David J. Nott
National University of Singapore
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Featured researches published by David J. Nott.
Statistics & Probability Letters | 2000
Anthony Y. C. Kuk; David J. Nott
The method of pairwise likelihood is investigated for analyzing clustered or longitudinal binary data. The pairwise likelihood is a product of bivariate likelihoods for within cluster pairs of observations, and its maximizer is the maximum pairwise likelihood estimator. We discuss the computational advantages of pairwise likelihood relative to competing approaches, present some efficiency calculations and argue that when cluster sizes are unequal a weighted pairwise likelihood should be used for the marginal regression parameters, whereas the unweighted pairwise likelihood should be used for the association parameters.
PLOS ONE | 2009
M. Chehani Alles; Margaret Gardiner-Garden; David J. Nott; Yixin Wang; John A. Foekens; Robert L. Sutherland; Elizabeth A. Musgrove; Christopher J. Ormandy
Background Breast cancers lacking the estrogen receptor (ER) can be distinguished from other breast cancers on the basis of poor prognosis, high grade, distinctive histopathology and unique molecular signatures. These features further distinguish estrogen receptor negative (ER−) tumor subtypes, but targeted therapy is currently limited to tumors over-expressing the ErbB2 receptor. Methodology/Principal Findings To uncover the pathways against which future therapies could be developed we undertook a meta-analysis of gene expression from five large microarray datasets relative to ER status. A measure of association with ER status was calculated for every Affymetrix HG-U133A probe set and the pathways that distinguished ER− tumors were defined by testing for enrichment of biologically defined gene sets using Gene Set Enrichment Analysis (GSEA). As expected, the expression of the direct transcriptional targets of the ER was muted in ER− tumors, but the expression of genes indirectly regulated by estrogen was enhanced. We also observed enrichment of independent MYC- and E2F-driven transcriptional programs. We used a cell model of estrogen and MYC action to define the interaction between estrogen and MYC transcriptional activity in breast cancer. We found that the basal subgroup of ER− breast cancer showed a strong MYC transcriptional response that reproduced the indirect estrogen response seen in estrogen receptor positive (ER+) breast cancer cells. Conclusions/Significance Increased transcriptional activity of MYC is a characteristic of basal breast cancers where it mimics a large part of an estrogen response in the absence of the ER, suggesting a mechanism by which these cancers achieve estrogen-independence and providing a potential therapeutic target for this poor prognosis sub group of breast cancer.
Journal of Computational and Graphical Statistics | 2004
David J. Nott; Peter Green
The need to explore model uncertainty in linear regression models with many predictors has motivated improvements in Markov chain Monte Carlo sampling algorithms for Bayesian variable selection. Currently used sampling algorithms for Bayesian variable selection may perform poorly when there are severe multicollinearities among the predictors. This article describes a new sampling method based on an analogy with the Swendsen-Wang algorithm for the Ising model, and which can give substantial improvements over alternative sampling schemes in the presence of multicollinearity. In linear regression with a given set of potential predictors we can index possible models by a binary parameter vector that indicates which of the predictors are included or excluded. By thinking of the posterior distribution of this parameter as a binary spatial field, we can use auxiliary variable methods inspired by the Swendsen-Wang algorithm for the Ising model to sample from the posterior where dependence among parameters is reduced by conditioning on auxiliary variables. Performance of the method is described for both simulated and real data.
Journal of Computational and Graphical Statistics | 2004
David J. Nott; Daniela Leonte
Bayesian approaches to prediction and the assessment of predictive uncertainty in generalized linear models are often based on averaging predictions over different models, and this requires methods for accounting for model uncertainty. When there are linear dependencies among potential predictor variables in a generalized linear model, existing Markov chain Monte Carlo algorithms for sampling from the posterior distribution on the model and parameter space in Bayesian variable selection problems may not work well. This article describes a sampling algorithm based on the Swendsen-Wang algorithm for the Ising model, and which works well when the predictors are far from orthogonality. In problems of variable selection for generalized linear models we can index different models by a binary parameter vector, where each binary variable indicates whether or not a given predictor variable is included in the model. The posterior distribution on the model is a distribution on this collection of binary strings, and by thinking of this posterior distribution as a binary spatial field we apply a sampling scheme inspired by the Swendsen-Wang algorithm for the Ising model in order to sample from the model posterior distribution. The algorithm we describe extends a similar algorithm for variable selection problems in linear models. The benefits of the algorithm are demonstrated for both real and simulated data.
Statistics and Computing | 2007
David S. Leslie; Robert Kohn; David J. Nott
Our article presents a general treatment of the linear regression model, in which the error distribution is modelled nonparametrically and the error variances may be heteroscedastic, thus eliminating the need to transform the dependent variable in many data sets. The mean and variance components of the model may be either parametric or nonparametric, with parsimony achieved through variable selection and model averaging. A Bayesian approach is used for inference with priors that are data-based so that estimation can be carried out automatically with minimal input by the user. A Dirichlet process mixture prior is used to model the error distribution nonparametrically; when there are no regressors in the model, the method reduces to Bayesian density estimation, and we show that in this case the estimator compares favourably with a well-regarded plug-in density estimator. We also consider a method for checking the fit of the full model. The methodology is applied to a number of simulated and real examples and is shown to work well.
Statistical Science | 2013
Linda S. L. Tan; David J. Nott
The effects of different parametrizations on the convergence of Bayesian computational algorithms for hierarchical models are well explored. Techniques such as centering, noncentering and partial noncentering can be used to accelerate convergence in MCMC and EM algorithms but are still not well studied for variational Bayes (VB) methods. As a fast deterministic approach to posterior approximation, VB is attracting increasing interest due to its suitability for large high-dimensional data. Use of different parametrizations for VB has not only computational but also statistical implications, as different parametrizations are associated with different factorized posterior approximations. We examine the use of partially noncentered parametrizations in VB for generalized linear mixed models (GLMMs). Our paper makes four contributions. First, we show how to implement an algorithm called nonconjugate variational message passing for GLMMs. Second, we show that the partially noncentered parametrization can adapt to the quantity of information in the data and determine a parametrization close to optimal. Third, we show that partial noncentering can accelerate convergence and produce more accurate posterior approximations than centering or noncentering. Finally, we demonstrate how the variational lower bound, produced as part of the computation, can be useful for model selection.
Journal of Computational and Graphical Statistics | 2012
David J. Nott; Siew Li Tan; Mattias Villani; Robert Kohn
Regression density estimation is the problem of flexibly estimating a response distribution as a function of covariates. An important approach to regression density estimation uses finite mixture models and our article considers flexible mixtures of heteroscedastic regression (MHR) models where the response distribution is a normal mixture, with the component means, variances, and mixture weights all varying as a function of covariates. Our article develops fast variational approximation (VA) methods for inference. Our motivation is that alternative computationally intensive Markov chain Monte Carlo (MCMC) methods for fitting mixture models are difficult to apply when it is desired to fit models repeatedly in exploratory analysis and model choice. Our article makes three contributions. First, a VA for MHR models is described where the variational lower bound is in closed form. Second, the basic approximation can be improved by using stochastic approximation (SA) methods to perturb the initial solution to attain higher accuracy. Third, the advantages of our approach for model choice and evaluation compared with MCMC-based approaches are illustrated. These advantages are particularly compelling for time series data where repeated refitting for one-step-ahead prediction in model choice and diagnostics and in rolling-window computations is very common. Supplementary materials for the article are available online.
Journal of the American Statistical Association | 2008
Remy Cottet; Robert J. Kohn; David J. Nott
We express the mean and variance terms in a double exponential regression model as additive functions of the predictors and use Bayesian variable selection to determine which predictors enter the model, and whether they enter linearly or flexibly. When the variance term is null we obtain a generalized additive model, which becomes a generalized linear model if the predictors enter the mean linearly. The model is estimated using Markov chain Monte Carlo simulation and the methodology is illustrated using real and simulated data sets.
Journal of Computational and Graphical Statistics | 2014
David J. Nott; Yanan Fan; Lucy Marshall; Scott A. Sisson
Bayes’ linear analysis and approximate Bayesian computation (ABC) are techniques commonly used in the Bayesian analysis of complex models. In this article, we connect these ideas by demonstrating that regression-adjustment ABC algorithms produce samples for which first- and second-order moment summaries approximate adjusted expectation and variance for a Bayes’ linear analysis. This gives regression-adjustment methods a useful interpretation and role in exploratory analysis in high-dimensional problems. As a result, we propose a new method for combining high-dimensional, regression-adjustment ABC with lower-dimensional approaches (such as using Markov chain Monte Carlo for ABC). This method first obtains a rough estimate of the joint posterior via regression-adjustment ABC, and then estimates each univariate marginal posterior distribution separately in a lower-dimensional analysis. The marginal distributions of the initial estimate are then modified to equal the separately estimated marginals, thereby providing an improved estimate of the joint posterior. We illustrate this method with several examples. Supplementary materials for this article are available online.
Technometrics | 2011
Mark Fielding; David J. Nott; Shie-Yui Liong
We consider Markov chain Monte Carlo (MCMC) computational schemes intended to minimize the number of evaluations of the posterior distribution in Bayesian inference when the posterior is computationally expensive to evaluate. Our motivation is Bayesian calibration of computationally expensive computer models. An algorithm suggested previously in the literature based on hybrid Monte Carlo and a Gaussian process approximation to the target distribution is extended in three ways. First, we consider combining the original method with tempering schemes in order to deal with multimodal posterior distributions. Second, we consider replacing the original target posterior distribution with the Gaussian process approximation, which requires less computation to evaluate. Third, we consider in the context of tempering schemes the replacement of the true target distribution with the approximation in the high temperature chains while retaining the true target in the lowest temperature chain. This retains the correct target distribution in the lowest temperature chain while avoiding the computational expense of running the computer model in moves involving the high temperatures. Application of our methodology is considered to calibration of a rainfall-runoff model where multimodality of the parameter posterior is observed.