Computational Statistics, STP 540, Spring 2025
Basic Course Information
Class time and place
Tu Th 12:00 PM - 1:15 PM 1/9/23 - 4/28/23 Tempe WXLR A304
Instructor: Robert McCulloch, robert.mcculloch@asu.edu
TA:
How-to-use-Canvas-Discussions.pdf
Syllabus: Syllabus
Some usefull books: books
Where we are and what I should be doing?
where and what
R and Python
Information on R
Information on Python
Suggested Projects
Inference for the parameters of a Gaussian Process
See Murphy chapter 15.1 to 15.2.5. Murphy.
See also Rasmussen-and-Williams.pdf.
See also chapter 5 of the book "Surrogates" by Robert Gramacy.
Learning a single layer neural network
see section 10.7 Fitting a Neural Network in "An Introduction to Statistical Learning", second edition
by James, Witten, Hastie, and Tibshirani.
Simple Chain Rule Gradient Computation for a Single Layer
Single Layer Neural networks, complete notes from Applied Machine Learning
EM algorithm for a mixture of normals
Some old projects:
Comparing the EM algorithm with the Gibbs sample for uninvariate normal mixtures
Gaussian Processes
Comparing the EM algorithm with Gibbs for univariate mixtures
Monte Carlo EM algorithm
Homework
How_to_Submit_Homework_in_Canvas.pdf
Homework 1
Due February 6.
Homework 2
Due February ??.
Kevin Murphy book on Machine Learning
Solutions
Homework 3
Homework 3, solutions
logit-funs.R
Notes
A first look at simple logistic regression
Let's review a basic nonlinear model in statistics: simple logistic regression.
We will write simple code to compute the likelihood.
We will look the idea of vectorization which applies in both R and python.
Later we will go into more details on how the likelihood is optimized.
Simple vectorized summing in python
Simple Logistic Regression Likelihood
Simple example of logit in R, Rmd
Simple example of logit in Python, notebook
Script to compute the log-likehood:
R code: Logit Example in R
Python code: Logit Example in Python
Plot logit likelihood using color palettes (e.g. viridis) in R
Advanced R, Wickham, Section 24.5.
".. vectorization means finding the existing R function that is implemented in C
and most closely applied to your problem."
Simple note on vectoriziation in python: vectorization in python
Of course, if you code directly in a lower level language like C++ you get the speed:
Calling C++ out of R using, Rcpp, a Makefile, and SHLIB
Calling C++ out of R using Rcpp using rstudio
Matrix Decompositions in Statistics
Quick Review of Some Keys Ideas in Linear Algebra
Simple python script to compare sklearn.Linear regression with (X'X)^{-1} X'y
Simple R script to compare lm with (X'X)^{-1} X'y
What Really IS a Matrix Determinant?
QR Matrix Factorization
Least Squares and Computation (with R and C++)
The Multivariate Normal and the Choleski and Eigen Decompositions
Look at cholesky and spectral in R
Singular Value Decomposition
simple example of svd in python
do_image-svd-approx.py
image approximation with SVD in R, thanks to Andrew Ritchey.
Optimization
Optimization
See chapters 4 and 8 of "Deep Learning" by Goodfellow, Bengio, and Courville.
Simple notes on single layer neural net: Single Layer
Section 3 recording, logit derivatives: recording
Section 4 recording, Taylor's Theorem: recording
Sections 8 and 9 recording, Momentum and Newton's method: recording
Mixture Models and the EM Algorithm
The EM Algorithm
See Chapter 11 of Murphy.
See Chapter 4 of Givens and Hoeting.
See Chapter 8.5 of Hastie, Tibshirani, and Friedman.
Introduction to Bayesian Statistics
Introduction to Bayesian Statistics and the Beta/Bernoulli Inference
Normal Mean Given Standard Deviation
Normal Standard Deviation Given Mean
Multinomial outcomes with the Dirichlet conjugate prior
Introduction to Bayesian Regression
Monte Carlo
Monte Carlo
See Chapter 6 of Givens and Hoeting.
Geweke paper
R script to try various truncated normal draws
Rmarkdown version, of R script to try various truncated normal draws
R script to try various importance sampling approaches for prior sensitivity
Rmarkdown version, of R script to try various importance sampling approaches and SIR for prior sensitivity
Prior based on odds ratio
SIR R script
MCMC: Markov Chain Monte Carlo
See Chapter 7 of Givens and Hoeting.
Markov Chains
Simple Example of a Markov Chain
Gibbs Sampling
Gibbs Sampling for hier means
Note: Hoff refers to ``A First Course in Bayesian Statistical Methods'', by Peter Hoff
Reversable Markov Chains
The Metropolis Algorithm
MH example with for normal data with non-conjugate prior on mean
Recorded Lectures
Gibbs sample for normal (mu,sigma)
General Gibbs sampler and introduction to hierarchical normal means
Gibbs Sampler for Hierarchical means
Metropolis Hastings Algorithm
State Space Models and FFBS
Hotels Problem
intro to state space models
FFBS
R code for hotels example
Forward Filtering for Simple Hotels model
The Bootstrap
(Efron and Hastie, chapters 10 and 11)
The Bootstrap
Thompson Sampling
Tutorial on Thompson Sampling
BART
Introduction to BART
Old BART Talk
Bayesian Additive Regression Trees, Computational Approaches
chapter in Computational Statistics in Data Science