Conditional Marginal Distributions Research Articles

A C1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^1$$\\end{document}-Itô’s Formula for Flows of Semimartingale Distributions

We provide an Itô’s formula for C1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^1$$\\end{document}-functionals of flows of conditional marginal distributions of continuous semimartingales. This is based on the notion of weak Dirichlet process, and extends the C1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^1$$\\end{document}-Itô’s formula in Gozzi and Russo (Stoch Process Appl 116(11):1563–1583, 2006) to this context. As the first application, we study a class of McKean–Vlasov optimal control problems, and establish a verification theorem which only requires C1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^1$$\\end{document}-regularity of its value function, which is equivalently the (viscosity) solution of the associated HJB master equation. It goes together with a novel duality result.

Negative binomial community network vector autoregression for multivariate integer-valued time series

Modeling multivariate integer-valued time series with appropriate methods is currently a popular research topic. In this paper, we propose a multivariate integer-valued autoregressive time series model based on a fixed network community structure. We use the negative binomial distribution as the conditional marginal distribution and a copula to construct the conditional joint distribution. The newly proposed model introduces the heterogeneity of nodes. Stability conditions are provided for both fixed and increasing dimensions. We estimate the parameters of the proposed model by maximizing the quasi-likelihood function with known and unknown community membership matrices, respectively. Corresponding asymptotic properties of parameter estimates are also provided. A simulation study is conducted to demonstrate the asymptotic behavior of the proposed model, and two real datasets are employed to compare the proposed model with other competitive models.

A novel single-loop estimation method for predictive failure probability-based global sensitivity analysis

The existing predictive failure probability (PFP)-based global sensitivity analysis methods may get stuck in practical application due to the large amount of calculation or insufficient precision. Therefore, a novel single-loop estimation method is proposed in this paper to effectively estimate PFP-based global sensitivity measures. Firstly, by introducing standard normal auxiliary variables and equivalent probability transformation, the overall uncertainty of each input variable is decomposed into its inherent uncertainty and distribution parameter uncertainty. Then, Bayes theorem-based formulations are derived for three PFP-based global sensitivity measures, where only the unconditional PFP and the conditional marginal and joint distributions of standard normal auxiliary variables and distribution parameters need to be known. These items can be evaluated simultaneously using only one set of functional calls. Finally, adaptive Kriging model is embedded into the proposed method in place of the time-demanding performance function to further enhance computational efficiency. The effectiveness of the proposed methods is validated through four benchmark reliability problems asnd one engineering problem.

Softplus negative binomial network autoregression

AbstractModelling multivariate time series of counts in a parsimonious way is a popular topic. In this paper, we consider an integer‐valued network autoregressive model with a non‐random neighbourhood structure, which uses negative binomial distribution as the conditional marginal distribution and the softplus function as the link function. The new model generalizes existing ones in the literature and has a great flexibility in modelling. Stationary conditions in cases of fixed dimension and increasing dimension are given. Parameters are estimated by maximizing the quasi‐likelihood function, and related asymptotic properties of the estimators are established. A simulation study is conducted to assess performances of the estimators, and a real data example is analysed to show superior performances of the proposed model compared with existing ones.

ENVIRONMENTAL CONTOUR ESTABLISHMENT BASED ON OPENLY AVAILABLE EMODNET WAVE AND WIND DATA FOLLOWING HEFFERNAN AND TAWN METHODOLOGIES

In this paper, I present methodologies and routines for inference of environmental contours based on openly available data from the European EMODnet service, specifically wind and wave timeseries from oil platform 6200146. The conditional marginal distribution models, known as environmental contours, is established based on measured wind and wave heights, at platform 6200146 located in the North Sea. The data is provided through the openly available data platform, EMODnet. The environmental contour model is established by fitting univariate distributions to each data-series independently, whereafter an extremal dependence structure is established following methodologies outlined in (Janet E. heffernan, 2004).

PyBanshee version (1.0): A Python implementation of the MATLAB toolbox BANSHEE for Non-Parametric Bayesian Networks with updated features

In this paper we discuss PyBanshee, which is a Python-based open-source implementation of the MATLAB toolbox BANSHEE. PyBanshee constitutes the first fully open-source package to quantify, visualize and validate Non-Parametric Bayesian Networks (NPBNs). The architecture of PyBanshee is heavily based on its MATLAB predecessor. It presents the full implementation of existing tools and introduces new modules. Specifically, PyBanshee allows for: (i) choosing fully parametric one-dimensional margins, (ii) choosing different sample sizes for the model-validation tests based on the Hellinger distance, (iii) drawing user-defined sample sizes of the NPBN, (iv) sample-based conditioning sampling (similarly to the closed-source proprietary package UNINET by LightTwist Software) and (v) visualizing the comparison between the histograms of the unconditional and conditional marginal distributions. New detailed examples demonstrating new features are provided.

Extension of Marginal Complementary Log\u2013Log Model and Separations of Marginal Homogeneity for Ordinal Categorical Data

The present paper considers a model that indicates the structure of inhomogeneity for marginal distributions for ordinal categorical data. The model is based on the complementary log–log transformation of marginal cumulative probability. A theorem that the marginal homogeneity model holds if and only if the proposed model and the marginal mean and variance equality model holds is given. Also, a model based on the conditional marginal distribution is considered under certain condition.

A Sampling-based Distributed Source Coding Scheme

In many practical distributed source coding (DSC) schemes that apply channel coding and iterative decoding, correlation estimation provides the likelihood information about the source bits to initialize the decoding algorithms. Therefore, the decoding depends strongly on the accuracy of this correlation estimation information. In this study, a sampling-based scheme for DSC is proposed that takes advantage of the source redundancy without requiring prior knowledge of its statistics. At the sender, the source sequence is sampled to obtain the sampled and unsampled sub-sequences. Then, the un-sampled sub-sequence is compressed by an arithmetic coder. Meanwhile the syndromes of the sampled sub-sequence are also calculated. At the receiver, the correlation between the side information and the un-sampled sub-sequence is used to estimate the conditional marginal distribution of the sampled sub-sequence. Then, the estimated information is used to initialize the likelihood information of the decoding algorithms. Finally, the likelihood information is combined with the received syndromes to perform iterative decoding to recover the original sampled sub-sequence. Experiment results show that the proposed scheme achieves better rate-distortion performance compared with the existing DSC schemes.

Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations

In this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For this class of allocations, analytical calculations are rarely available, and numerical computations based on Monte Carlo (MC) methods often provide inefficient estimates due to the rare-event character of the crisis events. We propose an MCMC estimator constructed from a sample path of a Markov chain whose stationary distribution is the conditional distribution given the crisis event. Efficient constructions of Markov chains, such as the Hamiltonian Monte Carlo and Gibbs sampler, are suggested and studied depending on the crisis event and the underlying loss distribution. The efficiency of the MCMC estimators is demonstrated in a series of numerical experiments.

Stochastic modeling of suspended sediment load in alluvial rivers

Abstract Sediment is a major source of non-point pollution. Suspended sediment can transport nutrients, toxicants and pesticides, and can contribute to eutrophication of rivers and lakes. Modeling suspended sediment in rivers is of particular importance in the field of environmental science and engineering. However, understanding and quantifying nonlinear interactions between river discharge and sediment dynamics has always been a challenge. In this paper, we introduce a parsimonious probabilistic model to describe the relationship between Suspended Sediment Load (SSL) and discharge volume. This model, rooted in multivariate probability theory and Bayesian Network, infers conditional marginal distribution of SSL for a given discharge level. The proposed framework relaxes the need for detailed information about the physical characteristics of the watershed, climatic forcings, and the nature of rainfall-runoff transformation, by drawing samples from the probability distribution functions (PDFs) of the underlying process (here, discharge and SSL data). Discharge and SSL PDFs can be simplified into a joint distribution that describes the relationship between SSL and discharge, in which the latter acts as a proxy for different predictors of SSL. The joint distribution is created based on historical discharge and SSL data, and stores information about the discharge-SSL relationship and sediment transport process of the watershed of interest. We test this framework for seven major rivers in the U.S., results of which show promising performance to predict SSL and its likelihood given different discharge levels.

Interdependent Durations with Incomplete Information

In this paper, we propose an interdependent durations model with incomplete information structure for multiple players. Our model generates a system of simultaneous equations of the conditional marginal distributions for duration outcomes, and implies that the corresponding copula function is the copula of the unobserved heterogeneity terms. We establish the uniqueness of the Bayesian Nash Equilibrium for the model resorting to a moderate social influence condition. We obtain identification of the finite dimensional parameters capturing the interaction effects and all nonparametric model primitives from the simultaneous equations of conditional marginal distributions and the dependence among unobserved heterogeneity through the conditional joint distribution of duration outcomes. Thus, the direct strategic interaction effects and the selection effects due to unobserved heterogeneity are separately identified.

Partial identification of functionals of the joint distribution of “potential outcomes”

In this paper, we present a systematic study of partial identification of two general classes of functionals of the joint distribution of two “potential outcomes” when a bivariate sample from the joint distribution is not available to the econometrician. Assuming the identification of the conditional marginal distributions of potential outcomes and the distribution of the covariate vector, we show that the identified sets for functionals in both classes are intervals and provide conditions under which the identified sets point identify the true value of the functionals. In addition, we establish sufficient and necessary conditions for the covariate information to be informative in the sense of shrinking the identified sets. We focus on the application of our general results to evaluating distributional treatment effects of a binary treatment in two commonly used frameworks in the literature for evaluating average treatment effects: the selection on observables framework and a latent threshold-crossing model. We characterize the role of the propensity score in the selection-on-observables framework and the role of endogenous selection in the latent threshold-crossing model. Examples of policy parameters that our results apply include the correlation coefficient between the potential outcomes, many inequality measures of the distribution of treatment effects, and median of the distribution of the individual treatment effect.

Infinitely Divisible Distributions in Integer‐Valued Garch Models

We propose an integer‐valued stochastic process with conditional marginal distribution belonging to the class of infinitely divisible discrete probability laws. With this proposal, we introduce a wide class of models for count time series that includes the Poisson integer‐valued generalized autoregressive conditional heteroscedastic (INGARCH) model (Ferland et al., 2006) and the negative binomial and generalized Poisson INGARCH models (Zhu, 2011, 2012a). The main probabilistic analysis of this process is developed stating, in particular, first‐order and second‐order stationarity conditions. The existence of a strictly stationary and ergodic solution is established in a subclass including the Poisson and generalized Poisson INGARCH models.

On the Capacity of the Interference Channel With a Cognitive Relay

The interference channel with a cognitive relay (IFC-CR) consists of the classical IFC with two independent source-destination pairs whose communication are aided by an additional node, referred to as the CR, that has a priori knowledge of both sources' messages. This a priori message knowledge is termed cognition and idealizes the relay learning the messages of the two sources from their transmissions over a wireless channel. This paper presents improved outer and inner bounds on the capacity region of the general memoryless IFC-CR that are shown to be tight for certain classes of channels. The new outer bound follows from arguments originally devised for broadcast channels, among which Sato's observation that the capacity region of channels with noncooperative receivers only depends on conditional marginal distributions of the channel output, not on their conditional joint distribution. A simplified expression for the inner bound is derived, which contains all previously proposed coding schemes. The new inner and outer bounds coincide for a class of channels satisfying some strong interference condition, i.e., for these channels there is no loss in optimality if both destinations decode both messages. This result parallels analogous results for the classical interference channel and for the cognitive interference channel and is the first known capacity result for the general IFC-CR. Numerical evaluations of the proposed inner and outer bounds are presented for the additive white Gaussian noise case.

Representation of Mutual Information Via Input Estimates

A relationship between information theory and estimation theory was recently shown for the Gaussian channel, relating the derivative of mutual information with the minimum mean-square error. This paper generalizes the link between information theory and estimation theory to arbitrary channels, giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs. We illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

Assessing the Performance of the Ensemble Kalman Filter for Land Surface Data Assimilation

Abstract The ensemble Kalman filter provides an easy-to-use, flexible, and efficient option for data assimilation problems. One of its attractive features in land surface applications is its ability to provide distributional information about variables, such as soil moisture, that can be highly skewed or even bimodal. The ensemble Kalman filter relies on normality approximations that improve its efficiency but can also compromise the accuracy of its distributional estimates. The effects of these approximations can be evaluated by comparing the conditional marginal distributions and moments estimated by the ensemble Kalman filter with those obtained from a sequential importance resampling (SIR) particle filter, which gives exact solutions for large ensemble sizes. Comparisons for two land surface examples indicate that the ensemble Kalman filter is generally able to reproduce nonnormal soil moisture behavior, including the skewness that occurs when the soil is either very wet or very dry. Its conditional mean estimates are very close to those generated by the SIR filter. Its higher-order conditional moments are somewhat less accurate than the means. Overall, the ensemble Kalman filter appears to provide a good approximation for nonlinear, nonnormal land surface problems, despite its dependence on normality assumptions.

Estimation and simulation of lognormal random fields

This paper describes several techniques for estimating and simulating lognormal random fields. The lognormal maximum entropy estimator is presented and compared with simple lognormal kriging. Conditional simulation is performed using the turning bands method combined with simple lognormal kriging. For Gaussian random fields, kriging and the maximum entropy estimator are shown to be equivalent. For lognormal random fields, however, simple lognormal kriging and the lognormal maximum entropy estimator differ. Conditional simulation via simulated annealing is also demonstrated but with generally unsatisfactory results. A hybrid approach involving the turning bands method and simple lognormal kriging yields satisfactory results in the sense that it generates conditional simulations that consistently reproduce conditional marginal distributions.

Measures of Departure from Marginal Homogeneity for Contingency Tables with Nominal Categories

For square contingency tables with nominal categories, four kinds of measure are proposed to represent the degree of departure from marginal homogeneity (MH). The measures are expressed by using the Shannon entropy or Gini concentration. They are used to measure how far the marginal distributions (or the conditional marginal distributions given that an observation will fall in one of the off-diagonal cells of the table) are distant from those with an MH structure. Two of these measures are also extended to T-way tables (T ≥ 3).

Dynamic conditional marginal distributions in reliability theory

Motivated by the need of studying a subset of components, ‘separate' from the other components, we introduce a new definition of ‘marginal distribution'. This is done by fixing the lives of the other components, but without the ‘knowledge' of the components of interest. Formally this is done by minimally repairing the components of no interest up to a predetermined time. Preservation properties of these ‘conditional marginal distributions', with respect to several stochastic orderings, are obtained. Also, inheritance of positive dependence properties, by the conditional marginal distributions, is shown. In addition, the preservations of dynamic multivariate aging properties, by the dynamic conditional marginal distributions, are obtained. The definitions and results are illustrated by a set of examples. Some applications for modelling ‘combinations' of sets of random lifetimes, and for bounding complex sets of random lifetimes, are described.

Dynamic conditional marginal distributions in reliability theory

Motivated by the need of studying a subset of components, ‘separate' from the other components, we introduce a new definition of ‘marginal distribution'. This is done by fixing the lives of the other components, but without the ‘knowledge' of the components of interest. Formally this is done by minimally repairing the components of no interest up to a predetermined time. Preservation properties of these ‘conditional marginal distributions', with respect to several stochastic orderings, are obtained. Also, inheritance of positive dependence properties, by the conditional marginal distributions, is shown. In addition, the preservations of dynamic multivariate aging properties, by the dynamic conditional marginal distributions, are obtained. The definitions and results are illustrated by a set of examples. Some applications for modelling ‘combinations' of sets of random lifetimes, and for bounding complex sets of random lifetimes, are described.