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.