Bayesian Inference in Estimation of Distribution Algorithms

Metaheuristics such as Estimation of Distribution Algorithms and the Cross-Entropy method use probabilistic modelling and inference to generate candidate solutions in optimization problems. The model fitting task in this class of algorithms has largely been carried out to date based on maximum likelihood. An alternative approach that is prevalent in statistics and machine learning is to use Bayesian inference. In this paper, we provide a framework for the application of Bayesian inference techniques in probabilistic model-based optimization. Based on this framework, a simple continuous Bayesian Estimation of Distribution Algorithm is described. We evaluate and compare this algorithm experimentally with its maximum likelihood equivalent, UMDAG c

An Optimal sequential procedure for a buying-selling problem with deterministic trend

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The Optimal multiple stopping rule for a sequence of independent normal random variables

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A Problem of sequential choice of multiple objects with given ranks

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Identifying Change-Points in Biological Sequences via Sequential Importance Sampling

The genomes of complex organisms, including the human genome, are highly structured. This structure takes the form of segmental patterns of variation in various properties and may be caused by the division of genomes into regions of distinct function, by the contingent evolutionary processes that gave rise to genomes, or by a combination of both. Whatever the cause, identifying the change-points between segments is potentially important, as a means of discovering the functional components of a genome, understanding the evolutionary processes involved, and fully describing genomic architecture. One property of genomes that is known to display a segmental pattern of variation is GC content. The GC content of a portion of DNA is the proportion of GC pairs that it contains. Sharp changes in GC content can be observed in human and other genomes. Such change-points may be the boundaries of functional elements or may play a structural role. We model genome sequences as a multiple change-point process, that is, a process in which sequential data are separated into segments by an unknown number of change-points, with each segment supposed to have been generated by a different process. We consider a Sequential Importance Sampling approach to change-point modeling using Monte Carlo simulation to find estimates of change-points as well as parameters of the process on each segment. Numerical experiments illustrate the effectiveness of the approach. We obtain estimates for the locations of change-points in artificially generated sequences and compare the accuracy of these estimates to those obtained via Markov chain Monte Carlo and a well-known method, IsoFinder. We also provide examples with real data sets to illustrate the usefulness of this method

Influence of regional surface soil moisture anomalies on forest fires in Siberia observed from satellites

Forest fires are frequent in the Siberian taiga and are predicted to increase in frequency as a result of increased fire risk under drought conditions, and prolonged fire seasons caused by climate change. There is, however, some uncertainty as to the extent to which drought influences forest fire frequency at a regional scale. Here, we present an analysis of satellite derived soil moisture anomaly data from ERS-1/2 (ERS: Earth Resources Satellite) scatterometer data and burned area maps from MODIS/AVHRR/ATSR (Moderate Resolution Imaging Spectroradiometer/Advanced Very High Resolution Radiometer/Along-Track Scanning Radiometer) over Central Siberia for the years 1992–2000. The purpose of this study is to investigate the relationship of remotely sensed soil moisture deviations from the long-term mean and fire within the boreal biome on a sub-continental scale. Results show that wet surface soil moisture conditions limit the extent of burned area. They can prevent the outbreak of fires but the magnitude of a negative (dry) deviation does not determine the maximum size of fire affected areas. It is known from the literature, however, that an ignition is more likely to occur under low surface wetness conditions, such as those that we observed during July and August in both permafrost and non-permafrost regions. Although the burned area under drier conditions in July is lowest over non-permafrost, the actual number of fires is as high as over continuous permafrost. Approximately 80% of all events occurred under such conditions during that month. The fire size was below 50 km2 under moist conditions. Larger burned areas have in general not been detected when the surface wetness deviation exceeded +5%

Adaptive independence samplers

Markov chain Monte Carlo (MCMC) is an important computational technique for generating samples from non-standard probability distributions. A major challenge in the design of practical MCMC samplers is to achieve efficient convergence and mixing properties. One way to accelerate convergence and mixing is to adapt the proposal distribution in light of previously sampled points, thus increasing the probability of acceptance. In this paper, we propose two new adaptive MCMC algorithms based on the Independent Metropolis–Hastings algorithm. In the first, we adjust the proposal to minimize an estimate of the cross-entropy between the target and proposal distributions, using the experience of pre-runs. This approach provides a general technique for deriving natural adaptive formulae. The second approach uses multiple parallel chains, and involves updating chains individually, then updating a proposal density by fitting a Bayesian model to the population. An important feature of this approach is that adapting the proposal does not change the limiting distributions of the chains. Consequently, the adaptive phase of the sampler can be continued indefinitely. We include results of numerical experiments indicating that the new algorithms compete well with traditional Metropolis–Hastings algorithms. We also demonstrate the method for a realistic problem arising in Comparative Genomics