We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

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January 17, 2013

Speaker: Oksana Chkrebtii

Title: Probabilistic Solution of Differential Equations for Bayesian Uncertainty Quantification and Inference

Abstract: In many scientific disciplines the time and space evolution of system states is naturally described by differential equation models, which define states implicitly as functions of their own rates of change. Inference for differential equation models requires an explicit representation of the states (the solution) that is typically not known in closed form, but can be approximated by a variety of discretization-based numerical methods. However, the associated numerical error analysis cannot currently be propagated through the statistical inverse problem, and is thus ignored in practice.

We resolve this problem by developing a Bayesian framework to characterize discretization uncertainty in models defined by high-dimensional systems of differential equations with unknown solutions. Viewing solution estimation as an inference problem allows us to quantify and propagate discretization error into uncertainty in the model parameters and subsequent predictions. Our approach provides a statistical alternative to deterministic numerical integration techniques for estimation of complex dynamic systems, particularly those that are chaotic, ill-conditioned, or contain unmodelled functional variability. We discuss properties, efficient computational algorithms, and application to a wide range of challenging high-dimensional forward and inverse problems.