139 research outputs found
A Simple Approach to Constructing Quasi-Sudoku-based Sliced Space-Filling Designs
Sliced Sudoku-based space-filling designs and, more generally, quasi-sliced
orthogonal array-based space-filling designs are useful experimental designs in
several contexts, including computer experiments with categorical in addition
to quantitative inputs and cross-validation. Here, we provide a straightforward
construction of doubly orthogonal quasi-Sudoku Latin squares which can be used
to generate sliced space-filling designs which achieve uniformity in one and
two-dimensional projections for both the full design and each slice. A
construction of quasi-sliced orthogonal arrays based on these constructed
doubly orthogonal quasi-Sudoku Latin squares is also provided and can, in turn,
be used to generate sliced space-filling designs which achieve uniformity in
one and two-dimensional projections for the full design and and uniformity in
two-dimensional projections for each slice. These constructions are very
practical to implement and yield a spectrum of design sizes and numbers of
factors not currently broadly available.Comment: 15 pages, 9 figure
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
Variational Bayes with Intractable Likelihood
Variational Bayes (VB) is rapidly becoming a popular tool for Bayesian
inference in statistical modeling. However, the existing VB algorithms are
restricted to cases where the likelihood is tractable, which precludes the use
of VB in many interesting situations such as in state space models and in
approximate Bayesian computation (ABC), where application of VB methods was
previously impossible. This paper extends the scope of application of VB to
cases where the likelihood is intractable, but can be estimated unbiasedly. The
proposed VB method therefore makes it possible to carry out Bayesian inference
in many statistical applications, including state space models and ABC. The
method is generic in the sense that it can be applied to almost all statistical
models without requiring too much model-based derivation, which is a drawback
of many existing VB algorithms. We also show how the proposed method can be
used to obtain highly accurate VB approximations of marginal posterior
distributions.Comment: 40 pages, 6 figure
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