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56
Bayesian hierarchical spatially correlated functional data analysis with application to colon carcinogenesis
 Biometrics
, 2008
"... Summary. In this article, we present new methods to analyze data from an experiment using rodent models to investigate the role of p27, an important cellcycle mediator, in early colon carcinogenesis. The responses modeled here are essentially functions nested within a twostage hierarchy. Standard ..."
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Cited by 26 (4 self)
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Summary. In this article, we present new methods to analyze data from an experiment using rodent models to investigate the role of p27, an important cellcycle mediator, in early colon carcinogenesis. The responses modeled here are essentially functions nested within a twostage hierarchy. Standard functional data analysis literature focuses on a single stage of hierarchy and conditionally independent functions with near white noise. However, in our experiment, there is substantial biological motivation for the existence of spatial correlation among the functions, which arise from the locations of biological structures called colonic crypts: this possible functional correlation is a phenomenon we term crypt signaling. Thus, as a point of general methodology, we require an analysis that allows for functions to be correlated at the deepest level of the hierarchy. Our approach is fully Bayesian and uses Markov chain Monte Carlo methods for inference and estimation. Analysis of this data set gives new insights into the structure of p27 expression in early colon carcinogenesis and suggests the existence of significant crypt signaling. Our methodology uses regression splines, and because of the hierarchical nature of the data, dimension reduction of the covariance matrix of the spline coefficients is important: we suggest simple methods for overcoming this problem.
On semiparametric regression with O’Sullivan penalized splines
 Australian and New Zealand Journal of Statistics
, 2008
"... An exposition on the use of O’Sullivan penalized splines in contemporary semiparametric regression, including mixed model and Bayesian formulations, is presented. O’Sullivan penalized splines are similar to Psplines, but have the advantage of being a direct generalization of smoothing splines. Ex ..."
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Cited by 24 (7 self)
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An exposition on the use of O’Sullivan penalized splines in contemporary semiparametric regression, including mixed model and Bayesian formulations, is presented. O’Sullivan penalized splines are similar to Psplines, but have the advantage of being a direct generalization of smoothing splines. Exact expressions for the O’Sullivan penalty matrix are obtained. Comparisons between the two types of splines reveal that O’Sullivan penalized splines more closely mimic the natural boundary behaviour of smoothing splines. Implementation in modern computing environments such as MATLAB, R and BUGS is discussed.
Penalized splines and reproducing kernel methods.
 The American Statistician,
, 2006
"... Two data analytic research areaspenalized splines and reproducing kernel methodshave become very vibrant since the mid1990s. This article shows how the former can be embedded in the latter via theory for reproducing kernel Hilbert spaces. This connection facilitates crossfertilization between t ..."
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Cited by 17 (1 self)
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Two data analytic research areaspenalized splines and reproducing kernel methodshave become very vibrant since the mid1990s. This article shows how the former can be embedded in the latter via theory for reproducing kernel Hilbert spaces. This connection facilitates crossfertilization between the two bodies of research. In particular, connections between support vector machines and penalized splines are established. These allow for significant reductions in computational complexity, and easier incorporation of special structure such as additivity.
Semiparametric Regression During 2003–2007
, 2008
"... Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a ..."
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Cited by 17 (5 self)
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Semiparametric regression is a fusion between parametric regression and nonparametric regression and the title of a book that we published on the topic in early 2003. We review developments in the field during the five year period since the book was written. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.
General design Bayesian generalized linear mixed models.” Statistical Science, 21(1), 35–51. Hadfield 17 A. Appendix A.1. Updating the latent variables l The conditional density of l is given by: P r(liy, θ, R, G) ∝ fi(yili)fN(eiriR −1 /i e /i, ri − ri
 P r(ljy, θ, R, G) ∝ ∏ pi(yili)fN(ej0, Rj
, 2006
"... Abstract. Linear mixed models are able to handle an extraordinary range of complications in regressiontype analyses. Their most common use is to account for withinsubject correlation in longitudinal data analysis. They are also the standard vehicle for smoothing spatial count data. However, when t ..."
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Cited by 13 (3 self)
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Abstract. Linear mixed models are able to handle an extraordinary range of complications in regressiontype analyses. Their most common use is to account for withinsubject correlation in longitudinal data analysis. They are also the standard vehicle for smoothing spatial count data. However, when treated in full generality, mixed models can also handle splinetype smoothing and closely approximate kriging. This allows for nonparametric regression models (e.g., additive models and varying coefficient models) to be handled within the mixed model framework. The key is to allow the random effects design matrix to have general structure; hence our label general design. For continuous response data, particularly when Gaussianity of the response is reasonably assumed, computation is now quite mature and supported by the R, SAS and SPLUS packages. Such is not the case for binary and count responses, where generalized linear mixed models (GLMMs) are required, but are hindered by the presence of intractable multivariate
Variational Bayesian inference for parametric and nonparametric regression with missing data
 JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
, 2011
"... Bayesian hierarchical models are attractive structures for conducting regression analyses when the data are subject to missingness. However, the requisite probability calculus is challenging and Monte Carlo methods typically are employed. We develop an alternative approach based on deterministic var ..."
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Cited by 13 (3 self)
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Bayesian hierarchical models are attractive structures for conducting regression analyses when the data are subject to missingness. However, the requisite probability calculus is challenging and Monte Carlo methods typically are employed. We develop an alternative approach based on deterministic variational Bayes approximations. Both parametric and nonparametric regression are treated. We demonstrate that variational Bayes can achieve good accuracy, but with considerably less computational overhead. The main ramification is fast approximate Bayesian inference in parametric and nonparametric regression models with missing data.
Biphasic growth in fish I: Theoretical foundations.
 J. Theor. Biol.,
, 2008
"... ], we developed a set of biphasic somatic growth models, where maturation is accompanied by a deceleration of growth due to allocation of energy to reproduction. Here, we use growth data from both hatcheryraised and wild populations of a large freshwater fish (lake trout, Salvelinus namaycush) to ..."
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Cited by 11 (0 self)
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], we developed a set of biphasic somatic growth models, where maturation is accompanied by a deceleration of growth due to allocation of energy to reproduction. Here, we use growth data from both hatcheryraised and wild populations of a large freshwater fish (lake trout, Salvelinus namaycush) to test these models. We show that a generic biphasic model provides a better fit to these data than the von Bertalanffy model. We show that the observed deceleration of somatic growth in females varies directly with gonad weight at spawning, with observed egg volumes roughly 50% of the egg volumes predicted under the unrealistic assumption of perfectly efficient energy transfer from somatic lipids to egg lipids. We develop a Bayesian procedure to jointly fit a biphasic model to observed growth and maturity data. We show that two variants of the generic biphasic model, both of which assume that annual allocation to reproduction is adjusted to maximise lifetime reproductive output, provide complementary fits to wild population data: maturation time and early adult growth are best described by a model with no constraints on annual reproductive investment, while the growth of older fish is best described by a model that is constrained so that the ratio of gonad size to somatic weight (g) is fixed. This behaviour is consistent with the additional observation that g increases with size and age among younger, smaller breeding females but reaches a plateau among older, larger females. We then fit both of these optimal models to growth and maturation data from nineteen wild populations to generate populationspecific estimates of 'adapted mortality' rate: the adult mortality consistent with observed growth and maturation schedules, given that both schedules are adapted to maximise lifetime reproductive output. We show that these estimates are strongly correlated with independent estimates of the adult mortality experienced by these populations.
Fast adaptive penalized splines
 Journal of Computational and Graphical Statistics
"... copyright holder. Copyright © 2011 by the authors ..."
Climatological Summary
 Department of Commerce
, 1963
"... The effect of platelet activating factor on the motility and acrosome reaction of ram spermatozoa ..."
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The effect of platelet activating factor on the motility and acrosome reaction of ram spermatozoa
Spikeandslab priors for function selection in structured additive regression models
 Journal of the American Statistical Association
"... Structured additive regression provides a general framework for complex Gaussian and nonGaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects and further regression terms. The large fl ..."
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Cited by 5 (1 self)
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Structured additive regression provides a general framework for complex Gaussian and nonGaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects and further regression terms. The large flexibility of structured additive regression makes function selection a challenging and important task, aiming at (1) selecting the relevant covariates, (2) choosing an appropriate and parsimonious representation of the impact of covariates on the predictor and (3) determining the required interactions. We propose a spikeandslab prior structure for function selection that allows to include or exclude single coefficients as well as blocks of coefficients representing specific model terms. A novel multiplicative parameter expansion is required to obtain good mixing and convergence properties in a Markov chain Monte Carlo simulation approach and is shown to induce desirable shrinkage properties. In simulation studies and with (real) benchmark classification data, we investigate sensitivity to hyperparameter settings and compare performance to competitors. The flexibility and applicability of our approach are demonstrated in an additive piecewise exponential model with timevarying effects for rightcensored survival times of intensive care patients with sepsis. Geoadditive and additive mixed logit model applications are discussed in an extensive appendix. Keywords: parameter expansion, penalized splines, stochastic search variable selection, generalized additive mixed models, spatial regression 1.