The Analysis of Data from Continuous Probability Distributions

Details The Analysis of Data from Continuous Probability Distributions The Analysis of Data from Continuous Probability Distributions

1997-06-10

arxiv.org/abs/physics/9706015v1

Physics

Data Analysis, Statistics and Probability

8 pages, 2 figures, REVTeX

Scientific paper

10.1103/PhysRevLett.79.3545

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.

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