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.

Construction and characterization of a highly complex retroviral library for lineage analysis.

Replication-incompetent retroviral vectors encoding histochemical reporter genes have been used for studying lineal relationships in a variety of species. A crucial element in the interpretation of data generated by this method is the identification of sibling relationships, or clonal boundaries. The use of a library of viruses in which each member is unique can greatly facilitate this aspect of the analysis. A previously reported murine retroviral library containing about 80 members demonstrated the utility of the library approach. However, the relatively low number of tags in the murine library necessitated using low infection rates in order to give confidence in clonal assignments. To obviate the need for low infection rates, a far more complex library was created and characterized. The CHAPOL library was constructed such that each member encodes a histochemical reporter gene and has a DNA tag derived from a degenerate oligonucleotide pool synthesized to have a complexity of > 1 x 10(7). The library was tested after infection of cells in vitro or in vivo. The DNA tag from each histochemically labeled cell or clone of cells was recovered by PCR and sequenced for unambiguous identification. Three hundred and twenty tags have been identified after infection, and so far no tag has been seen to result from more than one independent infection. Thus, an equal distribution of inserts is suggested, and Monte Carlo analysis predicts a complexity of > 10(4) members.