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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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