FUNDAMENTALS OF BAYESIAN INFERENCE Probability and Inference Single-Parameter Models Introduction to Multiparameter Models Asymptotics and Connections to Non-Bayesian Approaches Hierarchical Models FUNDAMENTALS OF BAYESIAN DATA ANALYSIS Model Checking Evaluating, Comparing, and Expanding Models Modeling Accounting for Data Collection Decision Analysis ADVANCED COMPUTATION Introduction to Bayesian Computation Basics of Markov Chain Simulation Computationally Efficient Markov Chain Simulation Modal and Distributional Approximations REGRESSION MODELS Introduction to Regression Models Hierarchical Linear Models Generalized Linear Models Models for Robust Inference Models for Missing Data NONLINEAR AND NONPARAMETRIC MODELS Parametric Nonlinear Models Basic Function Models Gaussian Process Models Finite Mixture Models Dirichlet Process Models APPENDICES A: Standard Probability Distributions B: Outline of Proofs of Asymptotic Theorems C: Computation in R and Stan Bibliographic Notes and Exercises appear at the end of each chapter.

Bayesian Data Analysis

This paper reviews the mathematical basis of maximum likelihood The likelihood function for macromolecular structures is extended to include prior phase information and experimental standard uncertainties The assumption that different parts of a structure might have different errors is considered A method for estimating σA using `free' reflections is described and its effects analysed The derived equations have been implemented in the program REFMAC This has been tested on several proteins at different stages of refinement (bacterial α-amylase, cytochrome c′, cross-linked insulin and oligopeptide binding protein) The results derived using the maximum-likelihood residual are consistently better than those obtained from least-squares refinement

Refinement of macromolecular structures by the maximum-likelihood method.

Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

This paper introduces an ARCH model (exponential ARCH) that (1) allows correlation between returns and volatility innovations (an important feature of stock market volatility changes), (2) eliminates the need for inequality constraints on parameters, and (3) allows for a straightforward interpretation of the "persistence" of shocks to volatility. In the above respects, it is an improvement over the widely-used GARCH model. The model is applied to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987. Copyright 1991 by The Econometric Society.

Conditional heteroskedasticity in asset returns: a new approach

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

/pdf/experimental-design-and-data-analysis-for-biologists-8ybva8d53x.pdf

Experimental Design and Data Analysis for Biologists

Nature of Bayesian Inference Standard Normal Theory Inference Problems Bayesian Assessment of Assumptions: Effect of Non-Normality on Inferences About a Population Mean with Generalizations Bayesian Assessment of Assumptions: Comparison of Variances Random Effect Models Analysis of Cross Classification Designs Inference About Means with Information from More than One Source: One-Way Classification and Block Designs Some Aspects of Multivariate Analysis Estimation of Common Regression Coefficients Transformation of Data Tables References Indexes.

Bayesian inference in statistical analysis

Bayesian Inference in Statistical Analysis

This article studies the problem of multiple change points in the variance of a sequence of independent observations. We propose a procedure to detect variance changes based on an iterated cumulative sums of squares (ICSS) algorithm. We study the properties of the centered cumulative sum of squares function and give an intuitive basis for the ICSS algorithm. For series of moderate size (i.e., 200 observations and beyond), the ICSS algorithm offers results comparable to those obtained by a Bayesian approach or by likelihood ratio tests, without the heavy computational burden required by these approaches. Simulation results comparing the ICSS algorithm to other approaches are presented.

https://rmgsc.cr.usgs.gov/outgoing/threshold_articles/Inclan_Tiao1994.pdf

Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance

This paper considers some recent developments in non-linear and linear time series analysis. It consists of two main components. The first emphasizes the advances in non-linear modelling and in Bayesian inference via the Gibbs sampler. Advantages and the usefulness of these advances are illustrated by real examples. The second component is concerned with adaptive forecasting. This shows that linear models can provide accurate forecasts provided that the parameters involved are estimated adaptively. In particular, we focus on forecasting long-memory time series. Again, a real example is used to illustrate the results.

Some advances in non‐linear and adaptive modelling in time‐series

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1989.tb01756.x

George C. Tiao

Papers

Bayesian inference in statistical analysis

Bayesian Inference in Statistical Analysis

Use of Cumulative Sums of Squares for Retrospective Detection of Changes of Variance

Some advances in non‐linear and adaptive modelling in time‐series

Model Specification in Multivariate Time Series