Monte Carlo analysis procedure

By Bayes s rule, the posterior probability on a Monte Carlo realization of a model equals the probability of observing the site-specific output data if the realization is correct, times the prior probability that the realization is correct, normalized such that the sum of the posterior probabilities of the Monte Carlo realizations equals 1. In Monte Carlo analysis, all realizations are equally likely (i.e., the pritM probability on each realization of an n-realization Monte Carlo simulation is 1/n). Therefore, the BMC acceptance-rejection procedure boils down to the following The probability that a model realization is correct, given new data, equals the relative likelihood of the having observed the new data if the realization is correct. 

The outline of the paper is as follows. In Sec. 1, the expression used to fit the VESUVIO data is derived. Sec. 2 describes the way in which the instrument resolution is incorporated into the data analysis. Sec. 3 describes the Monte Carlo (MC) procedure, used to test the fitting programs. In Secs. 4 to 6 the influence of instrumental effects on the results are evaluated, using MC simulations and also by comparing data taken under different experimental conditions. Sec. 4 considers the effects of the correction for the incident beam intensity. Sec. 5 considers the systematic errors generated by approximations made to incorporate the instrument resolution in the fitting programs. Sec. 6 discusses effects dependent on sample size, such as attenuation, multiple scat-... 

H. Meirovitch and E. Meirovitch, Efficiency of monte carlo minimization procedures and their use in analysis of nmr data obtained from flexible peptides. J. Comput. Chem. 18, 240-253 (1997). 

The remainder of this article is organized as follows. Section 2 presents the proposed degradation model for systems with degradation dependency. Monte Carlo simulation procedures to solve the model are presented in Section 3. Section 4 presents one case study on one subsystem of a residual heat removal system (Coudray Mattel 1984) from Electricite de France (EDF). Numerical results and analysis are presented in Section 5. Section 6 concludes the work. 

A particular advantage of the low-mode search is that it can be applied to botli cyclic ajic acyclic molecules without any need for special ring closure treatments. As the low-mod> search proceeds a series of conformations is generated which themselves can act as starting points for normal mode analysis and deformation. In a sense, the approach is a system ati( one, bounded by the number of low-frequency modes that are selected. An extension of th( technique involves searching random mixtures of the low-frequency eigenvectors using Monte Carlo procedure. 

For nonequilibrium statistical mechanics, the present development of a phase space probability distribution that properly accounts for exchange with a reservoir, thermal or otherwise, is a significant advance. In the linear limit the probability distribution yielded the Green-Kubo theory. From the computational point of view, the nonequilibrium phase space probability distribution provided the basis for the first nonequilibrium Monte Carlo algorithm, and this proved to be not just feasible but actually efficient. Monte Carlo procedures are inherently more mathematically flexible than molecular dynamics, and the development of such a nonequilibrium algorithm opens up many, previously intractable, systems for study. The transition probabilities that form part of the theory likewise include the influence of the reservoir, and they should provide a fecund basis for future theoretical research. The application of the theory to molecular-level problems answers one of the two questions posed in the first paragraph of this conclusion the nonequilibrium Second Law does indeed provide a quantitative basis for the detailed analysis of nonequilibrium problems. 

Hornberger and Spear s original application of generalized sensitivity analysis (GSA) used a binary acceptance-rejection procedure, i.e., they discarded a Monte Carlo realization if they thought that the prediction was inconsistent with the site-specific data (a nonbehavior ) or kept it if they thought it was consistent (a behavior ). The prior probability on each Monte Carlo realization was the reciprocal of the total number of realizations. After the acceptance-rejection procedure was applied, the updated (posterior) probability on each realization that was classified as a behavior was the reciprocal of the number of behaviors, and the posterior probability on nonbehaviors was zero. 

However, it is normally assumed that the conformers that bind to target sites will be those with a minimum potential energy. Since molecules may have large numbers of such metastable conformers a number of techniques, such as the Metropolis Monte Carlo method and comparative molecular field analysis (CoMFA), have been developed to determine the effect of conformational changes on the effectiveness of docking procedures. 

Conformational isomers represent minima on an energy surface, and all structures and the corresponding strain energies can be obtained by a careful analysis. This can be performed manually (such as in Sections 17.3 and 17.4) or automatically. An automatic procedure may involve a systematic search (grid search methods), a stochastic search (e.g., torsional Monte Carlo or cartesian stochastic, i.e., the random kick method) or molecular dynamics (see Chapter 5 and Section 16.5). Implemented in MOMEC is a random kick stochastic search module, and this has been shown to lead to excellent results, not only for conformational equilibria, but also for distributions of configurational isomers[37]. 

The first approach to simulation of protein thermophilic adaptation is to start from a purely statistical-mechanical analysis of protein thermostability. A specific Monte-Carlo procedure [the... 

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