Joint Distribution Research Articles

Multivariate asymptotic normality determined by high moments

We extend a general result showing that the asymptotic behavior of high moments, factorial or standard, of random variables, determines asymptotically normality, from the one dimensional to the multidimensional setting. This approach differs from the usual moment method which requires that the moments of each fixed order converge. We illustrate our results by considering a joint distribution of the numbers of bins (having the same, finite, capacity) containing a prescribed number of balls in a classical allocation scheme.

Effects of condylar neck inclination and counterclockwise rotation on the stress distribution of the temporomandibular joint.

Three different kinds of condylar inclination were manually modelled anteriorly inclined condylar neck, vertical condylar neck, and posteriorly inclined condylar neck. Three different maxillary impactions were simulated to evaluate the effect of counterclockwise rotation. The von Misses stresses of the disc, compressive stresses of the glenoid fossa, and compressive stresses of the condyle were the highest in the models with posteriorly inclined neck and lowest in the models with vertical condylar neck design. Stresses of the temporomandibular joint increase with the counterclockwise rotation of the maxilla-mandibular complex. The posteriorly inclined neck should be considered a risk factor for condylar resorption with increased counterclockwise rotation.

GenSynthPop: generating a spatially explicit synthetic population of individuals and households from aggregated data

Synthetic populations are representations of actual individuals living in a specific area. They play an increasingly important role in studying and modeling individuals and are often used to build agent-based social simulations. Traditional approaches for synthesizing populations use a detailed sample of the population (which may not be available) or combine data into a single joint distribution, and draw individuals or households from these. The latter group of existing sample-free methods fail to integrate (1) the best available data on spatial granular distributions, (2) multi-variable joint distributions, and (3) household level distributions. In this paper, we propose a sample-free approach where synthetic individuals and households directly represent the estimated joint distribution to which attributes are iteratively added, conditioned on previous attributes such that the relative frequencies within each joint group of attributes are maintained and fit granular spatial marginal distributions. In this paper we present our method and test it for the Zuid-West district of The Hague, the Netherlands, showing that spatial, multi-variable and household distributions are accurately reflected in the resulting synthetic population.

Possible Data-Generating Models of Longitudinal Continuous Outcomes and Intercurrent Events to Investigate Estimands

We aim to explore data-generating models to jointly simulate outcomes and intercurrent events for randomized clinical trials to enable the investigation of estimands. We develop four possible data-generating models for the joint distribution of longitudinal continuous clinical outcomes and intercurrent events under the scenario where they are observable: a selection model, a pattern-mixture mixed model, a shared-parameter model, and a joint model of longitudinally observed outcomes and a survival model for intercurrent events. We present a case study in a short-term depression trial with repeated measurements of continuous outcomes and two types of intercurrent events, and evaluate the potential and challenges of such data-generating models. Simulating randomized trials with outcomes and intercurrent events is a complex undertaking. We found that the four possible data-generating models can simulate different types of intercurrent events and associated longitudinal outcomes. They can be used to emulate envisaged patterns of intercurrent events and outcomes informed by prior available trial data or expectations. Model and parameter choice for a given application require further development. The four possible data-generating models could be used to investigate different estimands and their properties in-depth in the design stage. Thereby they are useful tools for the selection of estimands a priori.

STAREG: Statistical replicability analysis of high throughput experiments with applications to spatial transcriptomic studies.

Replicable signals from different yet conceptually related studies provide stronger scientific evidence and more powerful inference. We introduce STAREG, a statistical method for replicability analysis of high throughput experiments, and apply it to analyze spatial transcriptomic studies. STAREG uses summary statistics from multiple studies of high throughput experiments and models the the joint distribution of p-values accounting for the heterogeneity of different studies. It effectively controls the false discovery rate (FDR) and has higher power by information borrowing. Moreover, it provides different rankings of important genes. With the EM algorithm in combination with pool-adjacent-violator-algorithm (PAVA), STAREG is scalable to datasets with millions of genes without any tuning parameters. Analyzing two pairs of spatially resolved transcriptomic datasets, we are able to make biological discoveries that otherwise cannot be obtained by using existing methods.

Maximum entropy-based modeling of community-level hazard responses for civil infrastructures

Perturbed by natural hazards, community-level infrastructure networks operate like many-body systems, with behaviors emerging from coupling individual component dynamics with group correlations and interactions. It follows that we can borrow methods from statistical physics to study the response of infrastructure systems to natural disasters. This study aims to construct a joint probability distribution model to describe the post-hazard state of infrastructure networks and propose an efficient surrogate model of the joint distribution for large-scale systems. Specifically, we present maximum entropy modeling of the regional impact of natural hazards on civil infrastructures. Provided with the current state of knowledge, the principle of maximum entropy yields the “most unbiased“ joint distribution model for the performances of infrastructures. In the general form, the model can handle multivariate performance states and higher-order correlations. In a particular yet typical scenario of binary performance state variables with knowledge of their mean and pairwise correlation, the joint distribution reduces to the Ising model in statistical physics. In this context, we propose using a dichotomized Gaussian model as an efficient surrogate for the maximum entropy model, facilitating the application to large systems. Using the proposed method, we investigate the seismic collective behavior of a large-scale road network (with 8,694 nodes and 26,964 links) in San Francisco, showcasing the non-trivial collective behaviors of infrastructure systems.

Asymptotic limits of transient patterns in a continuous-space interacting particle system

We study a discrete-time interacting particle system with continuous state space, which is motivated by a mathematical model for turnover through branching in actin filament networks. It gives rise to transient clusters reminiscent of actin filament assemblies in the cortex of living cells. We reformulate the process in terms of the inter-particle distances and characterize their marginal and joint distributions. We construct a recurrence relation for the associated characteristic functions and pass to the large population limit, reminiscent of the Fleming–Viot super processes. The precise characterization of all marginal distributions established in this work opens the way to a detailed analysis of cluster dynamics. We also obtain a recurrence relation that enables us to compute the moments of the asymptotic single particle distribution characterizing the transient aggregates. Our results indicate that aggregates have a fat-tailed distribution.

Envelope spectrum neural network with adaptive domain weight harmonization for intelligent bearing fault diagnosis under cross-machine scenarios

Accurate bearing fault diagnosis technology is highly important for ensuring the safe operation of mechanical equipment. Fault diagnosis methods can be roughly divided into signal processing-based methods (SPM) and data-driven methods (DDMs), which rely on physical knowledge and data knowledge, respectively. However, SPM cannot adapt to large data samples and dynamic parameter variations. DDMs did not consider physical representation consistency. To address the above issues, an envelope spectrum neural network (ESNN) is proposed for cross-machine bearing fault diagnosis. First, a deep transfer convolution network (DTCN) is constructed as the basic diagnostic framework. Second, a knowledge-to-model conversion strategy (KMC) is built to create ESNN, which utilizes equivalent convolution functions to construct the first two layers of DTCN, guiding the model to learn physical knowledge. Subsequently, an adaptive domain weight harmonization (ADWH) mechanism is proposed that can dynamically combine marginal distributions and joint distributions and automatically learn hidden features contained in physical and data knowledge, thus alleviating domain shift issues. Experimental evaluations are conducted using fault datasets from three different machines. The results show that, compared to models without knowledge guidance, ESNN achieves a 6.4% improvement in diagnostic accuracy. Compared to many advanced models, ESNN can achieve a maximum diagnostic accuracy improvement of 35.94%. The code of the ESNN can be found at https://github.com/John-520/ESNN.

USMDA: Unsupervised Multisource Domain Adaptive ADHD prediction model using neuroimaging

There is an increasing number of large-scale cross-site database collections of neuroimaging markers (sMRI and fMRI) for studying neurodevelopmental illnesses (NDDs). Although a huge amount of data favors machine learning-based categorization algorithms, the unique heterogeneity of each site can impair cross-site generalization capacity. It is critical to create Unsupervised domain adaption methods for NDDs because obtaining appropriate diagnoses or labeling for NDDs might be problematic. In our work, we focus on Attention-deficit/hyperactivity disorder, which is the most common and frequently co-occurring NDD. We present an unsupervised multisource domain adaptation network (USMDA) with four primary components: Domain Alignment Module, Discrepancy Estimator, Pre-trained Model Generator, and Unsupervised Network. The Domain Alignment module is intended to incrementally and effectively align graph representations of the source and target domains. At the same time, the binary cross entropy regularizer is introduced for the first time during the training of a model learned on multiple source domains to improve existing feature alignment methods such as Transfer Joint Matching (TJM) and Joint Distribution Adaptation (JDA) by learning good unsupervised features. In an unsupervised network, the grid search optimization technique generates the optimal pseudo labels for unlabeled target data. We validate our proposed technique first on existing feature-level DA methods such as JDA, TJM, and Correlation alignment (CORAL), on the publically accessible dataset ADHD-200 and then by using binary cross-entropy in existing DA methods such as TJMCE and JDACE. The experimental results show that our proposed USMDAJDACE method when applied to multisite sMRI and fMRI ADHD data, can significantly outperform competitive methods for multi-center ADHD diagnosis.

Empirical framework for Cournot oligopoly with private information

AbstractWe propose an empirical framework for asymmetric Cournot oligopoly with private information about variable costs. First, considering a linear demand for a homogeneous product with a random intercept, we characterize the Bayesian Cournot–Nash equilibrium. Then we establish the identification of the joint distribution of demand and firm‐specific cost distributions. Following the identification steps, we propose a likelihood‐based estimation method and apply it to the global market for crude oil and quantify the welfare effect of private information. We also consider extensions of the model to include product differentiation, conduct parameters, nonlinear demand, or selective entry.

A probabilistic framework for offshore aquaculture suitability assessment using bivariate copulas

Aquaculture at sea is gaining increasing importance, not only as a (local) food source but also due to its potential of being combined with other offshore activities such as wind parks. Nevertheless, experience of offshore aquaculture is limited. This study aims to provide a framework to evaluate offshore aquaculture suitability accounting for the probabilistic dependence between relevant variables. This framework is applied to obtain suitability maps of aquaculture for the North Sea for the blue mussel Mytilus edulis and the sugar kelp Saccharina latissima. For each of these species, three ecological variables are selected and the optimal growth and critical survival limits are defined. Here, suitability is defined as the probability of meeting these conditions. Data on the selected variables is extracted from a large-scale 3D hydrodynamic and ecological model of the northwest European Shelf, of which daily extremes are sampled. The probabilistic model is developed using bivariate copula models, which are fitted to each variable pair to describe their joint distribution function at each studied location. Empirical distribution functions are used to describe the univariate distribution function of each variable and location. Using Monte-Carlo simulations, the probability of meeting the optimal and critical limits is estimated and suitability maps accounting for the probabilistic dependence between the variables are generated. In addition, suitability maps disregarding the dependence are generated and compared to those accounting for the probabilistic dependence. It was found that considering the dependence between variables significantly improves the accuracy of the results for optimal and critical growth conditions for both species. The presented method allows to identify potential areas where blue mussel and sugar kelp cultivation is the most suitable. For instance, in this study, a north-south elongated area west of the German and Danish coast appears to be most suitable for blue mussels, while estuaries and rivers are found the most suitable for the sugar kelp.

Disentangled latent factors for muti-cause treatment effect estimation

Abstract Existing methods estimate treatment effects from observational data and assume that covariates are all confounders. However, observed covariates may not directly represent confounding variables that influence both treatment and outcome. They always include variables that only affect the treatment or the outcome. In addition, for multi-dimensional binary treatments, disentangled methods are mainly designed for binary variables and ignore the impact of multi-cause treatment variables on the inference of latent factors. To address these two issues, based on variable decomposition and proxy inference, we propose the Disentangled Latent Factors for Multi-cause Treatment Estimation (DEMTE) algorithm. It utilizes an identifiable autoencoder to infer and disentangle latent factors based on the joint distribution of variables in observational data. DEMTE evaluates the treatment effect on the disentangled factors. Synthetic experiments and semi-synthetic experiments demonstrate the effectiveness of the inference and disentanglement techniques and our method achieves more accurate treatment effect estimation.

Domain generalization for machine compound fault diagnosis by Domain-Relevant Joint Distribution Alignment

In machine fault diagnosis, domain generalization methods have gained significant attention due to their advantage in non-requirement of priori target domain distribution. However, they pose great challenges in domain-relevant feature learning and incurs inferior unseen-domain classification when large domain divergence exists. To address this issuse, we propose a novel distribution alignment strategy named DRJDA (Domain-Relevant Joint Distribution Alignment) that matches the domain-joint distribution and domain-relevant distribution for domain generalization fault diagnosis. Specifically, the α-PE divergence is employed to minimize the distribution discrepancy, which is demonstrated to be explicitly derived as the maximum value of a quadratic function. Additionally, a parameter-free plug-and-play data augmentation module that performs feature-level instance mixture and style transfer to increase the generalization ability. Finally, data from the China Light-duty Vehicle Test Cycle (CLTC) tests are used as case studies, and the experiments carried out across 14 different domains prove the proficiency of the proposed DRJDA in learning domain-invariant feature when significant domain divergence exists, indicating its remarkable potential in compound fault diagnosis for industrial machinery.

Pricing formula of Lookback option in stochastic delay differential equation model

This paper deals with new explicit pricing formulae for Lookback option when underlying asset price processes are represented by stochastic delay differential equation (hereafter “SDDE”). We derive a lemma on the joint distribution of the minimum and itself of a Wiener process in the SDDE model. Using this lemma, we obtain the explicit pricing formulae for the Lookback option. Through some numerical comparison experiment, we assure the correctness of the obtained pricing formula.

TAIL DEPENDENCE OF COMMODITY FUTURES RETURNS IN THE AGRICULTURAL AND ENERGY SECTORS

The goal of this research was to examine tail dependence structures between selected commodity futures returns. Tail dependence, called also extremal dependence, was evaluated for the pairs of commodities coming from the same sector (energy or agricultural). The study covers the years 2018-2023, embracing the COVID-19 pandemic and the outbreak of the Russia-Ukraine war. To achieve the goal, bivariate dynamic models were applied to percentage log returns of commodity futures. Marginal distributions were described using the ARMA-GARCH models. Joint distributions were constructed using the symmetrized Joe-Clayton copula, which allowed to model asymmetric dependence in the tails of a distribution. Time variation of the copula parameters, here equal to tail dependence coefficients, was described using the evolution equations [Patton 2006]. In the energy sector, the dependence in both tails of analyzed distributions was relatively strong, dynamic and higher in the lower tail than in the upper tail. On the contrary, the agricultural sector lacks common patterns of tail dependency. This feature of the agricultural sector creates an opportunity for investors or risk managers to build well-diversified portfolios.

Flow-based Generative Emulation of Grids of Stellar Evolutionary Models

We present a flow-based generative approach to emulate grids of stellar evolutionary models. By interpreting the input parameters and output properties of these models as multidimensional probability distributions, we train conditional normalizing flows to learn and predict the complex relationships between grid inputs and outputs in the form of conditional joint distributions. Leveraging the expressive power and versatility of these flows, we showcase their ability to emulate a variety of evolutionary tracks and isochrones across a continuous range of input parameters. In addition, we describe a simple Bayesian approach for estimating stellar parameters using these flows and demonstrate its application to asteroseismic data sets of red giants observed by the Kepler mission. By applying this approach to red giants in open clusters NGC 6791 and NGC 6819, we illustrate how large age uncertainties can arise when fitting only to global asteroseismic and spectroscopic parameters without prior information on initial helium abundances and mixing length parameter values. We also conduct inference using the flow at a large scale by determining revised estimates of masses and radii for 15,388 field red giants. These estimates show improved agreement with results from existing grid-based modeling, reveal distinct population-level features in the red clump, and suggest that the masses of Kepler red giants previously determined using the corrected asteroseismic scaling relations have been overestimated by 5%–10%.

Point cloud data-driven modelling of high-strength steel wire corrosion pits considering orientation features

We propose a corrosion pit modelling approach of high-strength steel wires considering orientation features using surface point cloud data, collected by three-dimensional laser scanning. Corrosion pits were identified through density-based spatial clustering of applications with noise (DBSCAN). The identified corrosion pits could be modelled as a semiellipsoid considering orientation features. The Gaussian copula model was utilised to describe the joint distribution of the geometric parameters of the corrosion pits. This approach will be valuable for simulation of the surface morphology of corroded high-strength steel wires.

Consistency and causality of interconnected nonsignaling resources

Abstract This paper examines networks of n measuring parties sharing m nonsignaling resources that can be locally wired together: that is, each party follows a scheme to measure the resources in a cascaded fashion with inputs to later resources possibly depending on outputs of earlier-measured ones. A specific framework is provided for studying probability distributions arising in such networks, and this framework is used to directly prove some accepted, but often only implicitly invoked, facts: there is a uniquely determined and well-defined joint probability distribution for the outputs of all resources shared by the parties, and this joint distribution is nonsignaling. It is furthermore shown that is often sufficient to restrict consideration to only extremal nonsignaling resources when considering features and properties of such networks. Finally, the framework illustrates how the physical theory of nonsignaling boxes and local wirings is causal, supporting the applicability of the inflation technique to constrain such models.
For an application, we probe the example of (3,2,2) inequalities that witness genuine three-party nonlocality according to the local-operations-shared-randomness definition, and show how all other examples can be derived from that of Mao et al. [Phys. Rev. Lett. 129:150401 (2022)].

Dissimilar joining of aluminum alloy and low-alloy carbon steel by resistance spot welding

In this work, the resistance spot welding (RSW) process was performed to join aluminum alloy and low-alloy carbon steel plates. The macro characteristics including nugget diameters and indentation rates, microstructure and tensile-shear strength of RSW joints were investigated. The results showed that the nugget of the RSW joints comprises a ‘bowl’ shape nugget on the aluminum side and an elliptical shape nugget on the steel side. Also, the intermetallic compound (IMC) layers containing Fe4Al13 and Fe2Al5 were formed around the aluminum/steel interface with the steel side having a tongue-shape and the aluminum side having a needle-shape. According to metallurgical evaluation and temperature distribution of RSW joints analyzed by the finite element method, the nugget on the aluminum side contained the dendritic grains and equiaxed dendritic grains. The nugget on the steel side consisted of a large amount of bainite and a small amount of coarse lath martensite. The nugget diameters and the indentations rates of RSW joints increased when increasing either welding current or welding time, and decreased when increasing the electrode pressure. The maximum values of nugget diameter and indentation rate of RSW joints were 9.076 mm and 4.144% when using the welding current of 16 kA, welding time of 450 ms and electrode force of 3 kN. In tensile-shear tests, the RSW joints showed a shear-off fracture mode. When increasing the welding current, welding time or electrode force, the tensile-shear strength of RSW joints increased first, and then reached a maximum, and finally decreased. The welding current of 16 kA, the welding time of 300 ms, and the electrode pressure of 3 kN were considered as the optimal welding parameters in the present study which resulted in the maximum tensile-shear strength of 2.24 kN. In addition, the IMC layers of the RSW joints exhibited a uniform and continuous appearance with a thickness of approximately 1.9 μm, and the IMC layer in the central area was thicker than that in the edge area.

Transportability of model‐based estimands in evidence synthesis

In evidence synthesis, effect modifiers are typically described as variables that induce treatment effect heterogeneity at the individual level, through treatment‐covariate interactions in an outcome model parametrized at such level. As such, effect modification is defined with respect to a conditional measure, but marginal effect estimates are required for population‐level decisions in health technology assessment. For noncollapsible measures, purely prognostic variables that are not determinants of treatment response at the individual level may modify marginal effects, even where there is individual‐level treatment effect homogeneity. With heterogeneity, marginal effects for measures that are not directly collapsible cannot be expressed in terms of marginal covariate moments, and generally depend on the joint distribution of conditional effect measure modifiers and purely prognostic variables. There are implications for recommended practices in evidence synthesis. Unadjusted anchored indirect comparisons can be biased in the absence of individual‐level treatment effect heterogeneity, or when marginal covariate moments are balanced across studies. Covariate adjustment may be necessary to account for cross‐study imbalances in joint covariate distributions involving purely prognostic variables. In the absence of individual patient data for the target, covariate adjustment approaches are inherently limited in their ability to remove bias for measures that are not directly collapsible. Directly collapsible measures would facilitate the transportability of marginal effects between studies by: (1) reducing dependence on model‐based covariate adjustment where there is individual‐level treatment effect homogeneity or marginal covariate moments are balanced; and (2) facilitating the selection of baseline covariates for adjustment where there is individual‐level treatment effect heterogeneity.