Probabilistic Programming and Data Structures

2.

Probabilistic Programming Foundations

2.1.

Introduction to Probabilistic Modeling

2.1.1.

Uncertainty Representation

2.1.1.1.

Sources of Uncertainty

2.1.1.2.

Aleatory vs Epistemic Uncertainty

2.1.1.3.

Probability Distributions as Models

2.1.2.

Generative Models

2.1.2.1.

Definition and Characteristics

2.1.2.2.

Generative vs Discriminative Models

2.1.2.3.

Forward Sampling

2.1.3.

Probabilistic Variables

2.1.3.1.

Random Variables in Computational Models

2.1.3.2.

Parameterization of Distributions

2.1.3.3.

Hierarchical Structure

2.1.4.

Graphical Models

2.1.4.1.

Directed Acyclic Graphs

2.1.4.2.

Bayesian Networks

2.1.4.2.1.

Nodes and Edges

2.1.4.2.2.

Conditional Independence

2.1.4.2.3.

2.1.4.3.

Markov Random Fields

2.1.4.4.

2.1.4.4.1.

Repeated Structure Representation

2.1.4.4.2.

Index Variables

2.2.

Probabilistic Programming Language Components

2.2.1.

Random Primitives

2.2.1.1.

Built-in Distribution Library

2.2.1.2.

Parameterized Distributions

2.2.1.3.

Custom Distribution Definition

2.2.2.

Conditioning Mechanisms

2.2.2.1.

Observed Variables

2.2.2.2.

Conditioning on Data

2.2.2.3.

Soft vs Hard Constraints

2.2.3.

Control Flow in Probabilistic Programs

2.2.3.1.

Stochastic Branching

2.2.3.2.

Loops with Random Variables

2.2.3.3.

Recursive Probabilistic Functions

2.2.4.

Inference Interface

2.2.4.1.

Query Specification

2.2.4.2.

Posterior Computation

2.2.4.3.

Predictive Sampling

2.3.

Bayesian Inference in Probabilistic Programming

2.3.1.

Prior Specification

2.3.1.1.

Informative Priors

2.3.1.2.

Non-informative Priors

2.3.1.3.

Conjugate Priors

2.3.1.4.

Hierarchical Priors

2.3.2.

Likelihood Definition

2.3.2.1.

Data Generating Process

2.3.2.2.

Likelihood Functions

2.3.2.3.

Composite Likelihoods

2.3.3.

Posterior Computation

2.3.3.1.

Bayes' Rule Application

2.3.3.2.

Normalizing Constants

2.3.3.3.

Posterior Predictive Distribution

2.3.4.

2.3.4.1.

Marginal Likelihood

2.3.4.2.

Model Comparison

2.3.4.3.

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1. Foundational Concepts in Probability and Statistics

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3. Inference Algorithms for Probabilistic Programming