Describes a method of grouping and collapsing in using the Gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial. Review of related literature; Bayesian missing data probl...
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Describes a method of grouping and collapsing in using the Gibbs sampler and proves from an operator theory viewpoint that the method is in general beneficial. Review of related literature; Bayesian missing data problems; Applications.
For a stochastic matrix (Q(ij)T)i,j=1M with Q(ij)T is similar to exp(-U(ij)/T) at the off-diagonal positions, we develop an algorithm to evaluate the asymptotic convergence rate of all eigenvalues of Q(ij)T as T down ...
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For a stochastic matrix (Q(ij)T)i,j=1M with Q(ij)T is similar to exp(-U(ij)/T) at the off-diagonal positions, we develop an algorithm to evaluate the asymptotic convergence rate of all eigenvalues of Q(ij)T as T down 0 using Ventcel's optimal graphs. As an application we can compare the convergence rates of some random updating schemes used in image processing.
Maximum likelihood estimates (MLEs) in autologistic models and other exponential family models for dependent data can be calculated with Markov chain Monte Carlo methods (the metropolis algorithm or the Gibbs sampler)...
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Maximum likelihood estimates (MLEs) in autologistic models and other exponential family models for dependent data can be calculated with Markov chain Monte Carlo methods (the metropolis algorithm or the Gibbs sampler), which simulate ergodic Markov chains having equilibrium distributions in the model. From one realization of such a Markov chain, a Monte Carlo approximant to the whole likelihood function can be constructed. The parameter value (if any) maximizing this function approximates the MLE. When no parameter point in the model maximizes the likelihood, the MLE in the closure of the exponential family may exist and can be calculated by a two-phase algorithm, first finding the support of the MLE by linear programming and then finding the distribution within the family conditioned on the support by maximizing the likelihood for that family. These methods are illustrated by a constrained autologistic model for DNA fingerprint data. MLEs are compared with maximum pseudolikelihood estimates (MPLEs) and with maximum conditional likelihood estimates (MCLEs), neither of which produce acceptable estimates, the MPLE because it overestimates dependence, and the MCLE because conditioning removes the constraints.
Every time a tablecloth is draped over a table it will fold and pleat in unique ways. We report on a physically-based model and a simulation methodology, which when used together are able to reproduce many of the attr...
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The Gibbs sampler, the algorithm of metropolis and similar iterative simulation methods are potentially very helpful for summarizing multivariate distributions. Used naively, however, iterative simulation can give mis...
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This paper describes and analyses a novel distributed implementation of the simulated annealing algorithm to find a good solution to the travelling salesman problem. The implementation runs on a linear chain of proces...
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This paper describes and analyses a novel distributed implementation of the simulated annealing algorithm to find a good solution to the travelling salesman problem. The implementation runs on a linear chain of processors driven by a host processor, which plays only a supervisory role, so that the bulk of processing takes place on the chain and the efficiency of the algorithm remains high as the number of processors is increased.
A generalized simulated annealing method has been developed and applied to the optimization of functions (possibly constrained) having many local extrema. The method is illustrated in some difficult pedagogical exampl...
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A generalized simulated annealing method has been developed and applied to the optimization of functions (possibly constrained) having many local extrema. The method is illustrated in some difficult pedagogical examples and used to solve a problem analyzed by Bates (Technometrics, 25, pp. 373-376, 1983), for which we identify an improved optimum. The sensitivity of the solution to changes in the constraints and in other specifications of the problem is analyzed and discussed
In this paper, we apply the statistical mechanics formalism to study quadratic sum assignment problems (QSAP). This formalism allows us to exhibit, in the limit of large problems, the asymptotic behaviour of the optim...
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In this paper, we apply the statistical mechanics formalism to study quadratic sum assignment problems (QSAP). This formalism allows us to exhibit, in the limit of large problems, the asymptotic behaviour of the optimal value of the cost function. The conclusions of the study are confirmed by the results of metropolis computer simulations.
We apply a technique to simulate the canonical ensemble, mixing molecular dynamics and Monte Carlo techniques, in which particles suffer virtual hard shocks. In the limit of infinite time the system approaches a Boltz...
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We apply a technique to simulate the canonical ensemble, mixing molecular dynamics and Monte Carlo techniques, in which particles suffer virtual hard shocks. In the limit of infinite time the system approaches a Boltzmann distribution. A good approximation to the Boltzmann distribution is achieved in computationally accessible time for some model systems including the one-dimensional jellium.
Tato bakalářská práce pojednává o aplikacích metod Monte Carlo na různé problémy. Konkrétně byly užity algoritmy metropolis a Simulované žíhání na opti...
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Tato bakalářská práce pojednává o aplikacích metod Monte Carlo na různé problémy. Konkrétně byly užity algoritmy metropolis a Simulované žíhání na optimalizaci problému obchodního cestujícího a problému barvení grafů. Navíc bylo využito základního přístupu Monte Carla pro statistické analyzování elektronických obvodů, ve kterých různé komponenty vykazují náhodné odchylky v dané toleranci. Výsledky jsou vyhodnoceny pro různé konfigurace parametrů Monte Carlo metod.
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