Monte Carlo Sampling Algorithm Research Articles

Corrections to scaling in two-dimensional polymer statistics.

Writing 〈${\mathit{R}}_{\mathit{N}}^{2}$〉= ${\mathit{AN}}^{2\ensuremath{\nu}}$(1+${\mathit{BN}}^{\mathrm{\ensuremath{-}}{\mathrm{\ensuremath{\Delta}}}_{1}}$+${\mathit{CN}}^{\mathrm{\ensuremath{-}}1}$+\ensuremath{\cdot}\ensuremath{\cdot}\ensuremath{\cdot}) for the mean square end-to-end length 〈${\mathit{R}}_{\mathit{N}}^{2}$〉 of a self-avoiding polymer chain of N links, we have calculated ${\mathrm{\ensuremath{\Delta}}}_{1}$ for the two-dimensional continuum case from a finite perturbation method based on the ground state of Edwards self-consistent solution which predicts the (exact) \ensuremath{\nu}=3/4 exponent. This calculation yields ${\mathrm{\ensuremath{\Delta}}}_{1}$=1/2. A finite-size scaling analysis of data generated for the continuum using a biased sampling Monte Carlo algorithm supports this value, as does a reanalysis of exact data for two-dimensional lattices. \textcopyright{} 1996 The American Physical Society.

Monte carlo estimation for guaranteed-coverage non-normal tolerance intervals

We propose a Monte Carlo sampling algorithm for estimating guananteed-coverage tolerance factors for non-normal continuous distributions with known shape but u n p w n location and scale. The algorithm is based on reformulating this root-finding problem as a quantile-estimation problem. The reformulation leads to a geometrical interpretation of the tolerance-interval factor. For arbitrary distribution shapes, we analytically and empirically investigate various relationships among tolerance- interval coverage, confidence, and sample size.

Parametric link modification of both tails in binary regression

Common binary regression models such as logistic or probit regression have been extended to include parametric link transformation families. These binary regression models with parametric link are designed to avoid possible link misspecification and improve fit in some data sets. One and two parameter link families have been proposed in the literature (for a review see Stukel (1988)). However in real data examples published so far only one parameter link families have found to improve the fit significantly. This paper introduces a two parameter link family involving the modification of both tails of the link. An analysis based on computationally tractable Bayesian inference involving Monte Carlo sampling algorithms is presented extending earlier work of Czado (1992, 1993b). Finally, the usefulness of the two tailed link modification will be demonstrated in an example where single tail modification can be significantly improved upon by using a two tailed modification.

New Monte Carlo algorithm: Entropic sampling.

We present a new Monte Carlo sampling algorithm, with which one can obtain any desired distribution of the sampling in one Monte Carlo simulation. The free energy and the entropy of a system can thus be obtained from a simple exercise of this algorithm. The main idea is to sample directly the entropy of a system at infinite temperature. Importance sampling is shown to be a particular case of the new algorithm. The algorithm is tested against the exact partition function of the L=4 simple cubic Ising model. A comparison with the multicanonical ensemble for the L=12, q=10 Potts model shows that the new algorithm is more general and more efficient.

Free energy calculation of a soft sphere solid using an adaptive, importance sampling Monte Carlo algorithm

AbstractUsing an adaptive, importance sampling Monte Carlo algorithm, the free energy and equation of state of a soft sphere solid are calculated. The Monte Carlo integration technique to be described is unlike standard methods in that it can evaluate directly the partition function and consequently the free energy of a solid. The results for a soft sphere solid are compared with data obtained from a thermodynamic integration method due to Hoover et al.7 The equation of state obtained from Monte Carlo integration is in agreement with Hoover's method while the free energy calculations compare favorably only at densities greater than that of the freezing transition.

Conformational Energy Calculations on Polypeptides and Proteins: Use of a Statistical Mechanical Procedure for Evaluating Structure and Propertiesa

We are using a variety of theoretical and computational techniques to study protein structure, protein folding, and higher-order structures. Our earlier work involved treatments of liquid water and aqueous solutions of nonpolar and polar solutes, computations of the stabilities of the fundamental structures of proteins and their packing arrangements, conformations of small cyclic and open-chain peptides, structures of fibrous proteins (collagen), structures of homologous globular proteins, introduction of special procedures as constraints during energy minimization of globular proteins, and structures of enzyme-substrate complexes. Recently, we presented a new methodology for predicting polypeptide structure (described here); the method is based on the calculation of the probable and average conformation of a polypeptide chain by the application of equilibrium statistical mechanics in conjunction with an adaptive, importance sampling Monte Carlo algorithm. As a test, it was applied to Met-enkephalin.

Using Renormalization-Group Ideas in Monte Carlo Sampling

Renormalization-group methods are used to produce a novel Monte Carlo sampling algorithm which alleviates the problem of critical slowing down. The method is applied by means of a Kadanoff block-spin transformation to the one- and two-dimensional Ising models.

Isotropic and cloud source irradiation by monoenergetic neutrons and photons.

Previously developed computer codes and Monte Carlo sampling algorithms were used to calculate depth-dose distributions for isotropic and cloud source irradiations of a “man-equivalent” cylinder. These results can be applied directly to insult assessments to critical organs subjected to ICRU class A irradiation (maximum dose/minimum dose < 1.15) and a discussion is given on how organ insult assessments can be obtained for class B irradiations (not uniform because of radiation absorption).

Bayesian flexible hierarchical skew heavy-tailed multivariate meta regression models for individual patient data with applications.

A flexible class of multivariate meta-regression models are proposed for Individual Patient Data (IPD). The methodology is well motivated from 26 pivotal Merck clinical trials that compare statins (cholesterol lowering drugs) in combination with ezetimibe and statins alone on treatment-naïve patients and those continuing on statins at baseline. The research goal is to jointly analyze the multivariate outcomes, Low Density Lipoprotein Cholesterol (LDL-C), High Density Lipoprotein Cholesterol (HDL-C), and Triglycerides (TG). These three continuous outcome measures are correlated and shed much light on a subject's lipid status. The proposed multivariate meta-regression models allow for different skewness parameters and different degrees of freedom for the multivariate outcomes from different trials under a general class of skew t-distributions. The theoretical properties of the proposed models are examined and an efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for carrying out Bayesian inference under the proposed multivariate meta-regression model. In addition, the Conditional Predictive Ordinates (CPOs) are computed via an efficient Monte Carlo method. Consequently, the logarithm of the pseudo marginal likelihood and Bayesian residuals are obtained for model comparison and assessment, respectively. A detailed analysis of the IPD meta data from the 26 Merck clinical trials is carried out to demonstrate the usefulness of the proposed methodology.