225 research outputs found
Composite Gaussian process models for emulating expensive functions
A new type of nonstationary Gaussian process model is developed for
approximating computationally expensive functions. The new model is a composite
of two Gaussian processes, where the first one captures the smooth global trend
and the second one models local details. The new predictor also incorporates a
flexible variance model, which makes it more capable of approximating surfaces
with varying volatility. Compared to the commonly used stationary Gaussian
process model, the new predictor is numerically more stable and can more
accurately approximate complex surfaces when the experimental design is sparse.
In addition, the new model can also improve the prediction intervals by
quantifying the change of local variability associated with the response.
Advantages of the new predictor are demonstrated using several examples.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS570 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Structured variable selection and estimation
In linear regression problems with related predictors, it is desirable to do
variable selection and estimation by maintaining the hierarchical or structural
relationships among predictors. In this paper we propose non-negative garrote
methods that can naturally incorporate such relationships defined through
effect heredity principles or marginality principles. We show that the methods
are very easy to compute and enjoy nice theoretical properties. We also show
that the methods can be easily extended to deal with more general regression
problems such as generalized linear models. Simulations and real examples are
used to illustrate the merits of the proposed methods.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS254 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Population Quasi-Monte Carlo
Monte Carlo methods are widely used for approximating complicated,
multidimensional integrals for Bayesian inference. Population Monte Carlo (PMC)
is an important class of Monte Carlo methods, which utilizes a population of
proposals to generate weighted samples that approximate the target
distribution. The generic PMC framework iterates over three steps: samples are
simulated from a set of proposals, weights are assigned to such samples to
correct for mismatch between the proposal and target distributions, and the
proposals are then adapted via resampling from the weighted samples. When the
target distribution is expensive to evaluate, the PMC has its computational
limitation since the convergence rate is . To address
this, we propose in this paper a new Population Quasi-Monte Carlo (PQMC)
framework, which integrates Quasi-Monte Carlo ideas within the sampling and
adaptation steps of PMC. A key novelty in PQMC is the idea of importance
support points resampling, a deterministic method for finding an "optimal"
subsample from the weighted proposal samples. Moreover, within the PQMC
framework, we develop an efficient covariance adaptation strategy for
multivariate normal proposals. Lastly, a new set of correction weights is
introduced for the weighted PMC estimator to improve the efficiency from the
standard PMC estimator. We demonstrate the improved empirical convergence of
PQMC over PMC in extensive numerical simulations and a friction drilling
application.Comment: Submitted to Journal of Computational and Graphical Statistic
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