- Conceptual Framework of BDA
- MCMC
- Stan Example
- Stan at AdRoll
~~Contrast with Null Hypothesis Significance Testing~~-
~~Socks!~~

Tiny Data

guess about what the generative process is for the observed data

parameter values control shape of the distributions in the descriptive model

Steps in BDA

- Exploratory data analysis
- Define descriptive model
- Specify priors
- Create model & analyze results
- Posterior predictive check

Why can't we use ~~puppies~~ Bayes' Rule for everything?

Can't be solved analytically for complex models

...so instead we will approximate the posterior with Markov Chain Monte Carlo (MCMC) methods

Markov Chain Monte Carlo (MCMC)

Metropolis

Gibbs

Hamiltonian Monte Carlo

Review

Possibilities as parameter values

DSL for full bayesian inference written in C++

Interfaces for R, Python, Julia, Matlab & command line (plus MCMC analysis and visual summaries with shinyStan)

Stan Code Blocks

Linear Regression Code Example

LDA Code Example

Extended Example: Fairness of a coin

Steps in BDA 1

- Exploratory data analysis

Steps in BDA 2

- Define descriptive model

Steps in BDA 3

- Specify Prior

Steps in BDA 4 + 5

- Create model & analyze results & posterior predictive check

CPA estimator: bayesian ordered logit

Heatshield: bayesian test of proportions