Slides for `Elements of Statistical Computation’

Author

Longhai Li

Published

September 25, 2026

Table of Content

Venn diagram of data science disciplines: statistics, computer science and domain expertise1. Introduction IEEE 754 single-precision floating-point layout2. Computer Arithmetic Monte Carlo estimation of pi3. Monte Carlo
Gradient ascent on a likelihood surface4. Maximum Likelihood EM clustering of Old Faithful data5. EM Algorithm Bayes' theorem6. Bayesian Inference
Simpson's rule illustration7. Numerical Quadrature Laplace Approximations8. Laplace Approximation Rejection sampling of a bounded distribution9. Rejection Sampling
Draws from a proposal density reweighted by p/q: dot size grows with importance weight10. Importance Sampling Trace plot of three MCMC chains converging to the same distribution11. Markov Chain Monte Carlo

Image credits: (1) Data science disciplines Venn diagram, Colohisto, CC BY 4.0; (2) Float example, Stannered, CC BY-SA 3.0; (3) Pi 30K, nicoguaro, CC BY 3.0; (4) Gradient descent maximum likelihood, Justinkunimune, CC0; (5) EM Clustering of Old Faithful data, Chire, CC BY-SA 3.0; (6) Bayes’ Theorem MMB 01, mattbuck, CC BY-SA 3.0; (7) Simpson’s method illustration, Popletibus, CC BY-SA 4.0; (8) Pierre-Simon Laplace, Paulin Jean-Baptiste Guérin, public domain; (9) Rejection sampling of a bounded distribution with finite support, Armavica, CC BY-SA 4.0; (10) importance-weights figure generated in R for this page; (11) trace plot generated in R for this page. Images (1)–(9) are from Wikimedia Commons.