How does an algebraic geometer studying secant varieties further
the understanding of hypothesis tests in statistics? Why would a
statistician working on factor analysis raise open problems about
determinantal varieties? Connections of this type are at the heart
of the new field of "algebraic statistics." In this field,
mathematicians and statisticians come together to solve statistical
inference problems using concepts from algebraic geometry as well
as related computational and combinatorial techniques. The goal of
these lectures is to introduce newcomers from the different camps
to algebraic statistics. The introduction will be centered around
the following three observations: many important statistical models
correspond to algebraic or semi-algebraic sets of parameters; the
geometry of these parameter spaces determines the behaviour of
widely used statistical inference procedures; computational
algebraic geometry can be used to study parameter spaces and other
features of statistical models.
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