Stochastic classiﬁcation models

McCullagh, Peter; Yang, Jie

doi:10.4171/022-3/35

Cited by 23 publications

(33 citation statements)

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“…Note that both the dimension k and the placement of the 1s are random, representing the subclustering process. On the basis of the representation in McCullagh and Yang (2006), if the partition C has subclusters { S 1 ,…, S k }, then, if i ∈ S j , ψ i = η j and the random effect can be rewritten as where η =( η 1 ,…, η k ) and for j =1,…, k .…”

Section: Logistic Mixed Dirichlet Process Modelsmentioning

confidence: 99%

New Findings from Terrorism Data: Dirichlet Process Random-Effects Models for Latent Groups

Kyung

Gill

Casella

2011

Journal of the Royal Statistical Society Series C: Applied Statistics

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Summary. Data obtained describing terrorist events are particularly difficult to analyse, owing to the many problems that are associated with the data collection process, the inherent variability in the data themselves and the usually poor level of measurement coming from observing political actors who seek not to provide reliable data on their activities. Thus, there is a need for sophisticated modelling to obtain reasonable inferences from these data. Here we develop a logistic random-effects specification using a Dirichlet process to model the random effects. We first look at how such a model can best be implemented, and then we use the model to analyse terrorism data. We see that the richer Dirichlet process random-effects model, compared with a normal random-effects model, can remove more of the underlying variability from the data, uncovering latent information that would not otherwise have been revealed.

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Section: Logistic Mixed Dirichlet Process Modelsmentioning

confidence: 99%

New Findings from Terrorism Data: Dirichlet Process Random-Effects Models for Latent Groups

Kyung

Gill

Casella

2011

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…Huang and colleagues used the simulated data but did not use knowledge of the simulation model in their work. Permanental classification is a newly developed approach for classification analysis in which the spatial pattern of x is mapped based on a permanental process [McCullagh and Yang, ], which is a special class of a Cox process (double stochastic Poisson process) [Cox and Isham, ]. A hyperparameter α is incorporated in the permanental process for regulating the underlying marginal density with a cyclic approximation.…”

Section: Methodsmentioning

confidence: 99%

Applications of Machine Learning and Data Mining Methods to Detect Associations of Rare and Common Variants with Complex Traits

Austin

Bonner

et al. 2014

Genetic Epidemiology

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Machine learning methods (MLMs), designed to develop models using high-dimensional predictors, have been used to analyze genome-wide genetic and genomic data to predict risks for complex traits. We summarize the results from six contributions to our Genetic Analysis Workshop 18 working group; these investigators applied MLMs and data mining to analyses of rare and common genetic variants measured in pedigrees. To develop risk profiles, group members analyzed blood pressure traits along with single-nucleotide polymorphisms and rare variant genotypes derived from sequence and imputation analyses in large Mexican American pedigrees. Supervised MLMs included penalized regression with varying penalties, support vector machines, and permanental classification. Unsupervised MLMs included sparse principal components analysis and sparse graphical models. Entropy-based components analyses were also used to mine these data. None of the investigators fully capitalized on the genetic information provided by the complete pedigrees. Their approaches either corrected for the nonindependence of the individuals within the pedigrees or analyzed only those who were independent. Some methods allowed for covariate adjustment, whereas others did not. We evaluated these methods using a variety of metrics. Four contributors conducted primary analyses on the real data, and the other two research groups used the simulated data with and without knowledge of the underlying simulation model. One group used the answers to the simulated data to assess power and type I errors. Although the MLMs applied were substantially different, each research group concluded that MLMs have advantages over standard statistical approaches with these high-dimensional data.

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“…By contrast with the log‐Gaussian model, the prognostic log‐odds is not a kernel function. For an application of this model to classification, see McCullagh and Yang (2006).…”

Section: Two Parametric Modelsmentioning

confidence: 99%

Sampling Bias and Logistic Models

McCullagh

2008

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary. In a regression model, the joint distribution for each finite sample of units is determined by a function px(y) depending only on the list of covariate values x=(x(u1),…,x(un)) on the sampled units. No random sampling of units is involved. In biological work, random sampling is frequently unavoidable, in which case the joint distribution p(y,x) depends on the sampling scheme. Regression models can be used for the study of dependence provided that the conditional distribution p(y|x) for random samples agrees with px(y) as determined by the regression model for a fixed sample having a non‐random configuration x. The paper develops a model that avoids the concept of a fixed population of units, thereby forcing the sampling plan to be incorporated into the sampling distribution. For a quota sample having a predetermined covariate configuration x, the sampling distribution agrees with the standard logistic regression model with correlated components. For most natural sampling plans such as sequential or simple random sampling, the conditional distribution p(y|x) is not the same as the regression distribution unless px(y) has independent components. In this sense, most natural sampling schemes involving binary random‐effects models are biased. The implications of this formulation for subject‐specific and population‐averaged procedures are explored.

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Stochastic classiﬁcation models

Cited by 23 publications

References 0 publications

New Findings from Terrorism Data: Dirichlet Process Random-Effects Models for Latent Groups

New Findings from Terrorism Data: Dirichlet Process Random-Effects Models for Latent Groups

Applications of Machine Learning and Data Mining Methods to Detect Associations of Rare and Common Variants with Complex Traits

Sampling Bias and Logistic Models

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