# Note that this unstandardized posterior is not a proper 
+# probability distribution since it does not add to 1
 sum(unstd.posterior)
 
-#==============================================================================
+#==========================================================
 
 
-# 4) Standardize the posterior
+# 5) Standardize the posterior
 
 posterior <- unstd.posterior/sum(unstd.posterior)
 
-# This standardized posterior is a now proper probability distribution
+# This standardized posterior is a now proper probability 
+# distribution
 sum(posterior)
 
 # Visualize the posterior