Efficient data augmentation techniques for some classes of state space models

Data augmentation improves the convergence of iterative algorithms, such as the EM algorithm and Gibbs sampler by introducing carefully designed latent variables. In this article, we first propose a data augmentation scheme for the first-order autoregression plus noise model, where optimal values of working parameters introduced for recentering and rescaling of the latent states, can be derived analytically by minimizing the fraction of missing information in the EM algorithm. The proposed data augmentation scheme is then utilized to design efficient Markov chain Monte Carlo (MCMC) algorithms for Bayesian inference of some non-Gaussian and nonlinear state space models, via a mixture of normals approximation coupled with a block-specific reparametrization strategy. Applications on simulated and benchmark real datasets indicate that the proposed MCMC sampler can yield improvements in simulation efficiency compared with centering, noncentering and even the ancillarity-sufficiency interweaving strategy.Comment: Keywords: Data augmentation, State space model, Stochastic volatility model, EM algorithm, Reparametrization, Markov chain Monte Carlo, Ancillarity-sufficiency interweaving strateg

The impact of Group Intelligence software on enquiry-based learning

Despite the increasing use of groupware technologies in education, there is little evidence of their impact, especially within an enquiry-based learning (EBL) context. In this paper, we examine the use of a commercial standard Group Intelligence software called GroupSystems®ThinkTank. To date, ThinkTank has been adopted mainly in the USA and supports teams in generating ideas, categorising, prioritising, voting and multi-criteria decision-making and automatically generates a report at the end of each session. The software was used by students carrying out an EBL project, set by employers, for a full academic year. The criteria for assessing the impact of ThinkTank on student learning were those of creativity, participation, productivity, engagement and understanding. Data was collected throughout the year using a combination of interviews and questionnaires, and written feedback from employers. The overall findings show an increase in levels of productivity and creativity, evidence of a deeper understanding of their work but some variation in attitudes towards participation in the early stages of the project

Variational Inference for Generalized Linear Mixed Models Using Partially Noncentered Parametrizations

The effects of different parametrizations on the convergence of Bayesian computational algorithms for hierarchical models are well explored. Techniques such as centering, noncentering and partial noncentering can be used to accelerate convergence in MCMC and EM algorithms but are still not well studied for variational Bayes (VB) methods. As a fast deterministic approach to posterior approximation, VB is attracting increasing interest due to its suitability for large high-dimensional data. Use of different parametrizations for VB has not only computational but also statistical implications, as different parametrizations are associated with different factorized posterior approximations. We examine the use of partially noncentered parametrizations in VB for generalized linear mixed models (GLMMs). Our paper makes four contributions. First, we show how to implement an algorithm called nonconjugate variational message passing for GLMMs. Second, we show that the partially noncentered parametrization can adapt to the quantity of information in the data and determine a parametrization close to optimal. Third, we show that partial noncentering can accelerate convergence and produce more accurate posterior approximations than centering or noncentering. Finally, we demonstrate how the variational lower bound, produced as part of the computation, can be useful for model selection.Comment: Published in at http://dx.doi.org/10.1214/13-STS418 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org