1,122,813 research outputs found

    Nonclassical stochastic flows and continuous products

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    Contrary to the classical wisdom, processes with independent values (defined properly) are much more diverse than white noise combined with Poisson point processes, and product systems are much more diverse than Fock spaces. This text is a survey of recent progress in constructing and investigating nonclassical stochastic flows and continuous products of probability spaces and Hilbert spaces.Comment: A survey, 126 pages. Version 3 (final): former Question 9d4 is solved; 8a1 reformulated. Ref [41] added. For readability, sections are reordered (123456..->142536..). Cosmetic changes, mostly in 1b, 2a, 3d, (4a7) (v3 numbers) and Introductio

    Modelling mortality rates using GEE models

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    Generalised estimating equation (GEE) models are extensions of generalised linear models by relaxing the assumption of independence. These models are appropriate to analyze correlated longitudinal responses which follow any distribution that is a member of the exponential family. This model is used to relate daily mortality rate of Maltese adults aged 65 years and over with a number of predictors, including apparent temperature, season and year. To accommodate the right skewed mortality rate distribution a Gamma distribution is assumed. An identity link function is used for ease of interpretating the parameter estimates. An autoregressive correlation structure of order 1 is used since correlations decrease as distance between observations increases. The study shows that mortality rate and temperature are related by a quadratic function. Moreover, the GEE model identifies a number of significant main and interaction effects which shed light on the effect of weather predictors on daily mortality rates.peer-reviewe

    Stochastic Control Representations for Penalized Backward Stochastic Differential Equations

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    This paper shows that penalized backward stochastic differential equation (BSDE), which is often used to approximate and solve the corresponding reflected BSDE, admits both optimal stopping representation and optimal control representation. The new feature of the optimal stopping representation is that the player is allowed to stop at exogenous Poisson arrival times. The convergence rate of the penalized BSDE then follows from the optimal stopping representation. The paper then applies to two classes of equations, namely multidimensional reflected BSDE and reflected BSDE with a constraint on the hedging part, and gives stochastic control representations for their corresponding penalized equations.Comment: 24 pages in SIAM Journal on Control and Optimization, 201

    Edge Label Inference in Generalized Stochastic Block Models: from Spectral Theory to Impossibility Results

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    The classical setting of community detection consists of networks exhibiting a clustered structure. To more accurately model real systems we consider a class of networks (i) whose edges may carry labels and (ii) which may lack a clustered structure. Specifically we assume that nodes possess latent attributes drawn from a general compact space and edges between two nodes are randomly generated and labeled according to some unknown distribution as a function of their latent attributes. Our goal is then to infer the edge label distributions from a partially observed network. We propose a computationally efficient spectral algorithm and show it allows for asymptotically correct inference when the average node degree could be as low as logarithmic in the total number of nodes. Conversely, if the average node degree is below a specific constant threshold, we show that no algorithm can achieve better inference than guessing without using the observations. As a byproduct of our analysis, we show that our model provides a general procedure to construct random graph models with a spectrum asymptotic to a pre-specified eigenvalue distribution such as a power-law distribution.Comment: 17 page

    Stochastic Constraint Programming

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    To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number of complete algorithms and approximation procedures. Finally, we discuss a number of extensions of stochastic constraint programming to relax various assumptions like the independence between stochastic variables, and compare with other approaches for decision making under uncertainty.Comment: Proceedings of the 15th Eureopean Conference on Artificial Intelligenc
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