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Determining information about the state of a complex physical system from observations of its behavior is a fundamental problem in scientific inference and engineering design. Often, this can be formulated as the stochastic inverse problem of determining probability structures on parameters for a physics model corresponding to a probability structure on the output of the model. We describe a formulation and solution method for stochastic inverse problems that is based on functional analysis, differential geometry, and probability/measure theory. This approach yields a computationally tractable problem while avoiding alterations of the model like regularization and ad hoc assumptions about the probability structures. We present several examples, including a high-dimensional application to determination of parameter fields in storm surge models. We also describe work aimed at defining a notion of condition for stochastic inverse problems and tackling the related problem of designing sets of optimal observable quantities.

Zoom Link: https://uvic.zoom.us/j/81568752407?pwd=STJOVmQ3VUYwTUU1b3RzcGVCWVYyZz09

Numerous examples exist of infectious disease models that incorporate spatial distance and other covariates at the individual level. This has been most noticeable perhaps in agricultural case studies such as the UK 2001 foot and mouth disease epidemic. However, both in agriculture and public health, many salient covariates that display spatial structure are collected at a regional level. Here, we extend individual level infectious disease models of the type proposed by Deardon et al. (2010) to incorporate such spatially structured regional / aggregate level information. This is done primarily within the context of influenza data from Calgary, Canada. We discuss issues of both inference and computation.

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Abstract: Double generalized linear mixed effects models (DGLMM) form an extension of generalized linear models in which the dispersion, as well as the mean, may be modelled as a function of fixed covariates and random effects. I will discuss an application of a DGLMM with a normal response distribution to model the provisioning behaviour of adult pied-flycatchers. Specifically, the model examines changes in both the mean and variance of the amount of food brought to the nest by parents in response to changes in the size of their brood and other factors. I will also demonstrate a new R package, called dalmatian, that I have created to help other researchers fit DGLMM in a Bayesian framework.

Abstract: Permutation testing is a powerful non-parametric testing procedure that is applicable to a variety of testing scenarios and requires few assumptions. The main downfall of the permutation test is the excessive computation time required to run such a test making it impractical in some settings and unusable in others. We rectify this via application of variants of the Kahane-Khintchine inequality to construct an analytic upper bound on the permutation test p-value. Our method is applicable to two-sample and k-sample testing for univariate, multivariate, and functional data. We demonstrate its usefulness on a dataset of spoken phonemes, which makes use of two experimental designs: the Latin square design and the randomized block design. We will also briefly discuss applications to spatial statistics.