Analysis of Data from Continuous Probability Distributions

The Analysis of Data from Continuous Probability Distributions

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 distr...

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 samp...

Formalization of Continuous Probability Distributions

Continuous probability distributions are widely used to mathematically describe random phenomena in engineering and physical sciences. In this paper, we present a methodology that can be used to formalize any continuous random variable for which the inverse of the cumulative distribution function can be expressed in a closed mathematical form. Our methodology is primarily based on the Standard ...

Methods of Data Analysis Learning probability distributions

One of the key problems in non-parametric data analysis is to infer good models of probability distributions, assuming we are given as data a finite sample from that distribution. This problem is ill-posed for continuous distributions, even when they are low-dimensional: with finite data, there is no way to distinguish between (or exclude) distributions that are not regularized a priori, for ex...

Probability Distributions: Discrete vs. Continuous