8,328 research outputs found
Monte Carlo Estimation of the Density of the Sum of Dependent Random Variables
We study an unbiased estimator for the density of a sum of random variables
that are simulated from a computer model. A numerical study on examples with
copula dependence is conducted where the proposed estimator performs favourably
in terms of variance compared to other unbiased estimators. We provide
applications and extensions to the estimation of marginal densities in Bayesian
statistics and to the estimation of the density of sums of random variables
under Gaussian copula dependence
Approximating Probability Densities by Iterated Laplace Approximations
The Laplace approximation is an old, but frequently used method to
approximate integrals for Bayesian calculations. In this paper we develop an
extension of the Laplace approximation, by applying it iteratively to the
residual, i.e., the difference between the current approximation and the true
function. The final approximation is thus a linear combination of multivariate
normal densities, where the coefficients are chosen to achieve a good fit to
the target distribution. We illustrate on real and artificial examples that the
proposed procedure is a computationally efficient alternative to current
approaches for approximation of multivariate probability densities. The
R-package iterLap implementing the methods described in this article is
available from the CRAN servers.Comment: to appear in Journal of Computational and Graphical Statistics,
http://pubs.amstat.org/loi/jcg
Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models
This tutorial provides a gentle introduction to the particle
Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear
state-space models together with a software implementation in the statistical
programming language R. We employ a step-by-step approach to develop an
implementation of the PMH algorithm (and the particle filter within) together
with the reader. This final implementation is also available as the package
pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some
intuition as to how the algorithm operates and discuss some solutions to
problems that might occur in practice. To illustrate the use of PMH, we
consider parameter inference in a linear Gaussian state-space model with
synthetic data and a nonlinear stochastic volatility model with real-world
data.Comment: 41 pages, 7 figures. In press for Journal of Statistical Software.
Source code for R, Python and MATLAB available at:
https://github.com/compops/pmh-tutoria
Quantum Criticality and Incipient Phase Separation in the Thermodynamic Properties of the Hubbard Model
Transport measurements on the cuprates suggest the presence of a quantum
critical point hiding underneath the superconducting dome near optimal hole
doping. We provide numerical evidence in support of this scenario via a
dynamical cluster quantum Monte Carlo study of the extended two-dimensional
Hubbard model. Single particle quantities, such as the spectral function, the
quasiparticle weight and the entropy, display a crossover between two distinct
ground states: a Fermi liquid at low filling and a non-Fermi liquid with a
pseudogap at high filling. Both states are found to cross over to a marginal
Fermi-liquid state at higher temperatures. For finite next-nearest-neighbor
hopping t' we find a classical critical point at temperature T_c. This
classical critical point is found to be associated with a phase separation
transition between a compressible Mott gas and an incompressible Mott liquid
corresponding to the Fermi liquid and the pseudogap state, respectively. Since
the critical temperature T_c extrapolates to zero as t' vanishes, we conclude
that a quantum critical point connects the Fermi-liquid to the pseudogap
region, and that the marginal-Fermi-liquid behavior in its vicinity is the
analogous of the supercritical region in the liquid-gas transition.Comment: 18 pages, 9 figure
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