Monte Carlo statistical method

C. P. Robert and G. Casella, Monte Carlo Statistical Methods, Springer, New York, 2004. 

Robert CP, Casella G (2004) Monte Carlo statistical methods 2nd edn. Springer, New York... 

Casella, G., and Robert, C. (2004). Monte Carlo Statistical Methods, 2nd ed. New York Springer-Verlag. Cho, H., et al. (2007). Induction of dendritic cell-like phenotype in macrophages during foam cell formation. Physiol. Genomics, 29 149-160. 

Robert, C.P. Casella, C. 1999. Monte Carlo statistical methods. Springer. 

Quantum Monte Carlo (QMC) methods are computations that use a statistical integration to calculate integrals which could not be evaluated analytically. These calculations can be extremely accurate, but often at the expense of enormous CPU times. There are a number of methods for obtaining excited-state energies from QMC calculations. These methods will only be mentioned here and are explained more fully in the text by Hammond, Lester, and Reynolds. 

Monte Carlo search methods are stochastic techniques based on the use of random numbers and probability statistics to sample conformational space. The name Monte Carlo was originally coined by Metropolis and Ulam [4] during the Manhattan Project of World War II because of the similarity of this simulation technique to games of chance. Today a variety of Monte Carlo (MC) simulation methods are routinely used in diverse fields such as atmospheric studies, nuclear physics, traffic flow, and, of course, biochemistry and biophysics. In this section we focus on the application of the Monte Carlo method for... 

Figure 7-2. Typical graphic of the statistical inefficiency. In this example it is calculated for the case of benzophenone in water simulated with Monte Carlo Metropolis method. The behavior of S(Lb) versus Lb for chains with different sizes L. The dashed line represents the asymptotic value s of uncorrelated blocks as shown in Eq. (7-11)...

Experimental determination of excess molar quantities such as excess molar enthalpy and excess molar volume is very important for the discussion of solution properties of binary liquids. Recently, calculation of these thermodynamic quantities becomes possible by computer simulation of molecular dynamics (MD) and Monte Carlo (MC) methods. On the other hand, the integral equation theory has played an essential role in the statistical thermodynamics of solution. The simulation and the integral equation theory may be complementary but the integral equation theory has the great advantage over simulation that it is computationally easier to handle and it permits us to estimate the differential thermodynamic quantities. 

Principally exact solution of the vibrational Schrodinger equation can be found by applying the Diffusion Monte Carlo (DMC) method [40], where the a<-,cnracy for ground state calculations is limited only by the statistical noise, which can be reduced to a desired level bj a sufficient investment of computer time. 

Methods Using 3D Descriptors Advances in quantum-chemical calculations and the increasing power of personal computers have made a great impact on the development of methods to predict aqueous solubility directly from the 3D structures of molecules. Monte Carlo statistical mechanics simulations by Jorgensen and Duffy [45] were used to predict the solubility of 150 compounds (MAE = 0.56) using the equation... 

Robinson and Dalton use Monte Carlo statistical mechanics to explore concentration and shape dependencies of the chromophores. Monte Carlo methods provide valuable information about the distribution of a collection of chromophores but are not able to provide atomistic information about the systems. The Monte Carlo simulations performed by Robinson and Dalton employ an array of point dipoles on a periodic lattice with the given parameters for the shape of the chromophores and the chromophore spacing adjustable to achieve the desired chromophore concentration. The model system consisted of 1000 chromophores on a body-centered cubic... 

Data gaps can often be addressed by using a combination of exposure reconstruction techniques simultaneously this approach is common, and there are many examples of it in the peer-reviewed literature. A number of these studies are discussed and compared below. The use of a combination of methods may also be the most effective approach for exposure reconstruction for a particular scenario, given a unique dataset with certain robust elements and otho- relatively weak elements. Uncertainty analyses, such as a Monte Carlo statistical assessment, can also be used to address data gaps generated by uncertainty in existing data or information, as well as to increase the likelihood that true exposures are captured (Cohen Hubal et al. 

RMC is a variation of the standard Metropolis Monte Carlo (MMC) method (Metropolis et al., 1953 see also Chapters l and 5). The principle is that we wish to generate an ensemble of atoms, i.e. a structural model, which corresponds to a total structure factor (set of experimental data) within its errors. These are assumed to be purely statistical and to have a normal distribution. Usually the level and distribution of statistical errors in the data is not a problem, but systematic errors can be. We shall initially consider materials that are macro-scopically isotropic and that have no long range order, i.e. glasses, liquids and gases. The basic algorithm, as applied to a monatomic system with a single set of experimental data, is as follows ... 

MONTE CARLO EIGENVALUE METHODS IN QUANTUM MECHANICS AND STATISTICAL MECHANICS... 

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