A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Dynamic weighting in Monte Carlo and optimization

Dynamic importance weighting is proposed as a Monte Carlo method that has the capability to sample relevant parts of the configuration space even in the presence of many steep energy minima. The method relies on an additional dynamic variable (the importance weight) to help the system overcome steep barriers. A non-Metropolis theory is developed for the construction of such weighted samplers. Algorithms based on this method are designed for simulation and global optimization tasks arising from multimodal sampling, neural network training, and the traveling salesman problem. Numerical tests on these problems confirm the effectiveness of the method.

Enhanced conformational sampling in Monte Carlo simulations of proteins: application to a constrained peptide.

A Monte Carlo simulation method for globular proteins, called extended-scaled-collective-variable (ESCV) Monte Carlo, is proposed. This method combines two Monte Carlo algorithms known as entropy-sampling and scaled-collective-variable algorithms. Entropy-sampling Monte Carlo is able to sample a large configurational space even in a disordered system that has a large number of potential barriers. In contrast, scaled-collective-variable Monte Carlo provides an efficient sampling for a system whose dynamics is highly cooperative. Because a globular protein is a disordered system whose dynamics is characterized by collective motions, a combination of these two algorithms could provide an optimal Monte Carlo simulation for a globular protein. As a test case, we have carried out an ESCV Monte Carlo simulation for a cell adhesive Arg-Gly-Asp-containing peptide, Lys-Arg-Cys-Arg-Gly-Asp-Cys-Met-Asp, and determined the conformational distribution at 300 K. The peptide contains a disulfide bridge between the two cysteine residues. This bond mimics the strong geometrical constraints that result from a protein's globular nature and give rise to highly cooperative dynamics. Computation results show that the ESCV Monte Carlo was not trapped at any local minimum and that the canonical distribution was correctly determined.

Interactions between quantitative trait loci in soybean in which trait variation at one locus is conditional upon a specific allele at another.

A large recombinant inbred population of soybean has been characterized for 220 restriction fragment-length polymorphism (RFLP) markers. Values for agronomic traits also have been measured. Quantitative trait loci (QTL) for height, yield, and maturity were located by their linkage to RFLP markers. QTL controlling large amounts of trait variation were analyzed for the dependence of trait variation on particular alleles at a second locus by comparing cumulative distributions of the trait for each genotype (four genotypes per pair of loci). Interesting pairs of loci were analyzed statistically with maximum likelihood and Monte Carlo comparison of additive and epistatic models. For each locus affecting height, variation was conditional upon the presence of a particular allele at a second unlinked locus that itself explained little or no trait variation. The results show that interactions between QTL are frequent and control large effects. Interactions distinguished between different QTL in a single linkage group and between QTL that affect different traits closely linked to one RFLP marker--i.e., distinguished between pleiotropy and closely linked genes. The implications for the evolution of inbreeding plants and for the construction of agronomic breeding strategies are discussed.