38 research outputs found
Markov Chain Monte Carlo Based on Deterministic Transformations
In this article we propose a novel MCMC method based on deterministic
transformations T: X x D --> X where X is the state-space and D is some set
which may or may not be a subset of X. We refer to our new methodology as
Transformation-based Markov chain Monte Carlo (TMCMC). One of the remarkable
advantages of our proposal is that even if the underlying target distribution
is very high-dimensional, deterministic transformation of a one-dimensional
random variable is sufficient to generate an appropriate Markov chain that is
guaranteed to converge to the high-dimensional target distribution. Apart from
clearly leading to massive computational savings, this idea of
deterministically transforming a single random variable very generally leads to
excellent acceptance rates, even though all the random variables associated
with the high-dimensional target distribution are updated in a single block.
Since it is well-known that joint updating of many random variables using
Metropolis-Hastings (MH) algorithm generally leads to poor acceptance rates,
TMCMC, in this regard, seems to provide a significant advance. We validate our
proposal theoretically, establishing the convergence properties. Furthermore,
we show that TMCMC can be very effectively adopted for simulating from doubly
intractable distributions.
TMCMC is compared with MH using the well-known Challenger data, demonstrating
the effectiveness of of the former in the case of highly correlated variables.
Moreover, we apply our methodology to a challenging posterior simulation
problem associated with the geostatistical model of Diggle et al. (1998),
updating 160 unknown parameters jointly, using a deterministic transformation
of a one-dimensional random variable. Remarkable computational savings as well
as good convergence properties and acceptance rates are the results.Comment: 28 pages, 3 figures; Longer abstract inside articl
A Matrix--free Likelihood Method for Exploratory Factor Analysis of High-dimensional Gaussian Data
This paper proposes a novel profile likelihood method for estimating the
covariance parameters in exploratory factor analysis of high-dimensional
Gaussian datasets with fewer observations than number of variables. An
implicitly restarted Lanczos algorithm and a limited-memory quasi-Newton method
are implemented to develop a matrix-free framework for likelihood maximization.
Simulation results show that our method is substantially faster than the
expectation-maximization solution without sacrificing accuracy. Our method is
applied to fit factor models on data from suicide attempters, suicide ideators
and a control group.Comment: 10 pages, 5 figures, 4 table
Model-based Personalized Synthetic MR Imaging
Synthetic Magnetic Resonance (MR) imaging predicts images at new design
parameter settings from a few observed MR scans. Model-based methods, that use
both the physical and statistical properties underlying the MR signal and its
acquisition, can predict images at any setting from as few as three scans,
allowing it to be used in individualized patient- and anatomy-specific
contexts. However, the estimation problem in model-based synthetic MR imaging
is ill-posed and so regularization, in the form of correlated Gaussian Markov
Random Fields, is imposed on the voxel-wise spin-lattice relaxation time,
spin-spin relaxation time and the proton density underlying the MR image. We
develop theoretically sound but computationally practical matrix-free
estimation methods for synthetic MR imaging. Our evaluations demonstrate
excellent ability of our methods to synthetize MR images in a clinical
framework and also estimation and prediction accuracy and consistency. An added
strength of our model-based approach, also developed and illustrated here, is
the accurate estimation of standard errors of regional means in the synthesized
images.Comment: 13 pages, 5 figures, 5 table
Adjusting for Spatial Effects in Genomic Prediction
This paper investigates the problem of adjusting for spatial effects in genomic prediction. Despite being seldomly considered in genome-wide association studies (GWAS), spatial effects often affect phenotypic measurements of plants. We consider a Gaussian random field (GRF) model with an additive covariance structure that incorporates genotype effects, spatial effects and subpopulation effects. An empirical study shows the existence of spatial effects and heterogeneity across different subpopulation families while simulations illustrate the improvement in selecting genotypically superior plants by adjusting for spatial effects in genomic prediction