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Local degeneracy of Markov chain Monte Carlo methods

Kengo Kamatani (2014)

ESAIM: Probability and Statistics

We study asymptotic behavior of Markov chain Monte Carlo (MCMC) procedures. Sometimes the performances of MCMC procedures are poor and there are great importance for the study of such behavior. In this paper we call degeneracy for a particular type of poor performances. We show some equivalent conditions for degeneracy. As an application, we consider the cumulative probit model. It is well known that the natural data augmentation (DA) procedure does not work well for this model and the so-called...

Log-periodogram regression in asymmetric long memory

Josu Arteche (2000)

Kybernetika

The long memory property of a time series has long been studied and several estimates of the memory or persistence parameter at zero frequency, where the spectral density function is symmetric, are now available. Perhaps the most popular is the log periodogram regression introduced by Geweke and Porter–Hudak [gewe]. In this paper we analyse the asymptotic properties of this estimate in the seasonal or cyclical long memory case allowing for asymmetric spectral poles or zeros. Consistency and asymptotic...

Low-discrepancy point sets for non-uniform measures

Christoph Aistleitner, Josef Dick (2014)

Acta Arithmetica

We prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure μ on the d-dimensional unit cube. We improve a theorem of Beck, by showing that for any d ≥ 1, N ≥ 1, and any non-negative, normalized Borel measure μ on [ 0 , 1 ] d there exists a point set x 1 , . . . , x N [ 0 , 1 ] d whose star-discrepancy with respect to μ is of order D N * ( x 1 , . . . , x N ; μ ) ( ( l o g N ) ( 3 d + 1 ) / 2 ) / N . For the proof we use a theorem of Banaszczyk concerning the balancing of vectors, which implies an upper bound for the linear discrepancy...

Mean field limit for the one dimensional Vlasov-Poisson equation

Maxime Hauray (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

We consider systems of N particles in dimension one, driven by pair Coulombian or gravitational interactions. When the number of particles goes to infinity in the so called mean field scaling, we formally expect convergence towards the Vlasov-Poisson equation. Actually a rigorous proof of that convergence was given by Trocheris in [Tro86]. Here we shall give a simpler proof of this result, and explain why it implies the so-called “Propagation of molecular chaos”. More precisely, both results will...

Medidas de incertidumbre asociadas a J-divergencias.

Miquel Salicrú Pages, Miquel Calvo Llorca (1988)

Trabajos de Estadística

En este trabajo se presenta la familia de medidas de incertidumbre asociadas a J-divergencias, que resultan de la distancia entre una distribución y la distribución en la que todos los procesos son equiprobables. Se estudian propiedades teóricas de la familia atendiendo a la pérdida de incertidumbre, a la concavidad y a la condición de medida decisiva. Finalmente se compara a nivel muestral la medida de incertidumbre definida por la función φ(t) = -t log t con las medidas de entropía comúnmente...

Minimum variance importance sampling via Population Monte Carlo

R. Douc, A. Guillin, J.-M. Marin, C. P. Robert (2007)

ESAIM: Probability and Statistics

Variance reduction has always been a central issue in Monte Carlo experiments. Population Monte Carlo can be used to this effect, in that a mixture of importance functions, called a D-kernel, can be iteratively optimized to achieve the minimum asymptotic variance for a function of interest among all possible mixtures. The implementation of this iterative scheme is illustrated for the computation of the price of a European option in the Cox-Ingersoll-Ross model. A Central Limit theorem as well...

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Andries, Erik, Umarov, Sabir, Steinberg, Stanly (2006)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step) of the Cauchy problem for...

Multivariate multiple comparisons with a control in elliptical populations

Naoya Okamoto, Takashi Seo (2013)

Discussiones Mathematicae Probability and Statistics

The approximate upper percentile of Hotelling's T²-type statistic is derived in order to construct simultaneous confidence intervals for comparisons with a control under elliptical populations with unequal sample sizes. Accuracy and conservativeness of Bonferroni approximations are evaluated via a Monte Carlo simulation study. Finally, we explain the real data analysis using procedures derived in this paper.

Nonlinear filtering for observations on a random vector field along a random path. Application to atmospheric turbulent velocities

Christophe Baehr (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

To filter perturbed local measurements on a random medium, a dynamic model jointly with an observation transfer equation are needed. Some media given by PDE could have a local probabilistic representation by a Lagrangian stochastic process with mean-field interactions. In this case, we define the acquisition process of locally homogeneous medium along a random path by a Lagrangian Markov process conditioned to be in a domain following the path and conditioned to the observations. The nonlinear...

Numerical solution of a stochastic model of a ball-type vibration absorber

Fischer, Cyril, Náprstek, Jiří (2021)

Programs and Algorithms of Numerical Mathematics

The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplification, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect which can...

Numerical study of the systematic error in Monte Carlo schemes for semiconductors

Orazio Muscato, Wolfgang Wagner, Vincenza Di Stefano (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The paper studies the convergence behavior of Monte Carlo schemes for semiconductors. A detailed analysis of the systematic error with respect to numerical parameters is performed. Different sources of systematic error are pointed out and illustrated in a spatially one-dimensional test case. The error with respect to the number of simulation particles occurs during the calculation of the internal electric field. The time step error, which is related to the splitting of transport and electric field...

Currently displaying 81 – 100 of 185