notes.Rmd

---
title: "Stat 33B - Lecture 10"
date: April 1, 2020
output: pdf_document
---

Review: Homework 4
==================

Suppose we want to sample from the distribution on -1 to 1 shown in the plot
produced by this code:
```{r, dslide}
dslide = function(x) {
  ifelse(x > 1, 0,
    ifelse(x > 0, dnorm(x) / dnorm(0), dunif(x, -1, 0))
  )
}

curve(dslide, -2, 2, xlab = "Value", ylab = "Density (unscaled)")
curve(dunif(x, -1, 1), add = TRUE)
```

The exact steps in rejection sampling are:

1. Sample an x coordinate.
2. Sample a y coordinate.
3. Test whether the y value falls below the target distribution's density
   curve. If it does, then x is a new sample value. If it does not, then x is
   rejected.
4. Repeat steps 1-3 until reaching the desired number of sample values.


```{r}
rslide = function(n = 100) {
  accepted = 0
  iterations = 0
  results = numeric(n)
  while (accepted < n) {
    iterations = iterations + 1
    x = runif(1, -1, 1)
    y = runif(1, 0, 1.2)
    if (y < dslide(x)) {
      # Accepted
      accepted = accepted + 1
      results[accepted] = x
    }
  }
  
  list(results, acceptance = accepted / iterations)
}

set.seed(53)
samp = rslide(200000)
samp

plot(density(samp))


repeat {
  x = runif(1, -1, 1)
  y = runif(1, 0, 1.2)
  if (y < dslide(x)) {
    # Accepted
    accepted = accepted + 1
    results[accepted] = x
    if (accepeted == n)
      break
  }
}
```

Review: STAT 33B So Far
=======================

Topics:

* Vectors, data frames, and lists
* Types and classes
* Taking subsets with `[`, `[[`, `$`, and `subset()`
* ggplot2
* Tidy data and tidyr
* Relational data and `merge()`
* If-statements and loops
* Writing functions
* Scoping and environments

See the video lectures for a review of the last two.

Types and Classes
-----------------

Types describe how an object is stored in memory.

Classes describe how an object behaves. Objects may have more than one.

Common types and classes:
```{r}
typeof(4)

typeof("hi")

typeof(3+4i)

typeof(sin)

typeof(iris)

class(iris)

class(5)
class(TRUE)
typeof(TRUE)
```


Taking Subsets
--------------

Use `[` to get one or more elements. Keeps the container.


Use `[[` to get exactly one element. Drops the container.


Use `$` to get columns or list elements by name. Drops the container.


Examples:
```{r}
x = c(5, 3, 1.2)
x

x[c(1, 1, 2)]

x[[1]]

x[1]

mylist = list(a = 1:3, b = letters)
class(mylist[1])

class(mylist[[1]])

mylist["a"]

mylist[c(TRUE, FALSE)]
```


ggplot2
-------

Build up the plot in layers. Create layers with functions, add layers with `+`.

Fundamental layers are:

1. Data with `ggplot()`.
2. Geometry with `geom_` functions.
3. Aesthetics with `aes()`. Goes inside data or geometry layer.

Other layers described in the docs allow further customization.

Examples:
```{r}
library(ggplot2)

ggplot(iris, aes(x = Sepal.Length, y = Sepal.Width, color = Species)) + geom_point()
```


Tidy Data
---------

Tidy data are tabular data that satisfy 3 properties:

1. Each row is corresponds to one observation.
2. Each column corresponds to one covariate.
3. Each cell contains only one value.

Most common problems with data:

* Observations split across multiple rows. Fix with `pivot_wider()`.

* Multiple observations combined into a single row. Fix with `pivot_longer()`.


Relational Data
---------------

Relational data are data split across multiple related tables. Tables are
linked by "key" columns.

Often we need to "join" tables by matching rows using the key columns. The
`merge()` function joins tables.


Several kinds of joins:

* Inner join (default) keeps only matching rows.

* Left join (`all.x = TRUE`) keeps all rows in left table, matching rows in
  right table.

* Right join (`all.y = TRUE`) keeps all rows in right table, matching rows in
  left table.

* Full join (`all = TRUE`) keeps all rows in both tables.

Example:
```{r}
titles = readRDS("data/imdb/titles10s.rds")
cast = readRDS("data/imdb/cast10s.rds")
people = readRDS("data/imdb/people10s.rds")

lb = titles[titles$primaryTitle == "Lady Bird", ]
lb_cast = merge(lb, cast, all.x = TRUE)
merge(lb_cast, people, all.x = TRUE)
```


If-statements and Loops
-----------------------

Two kinds of if-statements:

* `if` is the thing to use in most cases
* `ifelse()` is vectorized

Examples:
```{r}
x = 10

if (x < 20) {
  message("Hello")
} else {
  message("Bye")
}

x = c(1, 2, 3, 4)
ifelse(x < 3, c(-1, -2, -3, -4), 10)

# Alternative:
x[x < 3] = c(-1, -2, -3, -4)[x < 3]
x[x >= 3] = 10
```

Four kinds of loops:

* Vectorization

* Apply functions
    + Use apply functions if you know the number of iterations and each
      iteration is independent

* `for`, `while`, `repeat`
    + Use `for` if you know the number of **iterations**
    * Use `while` or `repeat` if you don't know the number of iterations

* Recursion

Examples:
```{r}

```


R Gotchas
=========

Many of R's gotchas are listed in The R Inferno:

  <https://www.burns-stat.com/pages/Tutor/R_inferno.pdf>