Nicola G. Best

Bio: Nicola G. Best is an academic researcher from Imperial College London. The author has contributed to research in topics: Markov chain Monte Carlo & Bayesian probability. The author has an hindex of 12, co-authored 17 publications receiving 12416 citations.

Bayesian measures of model complexity and fit

Abstract: Summary. We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure pD for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest. In general pD approximately corresponds to the trace of the product of Fisher's information and the posterior covariance, which in normal models is the trace of the ‘hat’ matrix projecting observations onto fitted values. Its properties in exponential families are explored. The posterior mean deviance is suggested as a Bayesian measure of fit or adequacy, and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. Adding pD to the posterior mean deviance gives a deviance information criterion for comparing models, which is related to other information criteria and has an approximate decision theoretic justification. The procedure is illustrated in some examples, and comparisons are drawn with alternative Bayesian and classical proposals. Throughout it is emphasized that the quantities required are trivial to compute in a Markov chain Monte Carlo analysis.

Bayesian measures of model complexity and fit

Abstract: Summary. We consider the problem of comparing complex hierarchical models in which the number of parameters is not clearly defined. Using an information theoretic argument we derive a measure pD for the effective number of parameters in a model as the difference between the posterior mean of the deviance and the deviance at the posterior means of the parameters of interest. In general pD approximately corresponds to the trace of the product of Fisher's information and the posterior covariance, which in normal models is the trace of the ‘hat’ matrix projecting observations onto fitted values. Its properties in exponential families are explored. The posterior mean deviance is suggested as a Bayesian measure of fit or adequacy, and the contributions of individual observations to the fit and complexity can give rise to a diagnostic plot of deviance residuals against leverages. Adding pD to the posterior mean deviance gives a deviance information criterion for comparing models, which is related to other information criteria and has an approximate decision theoretic justification. The procedure is illustrated in some examples, and comparisons are drawn with alternative Bayesian and classical proposals. Throughout it is emphasized that the quantities required are trivial to compute in a Markov chain Monte Carlo analysis.

The deviance information criterion: 12 years on

Abstract: Summary The essentials of our paper of 2002 are briefly summarized and compared with other criteria for model comparison. After some comments on the paper's reception and influence, we consider criticisms and proposals forimprovement made by us and others.

A shared component model for detecting joint and selective clustering of two diseases.

Abstract: The study of spatial variations in disease rates is a common epidemiological approach used to describe the geographical clustering of diseases and to generate hypotheses about the possible 'causes' which could explain apparent differences in risk. Recent statistical and computational developments have led to the use of realistically complex models to account for overdispersion and spatial correlation. However, these developments have focused almost exclusively on spatial modelling of a single disease. Many diseases share common risk factors (smoking being an obvious example) and, if similar patterns of geographical variation of related diseases can be identified, this may provide more convincing evidence of real clustering in the underlying risk surface. We propose a shared component model for the joint spatial analysis of two diseases. The key idea is to separate the underlying risk surface for each disease into a shared and a disease-specific component. The various components of this formulation are modelled simultaneously by using spatial cluster models implemented via reversible jump Markov chain Monte Carlo methods. We illustrate the methodology through an analysis of oral and oesophageal cancer mortality in the 544 districts of Germany, 1986–1990.

Dynamic conditional independence models and Markov chain Monte Carlo methods

Abstract: In dynamic statistical modeling situations, observations arise sequentially, causing the model to expand by progressive incorporation of new data items and new unknown parameters. For example, in clinical monitoring, patients and data arrive sequentially, and new patient-specific parameters are introduced with each new patient. Markov chain Monte Carlo (MCMC) might be used for continuous updating of the evolving posterior distribution, but would need to be restarted from scratch at each expansion stage. Thus MCMC methods are often too slow for real-time inference in dynamic contexts. By combining MCMC with importance resampling, we show how real-time sequential updating of posterior distributions can be effected. The proposed dynamic sampling algorithms use posterior samples from previous updating stages and exploit conditional independence between groups of parameters to allow samples of parameters no longer of interest to be discarded, such as when a patient dies or is discharged. We apply the ...

Cochrane Handbook for Systematic Reviews of Interventions

Abstract: The Cochrane Handbook for Systematic Reviews of Interventions is the official document that describes in detail the process of preparing and maintaining Cochrane systematic reviews on the effects of healthcare interventions.

Out of the Crisis

Abstract: According to W. Edwards Deming, American companies require nothing less than a transformation of management style and of governmental relations with industry. In Out of the Crisis, originally published in 1982, Deming offers a theory of management based on his famous 14 Points for Management. Management's failure to plan for the future, he claims, brings about loss of market, which brings about loss of jobs. Management must be judged not only by the quarterly dividend, but by innovative plans to stay in business, protect investment, ensure future dividends, and provide more jobs through improved product and service. In simple, direct language, he explains the principles of management transformation and how to apply them.

Multimodel Inference Understanding AIC and BIC in Model Selection

Abstract: The model selection literature has been generally poor at reflecting the deep foundations of the Akaike information criterion (AIC) and at making appropriate comparisons to the Bayesian information...

Information Theory, Inference and Learning Algorithms

Abstract: Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

A general and simple method for obtaining R2 from generalized linear mixed-effects models

Abstract: Summary The use of both linear and generalized linear mixed-effects models (LMMs and GLMMs) has become popular not only in social and medical sciences, but also in biological sciences, especially in the field of ecology and evolution. Information criteria, such as Akaike Information Criterion (AIC), are usually presented as model comparison tools for mixed-effects models. The presentation of ‘variance explained’ (R2) as a relevant summarizing statistic of mixed-effects models, however, is rare, even though R2 is routinely reported for linear models (LMs) and also generalized linear models (GLMs). R2 has the extremely useful property of providing an absolute value for the goodness-of-fit of a model, which cannot be given by the information criteria. As a summary statistic that describes the amount of variance explained, R2 can also be a quantity of biological interest. One reason for the under-appreciation of R2 for mixed-effects models lies in the fact that R2 can be defined in a number of ways. Furthermore, most definitions of R2 for mixed-effects have theoretical problems (e.g. decreased or negative R2 values in larger models) and/or their use is hindered by practical difficulties (e.g. implementation). Here, we make a case for the importance of reporting R2 for mixed-effects models. We first provide the common definitions of R2 for LMs and GLMs and discuss the key problems associated with calculating R2 for mixed-effects models. We then recommend a general and simple method for calculating two types of R2 (marginal and conditional R2) for both LMMs and GLMMs, which are less susceptible to common problems. This method is illustrated by examples and can be widely employed by researchers in any fields of research, regardless of software packages used for fitting mixed-effects models. The proposed method has the potential to facilitate the presentation of R2 for a wide range of circumstances.