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Register a new userBayesian Network Models for Incomplete and Dynamic Data
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Added by
Marco Scutari
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
Authors
Marco Scutari
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Bayesian networks are a versatile and powerful tool to model complex phenomena and the interplay of their components in a probabilistically principled way. Moving beyond the comparatively simple case of completely observed, static data, which has received the most attention in the literature, in this paper we will review how Bayesian networks can model dynamic data and data with incomplete observations. Such data are the norm at the forefront of research and in practical applications, and Bayesian networks are uniquely positioned to model them due to their explainability and interpretability.
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Traffic flow count data in networks arise in many applications, such as automobile or aviation transportation, certain directed social network contexts, and Internet studies. Using an example of Internet browser traffic flow through site-segments of an international news website, we present Bayesian analyses of two linked classes of models which, in tandem, allow fast, scalable and interpretable Bayesian inference. We first develop flexible state-space models for streaming count data, able to adaptively characterize and quantify network dynamics efficiently in real-time. We then use these models as emulators of more structured, time-varying gravity models that allow formal dissection of network dynamics. This yields interpretable inferences on traffic flow characteristics, and on dynamics in interactions among network nodes. Bayesian monitoring theory defines a strategy for sequential model assessment and adaptation in cases when network flow data deviates from model-based predictions. Exploratory and sequential monitoring analyses of evolving traffic on a network of web site-segments in e-commerce demonstrate the utility of this coupled Bayesian emulation approach to analysis of streaming network count data.
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We derive new algorithms for online multiple testing that provably control false discovery exceedance (FDX) while achieving orders of magnitude more power than previous methods. This statistical advance is enabled by the development of new algorithmic ideas: earlier algorithms are more static while our new ones allow for the dynamical adjustment of testing levels based on the amount of wealth the algorithm has accumulated. We demonstrate that our algorithms achieve higher power in a variety of synthetic experiments. We also prove that SupLORD can provide error control for both FDR and FDX, and controls FDR at stopping times. Stopping times are particularly important as they permit the experimenter to end the experiment arbitrarily early while maintaining desired control of the FDR. SupLORD is the first non-trivial algorithm, to our knowledge, that can control FDR at stopping times in the online setting.
While there have been a lot of recent developments in the context of Bayesian model selection and variable selection for high dimensional linear models, there is not much work in the presence of change point in literature, unlike the frequentist counterpart. We consider a hierarchical Bayesian linear model where the active set of covariates that affects the observations through a mean model can vary between different time segments. Such structure may arise in social sciences/ economic sciences, such as sudden change of house price based on external economic factor, crime rate changes based on social and built-environment factors, and others. Using an appropriate adaptive prior, we outline the development of a hierarchical Bayesian methodology that can select the true change point as well as the true covariates, with high probability. We provide the first detailed theoretical analysis for posterior consistency with or without covariates, under suitable conditions. Gibbs sampling techniques provide an efficient computational strategy. We also consider small sample simulation study as well as application to crime forecasting applications.
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