The journey from statistical model to useful output has many steps, most of which are taught in other books and courses. The purpose of this book is to focus on one particular aspect of this journey: the development and implementation of statistical algorithms. It's often nice to think about statistical models and various inferential philosophies and techniques, but when the rubber meets the road, we need an algorithm and a computer program implementation to get the results we need from a combination of our data and our models. This book is about how we fit models to data and the algorithms that we use to do so. Examples are given using the R programming language.
Author(s): Roger D. Peng
Year: 2023
Language: English
Pages: 106
Welcome
Stay in Touch!
Setup
Introduction
Example: Linear Models
Principle of Optimization Transfer
Textbooks vs. Computers
Solving Nonlinear Equations
Bisection Algorithm
Rates of Convergence
Functional Iteration
Newton's Method
General Optimization
Steepest Descent
The Newton Direction
Quasi-Newton
Conjugate Gradient
Coordinate Descent
The EM Algorithm
EM Algorithm for Exponential Families
Canonical Examples
A Minorizing Function
Missing Information Principle
Acceleration Methods
Integration
Laplace Approximation
Independent Monte Carlo
Random Number Generation
Non-Uniform Random Numbers
Rejection Sampling
Importance Sampling
Markov Chain Monte Carlo
Background
Metropolis-Hastings
Gibbs Sampler
Monitoring Convergence
Simulated Annealing
