Contents

Idea

Mathematical statistics is about data analysis using different tools from mathematics like probability theory. The analyzed data is often assumed to exhibit some influence from Random processes.

One area where the use of mathematical statistics is of importance to Azimuth’s goals is in Earth sciences and Climate models, as a tool to enable an objective assessment of measurements, experiments and models. Another is decision theory.

Bayesian and frequentist approaches

These are the two major ‘philosophies’ which underlie two approaches to statistics.

Some relevant pages in Azimuth

Bayesian statistical decision theory

Hidden markov model

Importance sampling

Maximum likelihood estimator

Random process

Time series analysis

General

Mathematical statistics is a huge subject, and there is a multiplicity of textbooks. Any recommendation is therefore to be considered to be an example only.

• Jun Shao: Mathematical statistics. (ZMATH)
• E.T. Jaynes and G. Larry Bretthorst, Probability Theory: The Logic of Science
• James Clark: Models For Ecological Data: An Introduction
• Andrew Gelman, John Carlin, Hal Stern, Donald Rubin: Bayesian Data Analysis
• Devinderjit Sivia and John Skilling: Data Analysis: A Bayesian Tutorial
• Giulio D’Agostini: Bayesian Reasoning in Data Analysis
• Peter Congdon: Bayesian Statistical Modelling
• Phil Gregory: Bayesian Logical Data Analysis for the Physical Sciences
• Jim Albert: Bayesian Computation With R
• Christian Robert and George Casella: Monte Carlo Statistical Methods
• Daniel Wilks: Statistical Methods in the Atmospheric Sciences
• Hans von Storch and Francis W. Zweiers: Statistical Analysis in Climate Research
• Robert Shumway and David Stoffer: Time Series Analysis and Its Applications: With R Examples
• Hans Wackernagel: Multivariate Geostatistics
• Noel Cressie: Statistics for Spatial Data
• Sudipto Banerjee, Bradley Carlin, and Alan Gelfand, Hierarchical Modeling and Analysis for Spatial Data
• A. Saltelli et al.: Global Sensitivity Analysis: The Primer
• Thomas Santner, Brian Willians, and William Notz: The Design and Analysis of Computer Experiments
• Carl Rasmussen and Christopher Williams: Gaussian Processes for Machine Learning
• Ray Hilborn and Marc Mangel: The Ecological Detective

Software

See R.

category: area of research