The Analysis of Data from Continuous Probability Distributions

Abstract

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.