The Analysis of Data from Continuous Probability Distributions

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.

The inverse Born problem in contextual probability theories: quantum spin and continuous random variables

We revise contextual probability theory and the associated inverse Born problem, solved by the Quantum-Like Representation Algorithm (QLRA) in case of two discrete random variables. After pointing out the special feature and limitations of QLRA for two binary random variables, we generalize the QLRA procedure to solve the inverse Born problem to the case of three binary random variables. We analyze the quantum spin model in the light of our results and showed that can be easily obtained from a contextual probability model. We furthermore study the inverse Born problem in the case of two contin…

Display of probability densities for data from a continuous distribution

Based on cumulative distribution functions, Fourier series expansion and Kolmogorov tests, we present a simple method to display probability densities for data drawn from a continuous distribution. It is often more efficient than using histograms.

A note on the best invariant estimation of continuous probability distributions under mean square loss

We consider the nonparametric estimation problem of continuous probability distribution functions. For the integrated mean square error we provide the statistic corresponding to the best invariant estimator proposed by Aggarwal (1955) and Ferguson (1967). The table of critical values is computed and a numerical power comparison of the statistic with the traditional Cramér-von Mises statistic is done for several representative distributions.

任意连续概率分布族的约束替代数据

Constrained surrogates for arbitrary families of continuous probability distributions

提出一种通用框架，构造任意连续分布族的约束替代数据，实现无需参数估计的无偏模型检验，并应用于多个复杂系统领域。

Joint Probability Distributions for a Class of Non-Markovian Processes

We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H.C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single time probability distributions to the case of N-time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fractional time derivatives reflecting the non-Markovian character of the process.