I will talk about the key algorithms used in ABC, some of the ideas surrounding simulator-based models, how to code them, and some of the most recent advancements in the field.
- Chapter 1 - Foundations of ABC
- What is ABC: Introduces the problem of estimating the parameter posterior with an intractable likelihood.
- ABC Densities: Sets the notation and nomenclature for the rest of the course. I explore the ABC likelihood, the ABC posterior, the augmented ABC posterior and the kernel.
- ABC Kernel and Summary Statistics: Building on the previous section, I motivate the usage of the Kernel and why it is a good idea. I also briefly mention summary statistics.
- Chapter 2 - Rejection and Importance Sampling ABC
- Soft ABC: This is the first ABC algorithm in this set of notes. It resembles imporance sampling and sets the foundation for rejection ABC.
- Rejection ABC: I frame Rejection ABC as a special case of Soft ABC with a uniform kernel.
- Generalizations: Generalize Soft-ABC to IS-ABC and Rejection-ABC to Rejection-Sampling-ABC.
- Chapter 3 - Sampling Schemes for ABC
- MCMC-ABC: Explores MCMC-ABC as a standard Metropolis-Hastings targeting the augmented ABC posterior and derives the pseudocode for it.