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Abstract:
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A research frontier has emerged in scientific computation founded on the principle that numerical error in numerical methods, that for example solve differential equations, entails uncertainty that ought to be subjected to statistical analysis. This viewpoint raises exciting challenges for contemporary statistical and numerical analysis, including the design of statistical methods that enable the coherent propagation of probability measures through a computational and inferential pipeline. A probabilistic numerical method is equipped with a full distribution over its output, providing a calibrated assessment of uncertainty that is shown to be statistically valid at finite computational levels, as well as in asymptotic regimes. The area of Probabilistic Numerical Computation defines a nexus of ideas, philosophies, theories and methodologies bringing together Statistical Science, Applied Mathematics, Engineering and Computing Science and this talk seeks to make a case for the importance of this viewpoint. The talk will examine thoroughly the case for Probabilistic Numerical Methods in mathematical modeling and statistical computation with a number of case studies being presented.
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