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