Models and inference for structured stochastic systems

Florence Forbes 1
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : The context of my work is the analysis of structured stochastic models with statistical tools. The idea underlying such models is that stochastic systems that exhibit great complexity can be accounted for by combining simple local assumptions in a coherent way. This provides a key to modelling, computation, inference and interpretation. Such stochastic models have found applications in areas as diverse as signal and image processing, neuroscience, genetics and epidemiology. The needs of these areas have in turn stimulated important theoretical developments. However, these powerful and flexible techniques can still be restricted by necessary simplifying assumptions, such as precise measurement and independence between observations, and it long ago became clear that in many areas such assumptions can be both influential and misleading. Also there are several generic sources of complexity in data that require methods beyond the commonly-understood tools in mainstream statistical packages. Often data exhibit complex dependence structures, having to do for example with repeated measurements on individual items, or natural grouping of individual observations due to the method of sampling, spatial or temporal association, family relationship, and so on. Other sources of complexity are connected with the measurement process, such as having multiple measuring instruments or simulations generating high dimensional and heterogeneous data or such that data are dropped out or missing. Data can also come from a wide variety of sources (measurements or simulations) and be high dimensional and very heterogeneous or missing. Such complications in data-generating processes raise a number of challenges when dealing with modern data. My goal is to contribute to statistical modelling by offering theoretical concepts and computational tools to handle properly some of these issues. As regards dependencies and locality, a central part is played by the concept of conditional independence. It provides a precise description of the information conveyed by the value of one variable about others in a statistical model. Markov properties are statements about conditional independence assumptions and Markov models are the central subject of my research. The concept of conditional independence, whereby each variable is related locally (conditionally) to only a few other variables, is the key to both the construction and analysis of such models. When dealing with missing data, mixture models are a central starting point. They lead naturally to more general hidden structure models. Hidden structure models are also useful for taking into account heterogeneity in data. They concern many areas of statistical methodology (finite mixture analysis, hidden Markov models, random effect models,...). Due to their missing data structure, they induce specific difficulties for both estimating the model parameters and assessing performance. My two main domains of research are Markov models and mixture models. The main particularity of my work is the focus on the key idea of structure in models and data. This focus is unifying and promising in its ability to generalize the ingredients of the models, to broaden the scope of applications and to allow cross-fertilization between different areas. Besides, various successful applications illustrate how I managed to combine my two main domains of expertise.
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Habilitation à diriger des recherches
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Florence Forbes. Models and inference for structured stochastic systems. Modeling and Simulation. Université de Grenoble, 2010. ⟨tel-00578938⟩

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