Continuous Probability Distributions from Finite Data

Recent approaches to the problem of inferring a continuous probability distribution from a finite set of data have used a scalar field theory for the form of the prior probability distribution. This letter presents a more general form for the prior distribution that has a geometrical interpretation which is useful for tailoring prior distributions to the needs of each application. Examples are presented that demonstrate some of the capabilities of this approach, including the applicability of this approach to problems of more than one dimension.