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Working with roots

Christopher G. Small and Jinfang Wang

in Numerical Methods for Nonlinear Estimating Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.003.0004
Subject:
Mathematics, Probability / Statistics

This chapter studies the broad class of models which have difficult problems of nonlinearity and multiple roots. These models include the mixture models, a model for bivariate normal paired data with ... More


Nonparametric Bayesian Networks *

Katja Ickstadt, Bjöorn Bornkamp, Marco Grzegorczyk, Jakob Wieczorek, Malik R. Sheriff, Hernáan E. Grecco, and Eli Zamir

in Bayesian Statistics 9

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199694587
eISBN:
9780191731921
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199694587.003.0010
Subject:
Mathematics, Probability / Statistics

A convenient way of modelling complex interactions is by employing graphs or networks which correspond to conditional independence structures in an underlying statistical model. One main class of ... More


Particle Learning for Sequential Bayesian Computation *

Hedibert F. Lopes, Michael S. Johannes, Carlos M. Carvalho, and Nicholas G. Polson

in Bayesian Statistics 9

Published in print:
2011
Published Online:
January 2012
ISBN:
9780199694587
eISBN:
9780191731921
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199694587.003.0011
Subject:
Mathematics, Probability / Statistics

Particle learning provides a simulation‐based approach to sequential Bayesian computation. To sample from a posterior distribution of interest we use an essential state vector together with a ... More


Models for Liquid Water †

D. Eisenberg and W. Kauzmann

in The Structure and Properties of Water

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198570264
eISBN:
9780191715266
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198570264.003.0005
Subject:
Physics, Condensed Matter Physics / Materials

This chapter discusses models for water. Topics covered include small aggregate models, mixture and interstitial models, and distorted hydrogen-bond models.


On non-parametric statistical methods

Peter Hall

in Celebrating Statistics: Papers in honour of Sir David Cox on his 80th birthday

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566540
eISBN:
9780191718038
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566540.003.0007
Subject:
Mathematics, Probability / Statistics

This chapter describes some contemporary topics in non-parametric statistics and outlines their relation to computation, particularly some topics on pure mathematics. It opens with a brief comparison ... More


Mixture models for overdispersed data

Jonathan R. Rhodes

in Ecological Statistics: Contemporary theory and application

Published in print:
2015
Published Online:
April 2015
ISBN:
9780199672547
eISBN:
9780191796487
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199672547.003.0013
Subject:
Biology, Biomathematics / Statistics and Data Analysis / Complexity Studies, Ecology

Ecological data often do not conform to the assumptions of standard probability distributions and this has important implications for the validity of statistical inference. A common reason for this ... More


Group-Based Trajectory Modeling of Externalizing Behavior Problems from Childhood through Adulthood: Exploring Discrepancies in the Empirical Findings

Manfred H.M. van Dulmen, Elizabeth A. Goncy, Andrea Vest, and Daniel J. Flannery

in The Development of Persistent Criminality

Published in print:
2009
Published Online:
May 2009
ISBN:
9780195310313
eISBN:
9780199871384
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195310313.003.0014
Subject:
Psychology, Social Psychology

The purpose of this chapter is to investigate whether there are systematic factors that may help explain the large discrepancy in findings from group-based trajectory modeling studies of offending. ... More


Semi-Supervised Text Classification Using EM

Nigam Kamal, McCallum Andrew, and Mitchell Tom

in Semi-Supervised Learning

Published in print:
2006
Published Online:
August 2013
ISBN:
9780262033589
eISBN:
9780262255899
Item type:
chapter
Publisher:
The MIT Press
DOI:
10.7551/mitpress/9780262033589.003.0003
Subject:
Computer Science, Machine Learning

This chapter explores the use of generative models for semi-supervised learning with labeled and unlabeled data in domains of text classification. The widely used naive Bayes classifier for ... More


Comparison of Mixture Bayesian and Mixture Regression Approaches to Infer Gene Networks

Sandra L. Rodriguez–Zas and Bruce R. Southey

in Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics

Published in print:
2014
Published Online:
December 2014
ISBN:
9780198709022
eISBN:
9780191779619
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198709022.003.0004
Subject:
Mathematics, Probability / Statistics, Biostatistics

Most Bayesian network applications to gene network reconstruction assume a single distributional model across all the samples and treatments analyzed. This assumption is likely to be unrealistic ... More


Methodological Approaches to Modeling Criminal Trajectories

David M. Day and Margit Wiesner

in Criminal Trajectories: A Developmental Perspective

Published in print:
2019
Published Online:
January 2020
ISBN:
9781479880058
eISBN:
9781479888276
Item type:
chapter
Publisher:
NYU Press
DOI:
10.18574/nyu/9781479880058.003.0003
Subject:
Psychology, Social Psychology

Criminal offenders compose a heterogeneous population. Criminal trajectory research aims to capture this heterogeneity in terms of the frequency or severity of offending. This chapter describes the ... 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


Hierarchical modelling

Alan E Gelfand and Souparno Ghosh

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/9780199695607.003.0003
Subject:
Mathematics, Probability / Statistics

This chapter reviews the range of hierarchical modelling. It argues that hierarchical models provide the stochastic framework within which to develop integrative process models. The chapter is ... More


Latent Variable Models for Analyzing DNA Methylation

E. Andrés Houseman

in Probabilistic Graphical Models for Genetics, Genomics, and Postgenomics

Published in print:
2014
Published Online:
December 2014
ISBN:
9780198709022
eISBN:
9780191779619
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198709022.003.0015
Subject:
Mathematics, Probability / Statistics, Biostatistics

Deoxyribonucleic acid (DNA) methylation is tightly linked with cellular differentiation. For instance, it has been observed that DNA methylation in tumor cells encodes phenotypic information about ... More


Statistical machine learning

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/9780198714934.003.0006
Subject:
Mathematics, Logic / Computer Science / Mathematical Philosophy, Mathematical Physics

This chapter describes in detail how the main techniques of statistical machine learning can be constructed from the components described in earlier chapters. It presents these concepts in a way ... More


Revisiting Bayesian curve fitting using multivariate normal mixtures ∗

Stephen G Walker and George Karabatsos

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/9780199695607.003.0015
Subject:
Mathematics, Probability / Statistics

This chapter develops a Bayesian nonparametric regression model which relies on a standard Bayesian nonparametric form for the joint distribution of both the dependent and independent variables. The ... 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


Unsupervised yearning: Marr’s theory of the neocortex

Peter Dayan and David Willshaw

in Computational Theories and their Implementation in the Brain: The legacy of David Marr

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198749783
eISBN:
9780191831638
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749783.003.0009
Subject:
Psychology, Neuropsychology

Marr’s theory of neocortex is the ghost in his trinity of seminal contributions to theoretical neuroscience, being the most spirited and least appreciated. In this chapter, we review its ... More


Finite Mixture Examples; MAPIS Details

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/9780198505044.003.0018
Subject:
Mathematics, Probability / Statistics

Two detailed numerical examples are given in this chapter illustrating and comparing mainly the reversible jump Markov chain Monte Carlo (RJMCMC) and the maximum a posteriori/importance sampling ... More


Top-Down Predictions Determine Perceptions

Martin V. Butz and Esther F. Kutter

in How the Mind Comes into Being: Introducing Cognitive Science from a Functional and Computational Perspective

Published in print:
2017
Published Online:
July 2017
ISBN:
9780198739692
eISBN:
9780191834462
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198739692.003.0009
Subject:
Psychology, Cognitive Models and Architectures, Cognitive Psychology

While bottom-up visual processing is important, the brain integrates this information with top-down, generative expectations from very early on in the visual processing hierarchy. Indeed, our brain ... More


The role of probabilistic enhancement in phonologization

James Kirby

in Origins of Sound Change: Approaches to Phonologization

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199573745
eISBN:
9780191745249
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199573745.003.0011
Subject:
Linguistics, Phonetics / Phonology, Psycholinguistics / Neurolinguistics / Cognitive Linguistics

This chapter argues for the role of probabilistic enhancement in phonologization through computational simulation of an ongoing sound change in Seoul Korean. Two challenges faced by a phonologization ... More


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