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  1. Summary

    Discovering patterns from a set of text or, more generally, categorical data is an important problem in many disciplines such as biomedical research, linguistics, artificial intelligence and sociology. We consider here the well-known ‘market basket’ problem that is often discussed in the data mining community, and is also quite ubiquitous in biomedical research. The data under consideration are a set of ‘baskets’, where each basket contains a list of ‘items’. Our goal is to discover ‘themes’, which are defined as subsets of items that tend to co-occur in a basket. We describe a generative model, i.e. the theme dictionary model, for such data structures and describe two likelihood-based methods to infer themes that are hidden in a collection of baskets. We also propose a novel sequential Monte Carlo method to overcome computational challenges. Using both simulation studies and real applications, we demonstrate that the new approach proposed is significantly more powerful than existing methods, such as association rule mining and topic modelling, in detecting weak and subtle interactions in the data.

     
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  2. Summary

    Motivated by the statistical inference problem in population genetics, we present a new sequential importance sampling with resampling strategy. The idea of resampling is key to the recent surge of popularity of sequential Monte Carlo methods in the statistics and engin-eering communities, but existing resampling techniques do not work well for coalescent-based inference problems in population genetics. We develop a new method called ‘stopping-time resampling’, which allows us to compare partially simulated samples at different stages to terminate unpromising partial samples and to multiply promising samples early on. To illustrate the idea, we first apply the new method to approximate the solution of a Dirichlet problem and the likelihood function of a non-Markovian process. Then we focus on its application in population genetics. All our examples show that the new resampling method can significantly improve the computational efficiency of existing sequential importance sampling methods.

     
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