  Conventional statistics begins with a model, and assigns a likelihood of
obtaining any particular set of data. The opposite approach, beginning with the
data and assigning a likelihood to any particular model, is explored here for
the case of points drawn randomly from a continuous probability distribution. A
scalar field theory is used to assign a likelihood over the space of
probability distributions. The most likely distribution may be calculated,
providing an estimate of the underlying distribution and a convenient graphical
representation of the raw data. Fluctuations around this maximum likelihood
estimate are characterized by a robust measure of goodness-of-fit. Its
distribution may be calculated by integrating over fluctuations. The resulting
method of data analysis has some advantages over conventional approaches.
