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The Analysis of Data from Continuous Probability Distributions

Timothy E. Holy
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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.

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Timothy E. Holy. 1997-06-10. The Analysis of Data from Continuous Probability Distributions. https://doi.org/10.1103/physrevlett.79.3545

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