Results 1  10
of
35
Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models
, 1993
"... Ways of obtaining approximate Bayes factors for generalized linear models are described, based on the Laplace method for integrals. I propose a new approximation which uses only the output of standard computer programs such as GUM; this appears to be quite accurate. A reference set of proper priors ..."
Abstract

Cited by 96 (28 self)
 Add to MetaCart
Ways of obtaining approximate Bayes factors for generalized linear models are described, based on the Laplace method for integrals. I propose a new approximation which uses only the output of standard computer programs such as GUM; this appears to be quite accurate. A reference set of proper priors is suggested, both to represent the situation where there is not much prior information, and to assess the sensitivity of the results to the prior distribution. The methods can be used when the dispersion parameter is unknown, when there is overdispersion, to compare link functions, and to compare error distributions and variance functions. The methods can be used to implement the Bayesian approach to accounting for model uncertainty. I describe an application to inference about relative risks in the presence of control factors where model uncertainty is large and important. Software to implement the
Generalized functional linear models
 Ann. Statist
, 2005
"... We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the predictor function with a smooth parameter function, and the expe ..."
Abstract

Cited by 40 (5 self)
 Add to MetaCart
We propose a generalized functional linear regression model for a regression situation where the response variable is a scalar and the predictor is a random function. A linear predictor is obtained by forming the scalar product of the predictor function with a smooth parameter function, and the expected value of the response is related to this linear predictor via a link function. If in addition a variance function is specified, this leads to a functional estimating equation which corresponds to maximizing a functional quasilikelihood. This general approach includes the special cases of the functional linear model, as well as functional Poisson regression and functional binomial regression. The latter leads to procedures for classification and discrimination of stochastic processes and functional data. We also consider the situation where the link and variance functions are unknown and are estimated nonparametrically from the data, using a semiparametric quasilikelihood procedure. An essential step in our proposal is dimension reduction by approximating the predictor processes with a truncated KarhunenLoève expansion. We develop asymptotic inference for the proposed class of generalized regression models. In the proposed asymptotic approach, the truncation parameter increases with sample size, and a martingale central limit theorem is applied to establish the resulting increasing dimension asymptotics. We establish asymptotic normality for a properly scaled distance
Heterogeneities in Macroparasite Infections: Patterns and Processes
, 2002
"... ome rather complex. Some of the variation in parasite loads we observe is predictable. For example, in mammals and some other taxa, males tend to be more heavily infected than females, perhaps due to differences in immune function (Potdin 1996a, Schalk and Forbes 1997, McCurdy et al. 1998). Parasit ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
ome rather complex. Some of the variation in parasite loads we observe is predictable. For example, in mammals and some other taxa, males tend to be more heavily infected than females, perhaps due to differences in immune function (Potdin 1996a, Schalk and Forbes 1997, McCurdy et al. 1998). Parasite loads tend to increase with age and may plateau in older animals, though if acquired immunity is important (or there is parasiteinduced host mortality) then they may tdtimately decline again, so reducing the degree of parasite aggregation. Genetic differences in susceptibility to infection may also be important, though their extent and direction are much more difficult to predict. Other factors that may contribute to the observed heterogeneities in worm burdens are the condition of the host (which may be a function of parasite load), host behaviour, parasite genetics and seasonality. Comparative studies of aggregation suggest that the infection process and the habitat of the host may make
Projected Partial Likelihood and Its Application to Longitudinal Data
, 1995
"... this paper we provide a method for constructing such estimating functions. When applied to longitudinal data, this handles covariates and random dropout satisfactorily, as does partial likelihood; it avoids distributional assumptions, as does generalized estimating equations. It is obtained by proj ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
this paper we provide a method for constructing such estimating functions. When applied to longitudinal data, this handles covariates and random dropout satisfactorily, as does partial likelihood; it avoids distributional assumptions, as does generalized estimating equations. It is obtained by projecting the partial score function onto a collection of Hilbert spaces with inner product specified by conditional moments, conditioned on nested events. We also demonstrate, within a prequential frame of reference (Dawid 1984, 1991), that the estimating function is optimal among the largest collection of estimating functions that can be described by the postulated conditional moments.
2012): “Detecting differential expression in RNAsequence data using quasilikelihood with shrunken dispersion estimates
 Statistical Applications in Genetics and Molecular Biology, 11, Article 8
"... Next generation sequencing technology provides a powerful tool for measuring gene expression (mRNA) levels in the form of RNAsequence data. Method development for identifying differentially expressed (DE) genes from RNAseq data, which frequently includes many lowcount integers and can exhibit sev ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Next generation sequencing technology provides a powerful tool for measuring gene expression (mRNA) levels in the form of RNAsequence data. Method development for identifying differentially expressed (DE) genes from RNAseq data, which frequently includes many lowcount integers and can exhibit severe overdispersion relative to Poisson or binomial 1 distributions, is a popular area of ongoing research. Here we present quasilikelihood methods with shrunken dispersion estimates based on an adaptation of Smyth’s (2004) approach to estimating genespecific error variances for microarray data. Our suggested methods are computationally simple, analogous to ANOVA and compare favorably versus competing methods in detecting DE genes and estimating false discovery rates across a variety of simulations based on real data. 1
On the properties of GEE estimators in the presence of invariant covariates
 Biometrical J
, 1996
"... In this paper it is shown that the use of nonsingular block invariant matrices of covariates leads to `generalized estimating equations' estimators (GEE estimators; Liang, K.Y. & Zeger, S. (1986). Biometrika, 73(1), 1322) which are identical regardless of the `working' correlation matrix used. ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
In this paper it is shown that the use of nonsingular block invariant matrices of covariates leads to `generalized estimating equations' estimators (GEE estimators; Liang, K.Y. & Zeger, S. (1986). Biometrika, 73(1), 1322) which are identical regardless of the `working' correlation matrix used. Moreover, they are efficient (McCullagh, P. (1983). The Annals of Statistics, 11(1), 5967). If on the other hand only time invariant covariates are used the efficiency gain in choosing the `correct' vs. an `incorrect' correlation structure is shown to be negligible. The results of a simple simulation study suggest that although different GEE estimators are no more identical and are no more as efficient as an ML estimator, the differences are still negligible if both time and block invariant covariates are present. Key words: Generalized estimating equations; Invariant covariates; Asymptotic properties. 1 Introduction The `generalized estimating equations' approach (GEE approach) proposed...
Nonparametric Estimating Equations Based on a Penalized Information Criterion
, 2000
"... It has recently been observed that, given the meanvariance relation, one can improve on the accuracy of the quasilikelihood estimator by the adaptive estimator based on the estimation of the higher moments. The estimation of such moments is usually unstable, however, and consequently only for larg ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
It has recently been observed that, given the meanvariance relation, one can improve on the accuracy of the quasilikelihood estimator by the adaptive estimator based on the estimation of the higher moments. The estimation of such moments is usually unstable, however, and consequently only for large samples does the improvement become evident. The author proposes a nonparametric estimating equation that does not depend on the estimation such moments, but instead on the penalized minimization of asymptotic variance. His method provides a strong improvement over the quasilikelihood estimator and the adaptive estimators, for a wide range of sample sizes. R ESUM E Il a eteobserverecemment que pour une relation moyennevariance donnee, il est possible d'ameliorer la precision d'un estimateur de quasivraisemblance au moyen d'un estimateur adaptatif dependant des moments superieurs. L'estimation de tels moments etant toutefois instable, le gain d'e#cacite n'est appreciable que dans de ...
Spatial Scan Statistics in Loglinear Models
, 2008
"... The likelihood ratio spatial scan statistic has been widely used in spatial disease surveillance and spatial cluster detection applications. In order to better understand cluster mechanisms, an equivalent modelbased approach is proposed to the spatial scan statistic that unifies currently loosely c ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
The likelihood ratio spatial scan statistic has been widely used in spatial disease surveillance and spatial cluster detection applications. In order to better understand cluster mechanisms, an equivalent modelbased approach is proposed to the spatial scan statistic that unifies currently loosely coupled methods for including ecological covariates in the spatial scan test. In addition, the utility of the modelbased approach with a Waldbased scan statistic is demonstrated to account for overdispersion and heterogeneity in background rates. Simulation and case studies show that both the likelihood ratiobased and Waldbased scan statistics are comparable to the original spatial scan statistic.
Local mixture models of exponential families
, 2007
"... Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which this set of tools can be enriched in a natural and interpreta ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which this set of tools can be enriched in a natural and interpretable way is through mixing. This paper develops and applies the idea of local mixture modelling to exponential families. It shows that the highly interpretable and flexible models which result have enough structure to retain the attractive inferential properties of exponential families. In particular, results on identification, parameter orthogonality and logconcavity of the likelihood are proved.