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 paper presents a more general form for the prior distribution that has a geometrical interpretation and can improve the specificity of likely solutions. It is also demonstrated that a numerical sampling of the posterior probability distribution can be used as an alternative to a histogram for visualization and to make probabilistic inferences from the data.