# Terminology review continued

## Outline

### Topics

- Review additional terminology covered since Quiz 1.
- Also make sure to review the terminology before quiz 1.

### Rationale

Just as for quiz 1, part of quiz 2 involves knowing these terms without having to look them up.

While in “the real world” you can look things up, to attain mastery of a subject you need a critical mass of concepts in memory. Too much google look-ups prevent thinking at the speed of thought.

## Common distributions (PMFs and densities)

As in quiz 1, knowing the **support** (no need to memorize other details) is needed, but note additional distributions have been introduced see the list.

## General MCMC terms

- Markov chain Monte Carlo (MCMC)
- Contrasting advantages and disadvantages of MCMC vs SNIS

## Stan terminology

- Differentiating between Stan and R code
- “data block”
- “parameters block”
- “model block”
- “transformed parameters block”
- “generated quantities block”

## Metropolis-Hastings

- MH
- Proposal (and contrasting it with SNIS’s proposal)
- Symmetric proposal
- Test function \(g\)
- Target \(\pi\)
- Un-normalized target \(\gamma\)
- Normalization constant \(Z\)
- Notion of acceptance and rejection
- What happens in each case
- MH ratio (memorize that equation)
- Acceptance probability

## MCMC plots

- Trace plot
- Posterior histogram
- Rank plot

## Basic MCMC theory

- Consistency of MCMC
- Irreducibility
- Mixing (informal definition is OK)

## Notion of unidentifiability

- Informal definition
- Writing an example model

## Goodness-of-fit

- Goodness-of-fit
- Posterior predictive check

## Monte Carlo Standard Error (MCSE)

- MCSE
- Effective sample size (ESS)
- Central Limit Theorem (CLT) for IID: writing the result and assumptions formally.
- Central Limit Theorem (CLT) for Markov chain: writing the result formally and stating at least informally the conditions.
- Asymptotic variance
- Batch mean estimator

## Implementing custom distributions

- Log scale computation.
- Underflow.

## Data collection mechanisms

- Censoring
- Truncation
- Non-ignorable missingness
- Rao-blackwellization