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## Formalization of the Models and Inference

*Timothy J. O’Donnell and Noah D. Goodman*

### in Productivity and Reuse In Language: A Theory of Linguistic Computation and Storage

- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9780262028844
- eISBN:
- 9780262326803
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262028844.003.0003
- Subject:
- Linguistics, Sociolinguistics / Anthropological Linguistics

This chapter the mathematical details of the models studied in this book. It also discusses the inference algorithms used for each of the models and various other issues of practical concern for the ... More

## Generalized Linear Mixed Models

*Ludwig Fahrmeir and Thomas Kneib*

### in Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199533022
- eISBN:
- 9780191728501
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199533022.003.0003
- Subject:
- Mathematics, Probability / Statistics, Biostatistics

This chapter gives an introduction to linear and generalized linear mixed models. The primary goal is to describe concepts for statistical modelling and inference in this class of models that are ... More

## Nonparametric Bayesian machine learning and signal processing

*Max A. Little*

### in Machine Learning for Signal Processing: Data Science, Algorithms, and Computational Statistics

- Published in print:
- 2019
- Published Online:
- October 2019
- ISBN:
- 9780198714934
- eISBN:
- 9780191879180
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198714934.003.0010
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy, Mathematical Physics

We have seen that stochastic processes play an important foundational role in a wide range of methods in DSP. For example, we treat a discrete-time signal as a Gaussian process, and thereby obtain ... More

## Surviving fully Bayesian nonparametric regression models

*Timothy E. Hanson and Alejandro Jara*

### in Bayesian Theory and Applications

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199695607
- eISBN:
- 9780191744167
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199695607.003.0030
- Subject:
- Mathematics, Probability / Statistics

This chapter compares two Bayesian nonparametric models that generalize the accelerated failure time model, based on recent work on probability models for predictor-dependent probability ... More

## Semiparametric Mixed Models for Longitudinal Data

*Ludwig Fahrmeir and Thomas Kneib*

### in Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199533022
- eISBN:
- 9780191728501
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199533022.003.0004
- Subject:
- Mathematics, Probability / Statistics, Biostatistics

This chapter considers Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. Section 4.1 assumes Gaussian smoothness priors, focusing on Bayesian P-splines in combination ... More

## Introduction to replica theory

*Marc Mézard and Andrea Montanari*

### in Information, Physics, and Computation

- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780198570837
- eISBN:
- 9780191718755
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570837.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

In the past twenty-five years, the replica method has evolved into a rather sophisticated tool for attacking theoretical problems as diverse as spin glasses, protein folding, vortices in ... More

## Flexible Bayesian modelling for clustered categorical responses in developmental toxicology

*Kottas Athanasios and Fronczyk Kassandra*

### in Bayesian Theory and Applications

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199695607
- eISBN:
- 9780191744167
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199695607.003.0005
- Subject:
- Mathematics, Probability / Statistics

Developmental toxicity studies investigate birth defects caused by toxic chemicals. This chapter develops a Bayesian nonparametric modelling approach for risk assessment in developmental toxicity ... More

## Monte Carlo computational approaches in Bayesiancodon-substitution modelling

*Nicolas Rodrigue and Nicolas Lartillot*

### in Codon Evolution: Mechanisms and Models

- Published in print:
- 2012
- Published Online:
- May 2015
- ISBN:
- 9780199601165
- eISBN:
- 9780191810114
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:osobl/9780199601165.003.0004
- Subject:
- Biology, Evolutionary Biology / Genetics

This chapter reviews Markov Chain Monte Carlo (MCMC) approaches in codon-substitution modelling. It outlines the process of data analysis using the Bayesian framework. It describes the algorithms for ... More

## Finite Mixture Models

*Russell Cheng*

### in Non-Standard Parametric Statistical Inference

- Published in print:
- 2017
- Published Online:
- September 2017
- ISBN:
- 9780198505044
- eISBN:
- 9780191746390
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198505044.003.0017
- Subject:
- Mathematics, Probability / Statistics

Fitting a finite mixture model when the number of components, k, is unknown can be carried out using the maximum likelihood (ML) method though it is non-standard. Two well-known Bayesian Markov chain ... More

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