The Beta distribution is a Probability distribution that has support over the interval $[0, 1]$. It's most commonly used to express degree of belief in the value of a probability term.

What exactly is a Dirichlet process?

We start from the Dirichlet Distribution, which provides a vector of probabilities over states. The vector of probabilities must sum to 1, and they give Categorical Distribution probabilities, i.e. the probability of getting a draw from that category.

In contrast to the Dirichlet distribution, which has a fixed number of categories, the Dirichlet process describes a generative process for an infinite number of categories. There are a few algorithmic variants of the Dirichlet process, including the Chinese Restaurant Process, the Indian Buffet Process, and the Stick Breaking Process.

In practice, when computing with Dirichlet processes, we tend to use the Stick Breaking Process with a large but finite number of states.

Some learnings while training myself in statistics.

Distributions:

• Probability distribution
• Dirichlet Process
• Dirichlet Distribution
• Hidden Markov Model
• Estimating a multivariate Gaussian's parameters by gradient descent
• Gaussians come from processes that are additive

Statistical Estimation:

• Fermi estimation and Bayesian priors
• When is your statistical model right vs. good enough
• Maximum score estimator is used to maximize classification true positives and negatives

Papers that I'm writing:

• Hierarchical Bayesian models for high throughput biological measurement

Dealing with data:

• Multiple imputation is better than imputing single values

Probabilistic Programming:

• Anatomy of a probabilistic programming framework
• PROBPROG2020 conference