# Computational_statistics

Course materials for Computational Statistics, PhD course at EMAp.
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Course materials for Computational Statistics, PhD course at EMAp.
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# Computational Statistics ("Estatística Computacional")

Course materials for Computational Statistics, a PhD-level course at EMAp.

## Lecture notes and other resources

• We will be using the excellent materials from Professor Patrick Rebeschini (Oxford University) as a general guide for our course.

As complementary material,

Other materials, including lecture notes and slides may be posted here as the course progresses.

Here you can find a nascent annotated bibliography with landmark papers in the field. This review paper by Professor Hedibert Lopes is far better than anything I could conjure, however.

## Books

Books marked with [a] are advanced material.

Main

Supplementary

## Simulation

### Markov chains

• These notes from David Levin and Yuval Peres are excellent and cover a lot of material one might find interesting on Markov processes.

### Markov chain Monte Carlo

#### Hamiltonian Monte Carlo

The two definitive texts on HMC are Neal (2011) and Betancourt (2017). A nice set of notes is Vishnoi (2021). Moreover, Hoffman & Gelman (2014) describes the No-U-turn sampler.

#### Normalising Constants

This post by Radford Neal explains why the Harmonic Mean Estimator (HME) is a terrible estimator of the evidence.

#### Sequential Monte Carlo and Dynamic models

• This book by Nicolas Chopin and Omiros Papaspiliopoulos is a great introduction (as it says in the title) about SMC. SMC finds application in many areas, but dynamic (linear) models deserve a special mention. The seminal 1997 book by West and Harrison remains the de facto text on the subject.

## Optmisation

#### Simulated Annealing

• The original 1983 paper in Science open link by Kirpatrick et al is a great read.
• These visualisations of the traveling salesman problem might prove useful.

## Miscellanea

• In these notes, Terence Tao gives insights into concentration of measure, which is the reason why integrating with respect to a probability measure in high-dimensional spaces is hard.

• A Primer for the Monte Carlo Method, by the great Ilya Sobol, is one of the first texts on the Monte Carlo method.

• The Harris inequality, `E[fg] >= E[f]E[g]`, for `f` and `g` increasing, is a special case of the FKG inequality.

• In Markov Chain Monte Carlo Maximum Likelihood, Charlie Geyer shows how one can use MCMC to do maximum likelihood estimation when the likelihood cannot be written in closed-form. This paper is an example of MCMC methods being used outside of Bayesian statistics.

• This paper discusses the solution of Problem A in assigment 0 (2021).

#### Reparametrisation

Sometimes a clever way to make a target distribution easier to compute expectations with respect to is to reparametrise it. Here are some resources:

See #4. Contributed by @lucasmoschen.

#### Variance reduction

• Rao-Blackwellisation is a popular technique for obtaining estimators with lower variance. I recommend the recent International Statistical Review article by Christian Robert and Gareth Roberts on the topic.

### Extra (fun) resources

In these blogs and websites you will often find interesting discussions on computational, numerical and statistical aspects of applied Statistics and Mathematics.

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