8,072 research outputs found
Multidimensional integration through Markovian sampling under steered function morphing: a physical guise from statistical mechanics
We present a computational strategy for the evaluation of multidimensional
integrals on hyper-rectangles based on Markovian stochastic exploration of the
integration domain while the integrand is being morphed by starting from an
initial appropriate profile. Thanks to an abstract reformulation of Jarzynski's
equality applied in stochastic thermodynamics to evaluate the free-energy
profiles along selected reaction coordinates via non-equilibrium
transformations, it is possible to cast the original integral into the
exponential average of the distribution of the pseudo-work (that we may term
"computational work") involved in doing the function morphing, which is
straightforwardly solved. Several tests illustrate the basic implementation of
the idea, and show its performance in terms of computational time, accuracy and
precision. The formulation for integrand functions with zeros and possible sign
changes is also presented. It will be stressed that our usage of Jarzynski's
equality shares similarities with a practice already known in statistics as
Annealed Importance Sampling (AIS), when applied to computation of the
normalizing constants of distributions. In a sense, here we dress the AIS with
its "physical" counterpart borrowed from statistical mechanics.Comment: 3 figures Supplementary Material (pdf file named "JEMDI_SI.pdf"
Bayesian Methods for Exoplanet Science
Exoplanet research is carried out at the limits of the capabilities of
current telescopes and instruments. The studied signals are weak, and often
embedded in complex systematics from instrumental, telluric, and astrophysical
sources. Combining repeated observations of periodic events, simultaneous
observations with multiple telescopes, different observation techniques, and
existing information from theory and prior research can help to disentangle the
systematics from the planetary signals, and offers synergistic advantages over
analysing observations separately. Bayesian inference provides a
self-consistent statistical framework that addresses both the necessity for
complex systematics models, and the need to combine prior information and
heterogeneous observations. This chapter offers a brief introduction to
Bayesian inference in the context of exoplanet research, with focus on time
series analysis, and finishes with an overview of a set of freely available
programming libraries.Comment: Invited revie
Measuring edge importance: a quantitative analysis of the stochastic shielding approximation for random processes on graphs
Mathematical models of cellular physiological mechanisms often involve random
walks on graphs representing transitions within networks of functional states.
Schmandt and Gal\'{a}n recently introduced a novel stochastic shielding
approximation as a fast, accurate method for generating approximate sample
paths from a finite state Markov process in which only a subset of states are
observable. For example, in ion channel models, such as the Hodgkin-Huxley or
other conductance based neural models, a nerve cell has a population of ion
channels whose states comprise the nodes of a graph, only some of which allow a
transmembrane current to pass. The stochastic shielding approximation consists
of neglecting fluctuations in the dynamics associated with edges in the graph
not directly affecting the observable states. We consider the problem of
finding the optimal complexity reducing mapping from a stochastic process on a
graph to an approximate process on a smaller sample space, as determined by the
choice of a particular linear measurement functional on the graph. The
partitioning of ion channel states into conducting versus nonconducting states
provides a case in point. In addition to establishing that Schmandt and
Gal\'{a}n's approximation is in fact optimal in a specific sense, we use recent
results from random matrix theory to provide heuristic error estimates for the
accuracy of the stochastic shielding approximation for an ensemble of random
graphs. Moreover, we provide a novel quantitative measure of the contribution
of individual transitions within the reaction graph to the accuracy of the
approximate process.Comment: Added one reference, typos corrected in Equation 6 and Appendix C,
added the assumption that the graph is irreducible to the main theorem
(results unchanged
The exit problem for diffusions with time-periodic drift and stochastic resonance
Physical notions of stochastic resonance for potential diffusions in
periodically changing double-well potentials such as the spectral power
amplification have proved to be defective. They are not robust for the passage
to their effective dynamics: continuous-time finite-state Markov chains
describing the rough features of transitions between different domains of
attraction of metastable points. In the framework of one-dimensional diffusions
moving in periodically changing double-well potentials we design a new notion
of stochastic resonance which refines Freidlin's concept of quasi-periodic
motion. It is based on exact exponential rates for the transition probabilities
between the domains of attraction which are robust with respect to the reduced
Markov chains. The quality of periodic tuning is measured by the probability
for transition during fixed time windows depending on a time scale parameter.
Maximizing it in this parameter produces the stochastic resonance points.Comment: Published at http://dx.doi.org/10.1214/105051604000000530 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
A MATLAB Package for Markov Chain Monte Carlo with a Multi-Unidimensional IRT Model
Unidimensional item response theory (IRT) models are useful when each item is designed to measure some facet of a unified latent trait. In practical applications, items are not necessarily measuring the same underlying trait, and hence the more general multi-unidimensional model should be considered. This paper provides the requisite information and description of software that implements the Gibbs sampler for such models with two item parameters and a normal ogive form. The software developed is written in the MATLAB package IRTmu2no. The package is flexible enough to allow a user the choice to simulate binary response data with multiple dimensions, set the number of total or burn-in iterations, specify starting values or prior distributions for model parameters, check convergence of the Markov chain, as well as obtain Bayesian fit statistics. Illustrative examples are provided to demonstrate and validate the use of the software package.
Copulas in finance and insurance
Copulas provide a potential useful modeling tool to represent the dependence structure
among variables and to generate joint distributions by combining given marginal
distributions. Simulations play a relevant role in finance and insurance. They are used to
replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so
on. Using copulas, it is easy to construct and simulate from multivariate distributions based
on almost any choice of marginals and any type of dependence structure. In this paper we
outline recent contributions of statistical modeling using copulas in finance and insurance.
We review issues related to the notion of copulas, copula families, copula-based dynamic and
static dependence structure, copulas and latent factor models and simulation of copulas.
Finally, we outline hot topics in copulas with a special focus on model selection and
goodness-of-fit testing
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