Moments Calculation for the Doubly Truncated Multivariate Normal Density

In the present article, we derive an explicit expression for the truncated mean and variance for the multivariate normal distribution with arbitrary rectangular double truncation. We use the moment generating approach of Tallis (1961) and extend it to general μ, Σ and all combinations of truncation. As part of the solution, we also give a formula for the bivariate marginal density of truncated multinormal variates. We also prove an invariance property of some elements of the inverse covariance after truncation. Computer algorithms for computing the truncated mean, variance and the bivariate marginal probabilities for doubly truncated multivariate normal variates have been written in R and are presented along with three examples.

Quantifying the closeness to a set of random curves via the mean marginal likelihood

In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.

Mixture Kernel Density Estimation and Remedied Correlation Matrix on the EEG-Based Copula Model for the Assessment of Visual Discomfort

Since electroencephalogram (EEG) signals can directly provide information on changes in brain activity due to behaviour changes, how to assess visual discomfort through EEG signals attracts researchers’ attention. However, previous assessments based on time-domain EEG features lack sufficient consideration of the dependence among EEG signals, which may affect the discrimination to visual discomfort. Although the copula model can explore the dependence among variables, the EEG-based copula models still have the following deficiencies: (1) the methods ignoring the fine-grained information hidden in EEG signals could make the estimated marginal density function improper, and (2) the approaches neglecting the pseudo-correlation among data may inappropriately estimate the correlation matrix parameter of the copula density function. The mixture kernel density estimation (MKDE) and remedied correlation matrix (RCM) on the EEG-based copula model are proposed to mitigate the mentioned shortcomings. The simulation experiments show that MKDE can not only better estimate the marginal density function but also explore fine-grained information. The RCM can be closer to the real correlation matrix parameter. With the favourable quality of the proposed EEG-based model, it is used to extract time-domain EEG features to assess visual discomfort further. To our best knowledge, the extracted features present better discrimination to visual discomfort compared with the features extracted by the state-of-the-art method.

Probabilistic Message Passing for Decentralized Control of Stochastic Complex Systems

<pre>This paper proposes a novel probabilistic framework for the design of probabilistic message passing mechanism for complex and large dynamical systems that are operating and governing under a decentralized way. The proposed framework considers the evaluation of probabilistic messages that can be passed between mutually interacting quasi-independent subsystems that will not be restricted by the assumption of homogeneity or conformability of the subsystems components. The proposed message passing scheme is based on the evaluation of the marginal density functions of the states that need to be passed from one subsystem to another. An additional contribution is the development of stochastic controllability analysis of the controlled subsystems that constitute a complex system. To facilitate the understanding and the analytical analysis of the proposed message passing mechanism and the controllability analysis, theoretical developments are demonstrated on linear stochastic Gaussian systems. </pre>

Probabilistic Message Passing for Decentralized Control of Stochastic Complex Systems

<pre>This paper proposes a novel probabilistic framework for the design of probabilistic message passing mechanism for complex and large dynamical systems that are operating and governing under a decentralized way. The proposed framework considers the evaluation of probabilistic messages that can be passed between mutually interacting quasi-independent subsystems that will not be restricted by the assumption of homogeneity or conformability of the subsystems components. The proposed message passing scheme is based on the evaluation of the marginal density functions of the states that need to be passed from one subsystem to another. An additional contribution is the development of stochastic controllability analysis of the controlled subsystems that constitute a complex system. To facilitate the understanding and the analytical analysis of the proposed message passing mechanism and the controllability analysis, theoretical developments are demonstrated on linear stochastic Gaussian systems. </pre>

Bivariate Mixture of Inverse Weibull Distribution: Properties and Estimation

In this study, we construct a mixture of bivariate inverse Weibull distribution. We assumed that the parameters of two marginals have Bernoulli distributions. Several properties of the proposed model are obtained, such as probability marginal density function, probability marginal cumulative function, the product moment, the moment of the two variables x and y, the joint moment-generating function, and the correlation between x and y. The real dataset has been analyzed. We observed that the mixture bivariate inverse Weibull distribution provides a better fit than the other model.

A bivariate Kumaraswamy-exponential distribution with application

In this paper, we introduce a new bivariate Kumaraswamy exponential distribution, whose marginals are univariate Kumaraswamy exponential. Some probabilistic properties of this bivariate distribution are derived, such as joint density function, marginal density functions, conditional density functions, moments and stress-strength reliability. Also, we provide the expected information matrix with its elements in a closed form. Estimation of the parameters is investigated by the maximum likelihood, Bayesian and least squares estimation methods. A simulation study is carried out to compare the performance of the estimators by estimation methods. Further, one data set have been analyzed to show how the proposed distribution works in practice.