2,583 research outputs found
Fully simplified multivariate normal updates in non-conjugate variational message passing
No full textFully simplified expressions for Multivariate Normal updates in non-conjugate variational message passing approximate inference schemes are obtained. The simplicity of these expressions means that the updates can be achieved very eficiently. Since the Multivariate Normal family is the most common for approximating the joint posterior density function of a continuous parameter vector, these fully simplified updates are of great practical benefit. © 2014 Matt P. Wand
Mixed model-based additive models for sample extremes
No full textWe consider additive models fitting and inference when the response variable is a sample extreme. Non-linear covariate effects are handled using the mixed model representation of penalised splines. A fitting algorithm based on likelihood approximations is derived. The efficacy of the resulting methodology is demonstrated via application to simulated and real data. © 2008 Elsevier B.V. All rights reserved
Streamlined Variational Inference for Linear Mixed Models with Crossed Random Effects
No full textWe 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 hindered by lack of sparseness in the underlying least squares system. Because of this fact we also consider a hierarchy of relaxations of the mean field product restriction. The least stringent product restriction delivers a high degree of inferential accuracy. However, this accuracy must be mitigated against its higher storage and computing demands. Faster sparse storage and computing alternatives are also provided, but come with the price of diminished inferential accuracy. This article provides full algorithmic details of three variational inference strategies, presents detailed empirical results on their pros and cons and, thus, guides the users on their choice of variational inference approach depending on the problem size and computing resources. Supplementary materials for this article are available online
Bringing coals to Newcastle
No full text© 2016 The Royal Statistical Society Making effective public policy decisions is challenging at the best of times, but especially in the context of environmental regulation, which typically requires managing opposing interests and strong opinions from industry and private citizens. In this case study, Louise Ryan, Matt Wand and Alan Malecki show how statistical analysis can help resolve conflict and inform effective decision-making under uncertainty
Additive models for geo-referenced failure time data
No full textAsthma researchers have found some evidence that geographical variations in susceptibility to asthma could reflect the effect of community level factors such as exposure to violence. Our methodology was motivated by a study of age at onset of asthma among children of inner-city neighbourhoods in East Boston. Cox's proportional hazards model was not appropriate since there was not enough information about the nature of geographical variations so as to impose a parametric relationship. In addition, some of the known risk factors were believed to have non-linear log-hazard ratios. We extend the geoadditive models of Kamman and Wand to the case where the outcome measure is a possibly censored time to event. We reduce the problem to one of fitting a Poisson mixed model by using Poisson approximations in conjunction with a mixed model formulation of generalized additive modelling. Our method allows for low-rank additive modelling, provides likelihood-based estimation of all parameters including the amount of smoothing and can be implemented using standard software. We illustrate our method on the East Boston data. Copyright © 2005 John Wiley & Sons, Ltd
Application of the IS-MP-IA model to the German economy and policy implications
No full textExtending the IS-MP-IA model developed by Romer (2000) and applying the GARCH (Engle, 1982, 2001) methodology, the author finds that equilibrium GDP in Germany is positively affected by stock market performance and real exchange rate appreciation, and negatively influenced by the expected inflation rate, the government deficit/GDP ratio, and the U.S. federal funds rate. The relatively low deficit/GDP ratio of 1.83% in 2003 indicates that its fiscal condition was healthy. However, some other EU members may need to exercise fiscal discipline. Because real appreciation has a positive impact on output, a stronger euro may not be a concern for Germany but may be worried by those EU member nations which depend upon exports to stimulate their economies.
ks: Kernel Density Estimation and Kernel Discriminant Analysis for Multivariate Data in R
No full textKernel smoothing is one of the most widely used non-parametric data smoothing techniques. We introduce a new R package ks for multivariate kernel smoothing. Currently it contains functionality for kernel density estimation and kernel discriminant analysis. It is a comprehensive package for bandwidth matrix selection, implementing a wide range of data-driven diagonal and unconstrained bandwidth selectors.
Sparse Linear Mixed Model Selection via Streamlined Variational Bayes
No full textLinear 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 is of interest to select a parsimonious subset of those being
effectively relevant for predicting the response variable. Variational
approximations facilitate fast approximate Bayesian inference for the
parameters of a variety of statistical models, including linear mixed models.
However, for models having a high number of fixed or random effects, simple
application of standard variational inference principles does not lead to fast
approximate inference algorithms, due to the size of model design matrices and
inefficient treatment of sparse matrix problems arising from the required
approximating density parameters updates. We illustrate how recently developed
streamlined variational inference procedures can be generalized to make fast
and accurate inference for the parameters of linear mixed models with nested
random effects and global-local priors for Bayesian fixed effects selection.
Our variational inference algorithms achieve convergence to the same optima of
their standard implementations, although with significantly lower computational
effort, memory usage and time, especially for large numbers of random effects.
Using simulated and real data examples, we assess the quality of automated
procedures for fixed effects selection that are free from hyperparameters
tuning and only rely upon variational posterior approximations. Moreover, we
show high accuracy of variational approximations against model fitting via
Markov Chain Monte Carlo sampling
Online Semiparametric Regression via Sequential Monte Carlo
No full text\ua9 2025 Statistical Society of Australia. 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, 589–615, where online mean-field variational Bayes (MFVB) was employed. In this article we instead develop sequential Monte Carlo approaches to circumvent well-known inaccuracies inherent in variational approaches. For Gaussian response semiparametric regression models, our new algorithms share the online MFVB property of only requiring updating and storage of sufficient statistics quantities of streaming data. In the non-Gaussian case, accurate online semiparametric regression requires the full data to be kept in storage. The new algorithms allow for new options concerning accuracy–speed trade-offs for online semiparametric regression
Streamlined Computing for Variational Inference with Higher Level Random Effects
No full textWe 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
variational inference is restricted to mean field variational Bayes algorithms
for two-level random effects models. Here we provide the following extensions:
(1) explicit Gaussian response mean field variational Bayes algorithms for
three-level models, (2) explicit algorithms for the alternative variational
message passing approach in the case of two-level and three-level models, and
(3) an explanation of how arbitrarily high levels of nesting can be handled
based on the recently published matrix algebraic results of the authors. A
pay-off from (2) is simple extension to non-Gaussian response models. In
summary, we remove barriers for streamlining variational inference algorithms
based on either the mean field variational Bayes approach or the variational
message passing approach when higher level random effects are present
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