Motivated by the success of genetic algorithms and simulated annealing in hard optimization problems, the authors propose a new Markov chain Monte Carlo (MCMC) algorithm so called an evolutionary Monte Carlo algorithm. This algorithm has incorporated several attractive features of genetic algorithms and simulated annealing into the framework of MCMC. It works by simulating a population of Markov chains in parallel, where each chain is attached to a different temperature. The population is updated by mutation (Metropolis update), crossover (partial state swapping) and exchange operators (full state swapping). The algorithm is illustrated through examples of the Cp-based model selection and change-point identification. The numerical results and the extensive comparisons show that evolutionary Monte Carlo is a promising approach for simulation and optimization.

Abstract—Bayesian model averaging (BMA) can resolve the overfitting problem by explicitly incorporating the model uncertainty into the analysis procedure. Hence, it can be used to improve the generalization performance of Bayesian network classifiers. Until now, BMA of Bayesian network classifiers has only been performed in some restricted forms, e.g., the model is averaged given a single node-order, because of its heavy computational burden. However, it can be hard to obtain a good node-order when the available training dataset is sparse. To alleviate this problem, we propose BMA of Bayesian network classifiers over several distinct nodeorders obtained using the Markov chain Monte Carlo sampling technique. The proposed method was examined using two synthetic problems and four real-life datasets. First, we show that the proposed method is especially effective when the given dataset is very sparse. The classification accuracy of averaging over multiple node-orders was higher in most cases than that achieved using a single node-order in our experiments. We also present experimental results for test datasets with unobserved variables, where the quality of the averaged node-order is more important. Through these experiments, we show that the difference in classification performance between the cases of multiple node-orders and single node-order is related to the level of noise, confirming the relative benefit of averaging over multiple node-orders for incomplete data. We conclude that BMA of Bayesian network classifiers over multiple node-orders has an apparent advantage when the given dataset is sparse and noisy, despite the method’s heavy computational cost. Index Terms—Bayesian model averaging (BMA), Bayesian networks, classification, Markov chain Monte Carlo (MCMC), sparse data. I.

National statistical institutes routinely apply imputation methods based on statistical models to survey nonresponses. This area of research is very important because it is at the basis of the production of economic data which are as accurate as possible. The idea is to take stock of the experiences gathered in the field of imputation methodology and to try to bridge the gap between this area of research and statistical disclosure limitation. In this paper we review our experiences on model based disclosure limitation techniques. In general, these techniques substitute the observed value of a certain variable with the estimated value via a statistical model. In particular, we discuss the problems encountered and the possible solutions found with two different models: a regression tree model [2] for a categorical variable [17] and a hierarchical model for a continuous variable [9].

Microstructure workshop. I am especially grateful to Neil Shephard. All errors are my own responsibility. Security Bid/Ask Dynamics with Discreteness and Clustering: Simple Strategies for Modeling and Estimation This paper proposes a dynamic model of bid and ask quotes that incorporates a stochastic cost of market-making, discreteness (restriction of quotes to a fixed grid) and clustering (the tendency of quotes to lie on “natural ” multiples of the tick size). The Gibbs sampler provides a convenient vehicle for estimation. The model is estimated for daily and intradaily US Dollar/Deutschemark Reuters quotes.

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