28,824 research outputs found
Causal graphical models in systems genetics: A unified framework for joint inference of causal network and genetic architecture for correlated phenotypes
Causal inference approaches in systems genetics exploit quantitative trait
loci (QTL) genotypes to infer causal relationships among phenotypes. The
genetic architecture of each phenotype may be complex, and poorly estimated
genetic architectures may compromise the inference of causal relationships
among phenotypes. Existing methods assume QTLs are known or inferred without
regard to the phenotype network structure. In this paper we develop a
QTL-driven phenotype network method (QTLnet) to jointly infer a causal
phenotype network and associated genetic architecture for sets of correlated
phenotypes. Randomization of alleles during meiosis and the unidirectional
influence of genotype on phenotype allow the inference of QTLs causal to
phenotypes. Causal relationships among phenotypes can be inferred using these
QTL nodes, enabling us to distinguish among phenotype networks that would
otherwise be distribution equivalent. We jointly model phenotypes and QTLs
using homogeneous conditional Gaussian regression models, and we derive a
graphical criterion for distribution equivalence. We validate the QTLnet
approach in a simulation study. Finally, we illustrate with simulated data and
a real example how QTLnet can be used to infer both direct and indirect effects
of QTLs and phenotypes that co-map to a genomic region.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS288 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Accelerating Asymptotically Exact MCMC for Computationally Intensive Models via Local Approximations
We construct a new framework for accelerating Markov chain Monte Carlo in
posterior sampling problems where standard methods are limited by the
computational cost of the likelihood, or of numerical models embedded therein.
Our approach introduces local approximations of these models into the
Metropolis-Hastings kernel, borrowing ideas from deterministic approximation
theory, optimization, and experimental design. Previous efforts at integrating
approximate models into inference typically sacrifice either the sampler's
exactness or efficiency; our work seeks to address these limitations by
exploiting useful convergence characteristics of local approximations. We prove
the ergodicity of our approximate Markov chain, showing that it samples
asymptotically from the \emph{exact} posterior distribution of interest. We
describe variations of the algorithm that employ either local polynomial
approximations or local Gaussian process regressors. Our theoretical results
reinforce the key observation underlying this paper: when the likelihood has
some \emph{local} regularity, the number of model evaluations per MCMC step can
be greatly reduced without biasing the Monte Carlo average. Numerical
experiments demonstrate multiple order-of-magnitude reductions in the number of
forward model evaluations used in representative ODE and PDE inference
problems, with both synthetic and real data.Comment: A major update of the theory and example
Efficiency Analysis of Swarm Intelligence and Randomization Techniques
Swarm intelligence has becoming a powerful technique in solving design and
scheduling tasks. Metaheuristic algorithms are an integrated part of this
paradigm, and particle swarm optimization is often viewed as an important
landmark. The outstanding performance and efficiency of swarm-based algorithms
inspired many new developments, though mathematical understanding of
metaheuristics remains partly a mystery. In contrast to the classic
deterministic algorithms, metaheuristics such as PSO always use some form of
randomness, and such randomization now employs various techniques. This paper
intends to review and analyze some of the convergence and efficiency associated
with metaheuristics such as firefly algorithm, random walks, and L\'evy
flights. We will discuss how these techniques are used and their implications
for further research.Comment: 10 pages. arXiv admin note: substantial text overlap with
arXiv:1212.0220, arXiv:1208.0527, arXiv:1003.146
Statistical and Computational Tradeoff in Genetic Algorithm-Based Estimation
When a Genetic Algorithm (GA), or a stochastic algorithm in general, is
employed in a statistical problem, the obtained result is affected by both
variability due to sampling, that refers to the fact that only a sample is
observed, and variability due to the stochastic elements of the algorithm. This
topic can be easily set in a framework of statistical and computational
tradeoff question, crucial in recent problems, for which statisticians must
carefully set statistical and computational part of the analysis, taking
account of some resource or time constraints. In the present work we analyze
estimation problems tackled by GAs, for which variability of estimates can be
decomposed in the two sources of variability, considering some constraints in
the form of cost functions, related to both data acquisition and runtime of the
algorithm. Simulation studies will be presented to discuss the statistical and
computational tradeoff question.Comment: 17 pages, 5 figure
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