M. P. Wand
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View article: Scalable Subset Selection in Linear Mixed Models
Scalable Subset Selection in Linear Mixed Models Open
Linear mixed models (LMMs), which incorporate fixed and random effects, are key tools for analyzing heterogeneous data, such as in personalized medicine. Nowadays, this type of data is increasingly wide, sometimes containing thousands of c…
View article: Online semiparametric regression via sequential Monte Carlo
Online semiparametric regression via sequential Monte Carlo Open
Summary We develop and describe online algorithms for performing online semiparametric regression analyses. Earlier work on this topic is by Luts, Broderick and Wand (2014), Journal of Computational and Graphical Statististics , 23 , 589–6…
View article: The Grouped Horseshoe Distribution and Its Statistical Properties
The Grouped Horseshoe Distribution and Its Statistical Properties Open
The Grouped Horseshoe distribution arises from hierarchical structures in the recent Bayesian methodological literature aimed at selection of groups of regression coefficients. We isolate this distribution and study its properties concerni…
View article: A variational inference framework for inverse problems
A variational inference framework for inverse problems Open
We present a framework for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy performances and re…
View article: Precise Asymptotics for Linear Mixed Models with Crossed Random Effects
Precise Asymptotics for Linear Mixed Models with Crossed Random Effects Open
We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the resu…
View article: The Grouped Horseshoe distribution and its statistical properties
The Grouped Horseshoe distribution and its statistical properties Open
The Grouped Horseshoe distribution arises from hierarchical structures in the recent Bayesian methodological literature aimed at selection of groups of regression coefficients. We isolate this distribution and study its properties concerni…
View article: Second term improvement to generalized linear mixed model asymptotics
Second term improvement to generalized linear mixed model asymptotics Open
A recent article by Jiang et al. (2022) on generalized linear mixed model asymptotics derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If m denotes the number of groups and n is the average wi…
View article: Online Semiparametric Regression via Sequential Monte Carlo
Online Semiparametric Regression via Sequential Monte Carlo Open
We develop and describe online algorithms for performing online semiparametric regression analyses. Earlier work on this topic is in Luts, Broderick & Wand (J. Comput. Graph. Statist., 2014) where online mean field variational Bayes was em…
View article: High-Dimensional Bernstein Von-Mises Theorems for Covariance and Precision Matrices
High-Dimensional Bernstein Von-Mises Theorems for Covariance and Precision Matrices Open
This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis focus…
View article: Second Term Improvement to Generalised Linear Mixed Model Asymptotics
Second Term Improvement to Generalised Linear Mixed Model Asymptotics Open
A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…
View article: Dispersion Parameter Extension of Precise Generalized Linear Mixed Model Asymptotics
Dispersion Parameter Extension of Precise Generalized Linear Mixed Model Asymptotics Open
We extend a recently established asymptotic normality theorem for generalized linear mixed models to include the dispersion parameter. The new results show that the maximum likelihood estimators of all model parameters have asymptotically …
View article: Streamlined Variational Inference for Linear Mixed Models with Crossed Random Effects
Streamlined Variational Inference for Linear Mixed Models with Crossed Random Effects Open
We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groups are arbitrarily large, streamlining is hin…
View article: Bayesian Generalized Additive Model Selection Including a Fast Variational Option
Bayesian Generalized Additive Model Selection Including a Fast Variational Option Open
We use Bayesian model selection paradigms, such as group least absolute shrinkage and selection operator priors, to facilitate generalized additive model selection. Our approach allows for the effects of continuous predictors to be categor…
View article: Sparse linear mixed model selection via streamlined variational Bayes
Sparse linear mixed model selection via streamlined variational Bayes Open
Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it i…
View article: Sparse Linear Mixed Model Selection via Streamlined Variational Bayes
Sparse Linear Mixed Model Selection via Streamlined Variational Bayes Open
Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it i…
View article: Fast approximate inference for multivariate longitudinal data
Fast approximate inference for multivariate longitudinal data Open
Summary Collecting information on multiple longitudinal outcomes is increasingly common in many clinical settings. In many cases, it is desirable to model these outcomes jointly. However, in large data sets, with many outcomes, computation…
View article: A variational inference framework for inverse problems
A variational inference framework for inverse problems Open
A framework is presented for fitting inverse problem models via variational Bayes approximations. This methodology guarantees flexibility to statistical model specification for a broad range of applications, good accuracy and reduced model…
View article: Density Estimation via Bayesian Inference Engines
Density Estimation via Bayesian Inference Engines Open
We explain how effective automatic probability density function estimates can be constructed using contemporary Bayesian inference engines such as those based on no-U-turn sampling and expectation propagation. Extensive simulation studies …
View article: Streamlined variational inference for higher level group-specific curve models
Streamlined variational inference for higher level group-specific curve models Open
A two-level group-specific curve model is such that the mean response of each member of a group is a separate smooth function of a predictor of interest. The three-level extension is such that one grouping variable is nested within another…
View article: The Inverse G-Wishart Distribution and Variational Message Passing
The Inverse G-Wishart Distribution and Variational Message Passing Open
Message passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily graphical large models. The notion of a factor graph fragment allows for compartmentalization of algebra and comput…
View article: STREAMLINED SOLUTIONS TO MULTILEVEL SPARSE MATRIX PROBLEMS
STREAMLINED SOLUTIONS TO MULTILEVEL SPARSE MATRIX PROBLEMS Open
We define and solve classes of sparse matrix problems that arise in multilevel modelling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation, in which data…
View article: Streamlined Variational Inference for Linear Mixed Models with Crossed Random Effects
Streamlined Variational Inference for Linear Mixed Models with Crossed Random Effects Open
We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groups are arbitrarily large, streamlining is hin…
View article: Fast and Accurate Binary Response Mixed Model Analysis via Expectation Propagation
Fast and Accurate Binary Response Mixed Model Analysis via Expectation Propagation Open
Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to …
View article: Streamlined Variational Inference for Higher Level Group-Specific Curve Models
Streamlined Variational Inference for Higher Level Group-Specific Curve Models Open
A two-level group-specific curve model is such that the mean response of each member of a group is a separate smooth function of a predictor of interest. The three-level extension is such that one grouping variable is nested within another…
View article: Streamlined Computing for Variational Inference with Higher Level Random Effects
Streamlined Computing for Variational Inference with Higher Level Random Effects Open
We derive and present explicit algorithms to facilitate streamlined computing for variational inference for models containing higher level random effects. Existing literature, such as Lee and Wand (2016), is such that streamlined variation…
View article: Solutions to Sparse Multilevel Matrix Problems
Solutions to Sparse Multilevel Matrix Problems Open
We define and solve classes of sparse matrix problems that arise in multilevel modeling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation in which data o…