On simulation of random vectors by given densities in regions and on their boundaries

1994 ◽  
Vol 31 (1) ◽  
pp. 205-220 ◽  
Author(s):  
K. A. Borovkov
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Stochastic Simulation ◽  
Universal Method ◽  
Random Vectors ◽  
Remarkable Feature ◽  
Dynamic Monte Carlo ◽  
Simple Simulation ◽  
Simulation Based ◽  
Open Region

We suggest a new universal method of stochastic simulation, allowing us to generate rather efficiently random vectors with arbitrary densities in a connected open region or on its boundary. Our method belongs to the class of dynamic Monte Carlo procedures and is based on a special construction of a Markov chain on the boundary of the region. Its remarkable feature is that this chain admits a simple simulation, based on a universal (depending only on the dimensionality of the space) stochastic driver.

On simulation of random vectors by given densities in regions and on their boundaries

1994 ◽  
Vol 31 (01) ◽  
pp. 205-220
Author(s):  
K. A. Borovkov
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Stochastic Simulation ◽  
Universal Method ◽  
Random Vectors ◽  
Remarkable Feature ◽  
Dynamic Monte Carlo ◽  
Simple Simulation ◽  
Simulation Based ◽  
Open Region

We suggest a new universal method of stochastic simulation, allowing us to generate rather efficiently random vectors with arbitrary densities in a connected open region or on its boundary. Our method belongs to the class of dynamic Monte Carlo procedures and is based on a special construction of a Markov chain on the boundary of the region. Its remarkable feature is that this chain admits a simple simulation, based on a universal (depending only on the dimensionality of the space) stochastic driver.

scholarly journals Exact likelihood-free Markov chain Monte Carlo for elliptically contoured distributions

2015 ◽  
Vol 14 (4) ◽  
Author(s):  
Patrick Muchmore ◽  
Paul Marjoram
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Stationary Distribution ◽  
Large Family ◽  
Multivariate Normal ◽  
Elliptically Contoured Distributions ◽  
Simulation Based ◽  
A Chain ◽  
Elliptically Contoured

AbstractRecent results in Markov chain Monte Carlo (MCMC) show that a chain based on an unbiased estimator of the likelihood can have a stationary distribution identical to that of a chain based on exact likelihood calculations. In this paper we develop such an estimator for elliptically contoured distributions, a large family of distributions that includes and generalizes the multivariate normal. We then show how this estimator, combined with pseudorandom realizations of an elliptically contoured distribution, can be used to run MCMC in a way that replicates the stationary distribution of a likelihood based chain, but does not require explicit likelihood calculations. Because many elliptically contoured distributions do not have closed form densities, our simulation based approach enables exact MCMC based inference in a range of cases where previously it was impossible.

scholarly journals Simple Planar Truss (Linear, Nonlinear and Stochastic Approach)

2016 ◽  
Vol 66 (2) ◽  
pp. 5-12 ◽  
Author(s):  
Karel Frydrýšek ◽  
Roland Jančo
Keyword(s):  
Plastic Deformation ◽  
Monte Carlo ◽  
Stochastic Simulation ◽  
Reliability Assessment ◽  
Stochastic Approach ◽  
Maclaurin Series ◽  
Monte Carlo Approach ◽  
Reliability Method ◽  
Simulation Based ◽  
Linear And Nonlinear

Abstract This article deals with a simple planar and statically determinate pin-connected truss. It demonstrates the processes and methods of derivations and solutions according to 1st and 2nd order theories. The article applies linear and nonlinear approaches and their simplifications via a Maclaurin series. Programming connected with the stochastic Simulation-Based Reliability Method (i.e. the direct Monte Carlo approach) is used to conduct a probabilistic reliability assessment (i.e. a calculation of the probability that plastic deformation will occur in members of the truss).

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