Joint Distribution Research Articles

Thick Data Analytics (TDA): An Iterative and Inductive Framework for Algorithmic Improvement

A gap remains between developing risk prediction models and deploying models to support real-world decision making, especially in high-stakes situations. Human-experts’ reasoning abilities remain critical in identifying potential improvements and ensuring safety. We propose a thick data analytics (TDA) framework for eliciting and combining expert-human insight into the evaluation of models. The insight is 3-fold: (a) statistical methods are limited to using joint distributions of observable quantities for predictions but often there is more information available in a real-world than what is usable for algorithms, (b) domain experts can access more information (e.g., patient files) than an algorithm and bring additional knowledge into their assessments through leveraging insights and experiences, and (c) experts can re-frame and re-evaluate prediction problems to suit real-world situations. Here, we revisit an example of predicting temporal risk for intensive care admission within 24 hr of hospitalization. We propose a sampling procedure for identifying informative cases for deeper inspection. Expert feedback is used to understand sources of information to improve model development and deployment. We recommend model assessment based on objective evaluation metrics derived from subjective evaluations of the problem formulation. TDA insights facilitate iterative model development toward safer, actionable, and acceptable risk predictions.

Joint effects of air pollution and neighborhood socioeconomic status on cognitive decline - Mediation by depression, high cholesterol levels, and high blood pressure

Air pollution and neighborhood socioeconomic status (N-SES) are associated with adverse cardiovascular health and neuropsychiatric functioning in older adults. This study examines the degree to which the joint effects of air pollution and N-SES on the cognitive decline are mediated by high cholesterol levels, high blood pressure (HBP), and depression. In the Emory Healthy Aging Study, 14,390 participants aged 50+ years from Metro Atlanta, GA, were assessed for subjective cognitive decline using the cognitive function instrument (CFI). Information on the prior diagnosis of high cholesterol, HBP, and depression was collected through the Health History Questionnaire. Participants' census tracts were assigned 3-year average concentrations of 12 air pollutants and 16 N-SES characteristics. We used the unsupervised clustering algorithm Self-Organizing Maps (SOM) to create 6 exposure clusters based on the joint distribution of air pollution and N-SES in each census tract. Linear regression analysis was used to estimate the effects of the SOM cluster indicator on CFI, adjusting for age, race/ethnicity, education, and neighborhood residential stability. The proportion of the association mediated by high cholesterol levels, HBP, and depression was calculated by comparing the total and direct effects of SOM clusters on CFI. Depression mediated up to 87 % of the association between SOM clusters and CFI. For example, participants living in the high N-SES and high air pollution cluster had CFI scores 0.05 (95 %-CI:0.01,0.09) points higher on average compared to those from the high N-SES and low air pollution cluster; after adjusting for depression, this association was attenuated to 0.01 (95 %-CI:-0.04,0.05). HBP mediated up to 8 % of the association between SOM clusters and CFI and high cholesterol up to 5 %. Air pollution and N-SES associated cognitive decline was partially mediated by depression. Only a small portion (<10 %) of the association was mediated by HBP and high cholesterol.

Consignment contract in a supply chain with price, demand and yield randomness: A distributionally robust approach

We investigate a supply chain consisting of a supplier and an e-commence platform who sign a consignment contract with uncertainty in price, demand, and yield. Due to the challenges of actually determining the joint distribution of random variables, we assume that only the partial distributional information is available for these three uncertainties. To address the issue of distributional ambiguity and to more accurately account for arbitrary correlations among these uncertainties, we introduce a moment-based distributionally robust optimization (DRO) approach that assumes only the first and second moments of these three uncertainties are known. Given an exogenous consignment rate, we derive the closed-form expression for the supplier’s optimal production decision and her worst-case expected profit. We study the impact of random price and random yield within the ambiguity set on the supplier’s production decision and the worst-case expected profit. From the e-commerce platform’s perspective, we further examine the contract design problem when the consignment rate is endogenous and analyze equilibrium solutions for both contracting parties. Our results show that the additional consideration of price or yield uncertainty within the ambiguity set does not always mitigate or enhance the degree of conservatism of the contracting parties, which is closely related to the correlation between any two types of uncertainty, as well as the degree of uncertainty itself.

Deep Joint Semantic Adaptation Network for Multi-source Unsupervised Domain Adaptation

Multi-source Unsupervised Domain Adaptation (MUDA) transfers knowledge learned from multiple labeled source domains to an unlabeled target domain by minimizing the domain shift between multiple source domains and the target domain. Recent studies on MUDA have focused on aligning the distribution of each pair of source and target domains in separate feature spaces to reduce their domain shift. However, these approaches suffer from two main shortcomings. First, they usually focus on the global domain shift which lacks consideration of the joint distribution of category-corresponded subdomains. Second, out-of-distribution samples far from the sample center are hard to align by the global domain alignment. Therefore, we propose a novel Deep Joint Semantic Adaptive Network (DJSAN) for MUDA. Specifically, a new maximum mean discrepancy-based metric, Joint Semantic Maximum Mean Discrepancy (JSMMD), is proposed, which can uniformly optimize the cross-domain joint distribution of category-corresponded subdomains on multiple task-specific layers. Moreover, to deal with the out-of-distribution hard samples, we propose an across-domain data augmentation method called Source-Target Domain Mixing (STDMix) to enhance the robustness of the model, which synthesizes the source domain and target domain into a new domain at a fixed ratio and utilizes information entropy to provide reliable pseudo-labels for samples in the target domain. Experimental results on three public datasets, i.e., Office-31, Digits-five, and Office-Home, show that our proposed method achieves improvements of 0.3%, 1.8%, and 2.7% in average accuracy, respectively.

Statistical indices of masculinity-femininity: A theoretical and practical framework

Statistical indices of masculinity-femininity (M-F) summarize multivariate profiles of sex-related traits as positions on a single continuum of individual differences, from masculine to feminine. This approach goes back to the early days of sex differences research; however, a systematic discussion of alternative M-F indices (including their meaning, their mutual relations, and their psychometric properties) has been lacking. In this paper I present an integrative theoretical framework for the statistical assessment of masculinity-femininity, and provide practical guidance to researchers who wish to apply these methods to their data. I describe four basic types of M-F indices: sex-directionality, sex-typicality, sex-probability, and sex-centrality. I examine their similarities and differences in detail, and consider alternative ways of computing them. Next, I discuss the impact of measurement error on the validity of these indices, and outline some potential remedies. Finally, I illustrate the concepts presented in the paper with a selection of real-world datasets on body morphology, brain morphology, and personality. An R function is available to easily calculate multiple M-F indices from empirical data (with or without correction for measurement error) and draw summary plots of their individual and joint distributions.

Microstructure and residual stress distribution of electron beam-welded joints of a 50 mm-thick TA15 titanium alloy plate

Abstract Vacuum electron beam welding was applied to a 50 mm-thick TA15 titanium alloy plate. Microstructure observation and microhardness testing were performed. Meanwhile, the residual stress on the surface at different distances from the weld centre was measured via the hole drilling method. A finite element model for electron beam welding of the TA15 titanium alloy plate was constructed on commercial finite element software. Experimental results showed that the microstructure of the weld zone consisted of a basket martensitic phase. The highest microhardness in the weld zone was 409 HV, and the microhardness of the base metal was the lowest. The maximum gradient change area was located at the HAZ near the base metal. The peak value of longitudinal residual stress from the simulation was 880 MPa, which was in the weld metal. The sharp change area of longitudinal residual stress gradient was located in the base metal near HAZ.

Informative Modes of Seismicity in Nearest‐Neighbor Earthquake Proximities

AbstractWe analyze nearest‐neighbor proximities of earthquakes in California based on the joint distribution (T, R) of rescaled time T and rescaled distance R between pairs of earthquakes (Zaliapin &amp; Ben‐Zion, 2013a, https://doi.org/10.1002/jgrb.50179), using seismic catalogs from several regions and several catalogs for the San Jacinto Fault Zone (SJFZ). The study aims to identify informative modes in nearest‐neighbor diagrams beyond the general background and clustered modes, and to assess seismic catalogs derived by different methods. The results show that earthquake clusters with large and small‐to‐medium mainshocks have approximately diagonal and horizontal (T, R) distributions of the clustered mode, respectively, reflecting different triggering distances of mainshocks. Earthquakes in the creeping section of San Andreas Fault have a distinct “repeaters mode” characterized by very large rescaled times T and very small rescaled distances R, due to nearly identical locations of repeating events. Induced seismicity in the Geysers and Coso geothermal fields follow mostly the background mode, but with larger rescaled times T and smaller rescaled distances R compared to tectonic background seismicity. We also document differences in (T, R) distributions of catalogs constructed by different techniques (analyst‐picks, template‐matching and deep‐learning) for the SJFZ, and detect a mode with very large R and small T in the template‐matching and deep‐learning based catalogs. This mode may reflect dynamic triggering by passing waves and/or catalog artifacts.

Inertia suppresses signatures of activity of active Brownian particles in a harmonic potential.

A harmonically trapped active Brownian particle exhibits two types of positional distributions-one has a single peak and the other has a single well-that signify steady-state dynamics with low and high activity, respectively. Adding inertia to the translational motion preserves this strict classification of either single-peak or single-well densities but shifts the dividing boundary between the states in the parameter space. We characterize this shift for the dynamics in one spatial dimension using the static Fokker-Planck equationfor the full joint distribution of the state space. We derive local results analytically with a perturbation method for a small rotational velocity and then extend them globally with a numerical approach.

Graphical Modeling for Multi-Source Domain Adaptation.

Multi-Source Domain Adaptation (MSDA) focuses on transferring the knowledge from multiple source domains to the target domain, which is a more practical and challenging problem compared to the conventional single-source domain adaptation. In this problem, it is essential to model multiple source domains and target domain jointly, and an effective domain combination scheme is also highly required. The graphical structure among different domains is useful to tackle these challenges, in which the interdependency among various instances/categories can be effectively modeled. In this work, we propose two types of graphical models, i.e. Conditional Random Field for MSDA (CRF-MSDA) and Markov Random Field for MSDA (MRF-MSDA), for cross-domain joint modeling and learnable domain combination. In a nutshell, given an observation set composed of a query sample and the semantic prototypes (i.e. representative category embeddings) on various domains, the CRF-MSDA model seeks to learn the joint distribution of labels conditioned on the observations. We attain this goal by constructing a relational graph over all observations and conducting local message passing on it. By comparison, MRF-MSDA aims to model the joint distribution of observations over different Markov networks via an energy-based formulation, and it can naturally perform label prediction by summing the joint likelihoods over several specific networks. Compared to the CRF-MSDA counterpart, the MRF-MSDA model is more expressive and possesses lower computational cost. We evaluate these two models on four standard benchmark data sets of MSDA with distinct domain shift and data complexity, and both models achieve superior performance over existing methods on all benchmarks. In addition, the analytical studies illustrate the effect of different model components and provide insights about how the cross-domain joint modeling performs.

Information Content of Inflation Expectations: A Copula-Based Model

Abstract This paper introduces a holistic framework that integrates copula modeling and information-theoretic measures to examine the information content of inflation expectations. Copulas are used to capture the dynamic dependence between inflation and expectations, accounting for extreme events and tail dependence. Information-theoretic measures are employed to quantify the information that expectations provide about inflation. Theoretical results establish a link between copula entropy and mutual information, propose a lower bound for copula entropy, and provide a practical tool for central banks to anchor expectations to achieve inflation targets. Empirical findings reveal higher uncertainty in the tails of the joint distribution and underscore the meaningful information carried by expected inflation for forecasting inflation, particularly with shorter-term expectations.

EFFICIENT EVALUATION OF DOUBLE-BARRIER OPTIONS

In the paper, we develop a very fast and accurate method for pricing double barrier options with continuous monitoring in wide classes of Lévy models; the calculations are in the dual space, and the Wiener–Hopf factorization is used. For wide regions in the parameter space, the precision of the order of [Formula: see text] is achievable in seconds, and of the order of [Formula: see text]–[Formula: see text] — in fractions of a second. The Wiener–Hopf factors and repeated integrals in the pricing formulas are calculated using sinh-deformations of the lines of integration, the corresponding changes of variables and the simplified trapezoid rule. If the Bromwich integral is calculated using the Gaver–Wynn Rho acceleration instead of the sinh-acceleration, the CPU time is typically smaller but the precision is of the order of [Formula: see text]–[Formula: see text], at best. Explicit pricing algorithms and numerical examples are for no-touch options, digitals (equivalently, for the joint distribution function of a Lévy process and its supremum and infimum processes), and call options. Several graphs are produced to explain fundamental difficulties for accurate pricing of barrier options using time discretization and interpolation-based calculations in the state space.

A SIMPLE AND FLEXIBLE TEST OF SAMPLE EXCHANGEABILITY WITH APPLICATIONS TO STATISTICAL GENOMICS.

In scientific studies involving analyses of multivariate data, basic but important questions often arise for the researcher: Is the sample exchangeable, meaning that the joint distribution of the sample is invariant to the ordering of the units? Are the features independent of one another, or perhaps the features can be grouped so that the groups are mutually independent? In statistical genomics, these considerations are fundamental to downstream tasks such as demographic inference and the construction of polygenic risk scores. We propose a non-parametric approach, which we call the V test, to address these two questions, namely, a test of sample exchangeability given dependency structure of features, and a test of feature independence given sample exchangeability. Our test is conceptually simple, yet fast and flexible. It controls the Type I error across realistic scenarios, and handles data of arbitrary dimensions by leveraging large-sample asymptotics. Through extensive simulations and a comparison against unsupervised tests of stratification based on random matrix theory, we find that our test compares favorably in various scenarios of interest. We apply the test to data from the 1000 Genomes Project, demonstrating how it can be employed to assess exchangeability of the genetic sample, or find optimal linkage disequilibrium (LD) splits for downstream analysis. For exchangeability assessment, we find that removing rare variants can substantially increase the -value of the test statistic. For optimal LD splitting, the V test reports different optimal splits than previous approaches not relying on hypothesis testing. Software for our methods is available in R (CRAN: flintyR) and Python (PyPI: flintyPy).

Cross-Subject Brain–Computer Interfaces with Joint Distribution Alignment

Distributions of electroencephalogram (EEG) data vary greatly across different subjects. It is a very important issue how to generalize models across subjects. In this paper, an algorithm is proposed to build high-performance cross-subject motor-imagery brain–computer interfaces (BCIs) for a new subject. First, a novel distance metric is proposed to quantify the joint distribution discrepancy (JDD) between data from different subjects. It gives better evaluations for discrepancies between different distributions than conventional probabilistic metrics. Moreover, it can be extended to design many novel algorithms. Second, a support vector machine combined with JDD (JDMSVM) is proposed for cross-subject classification. For dataset dataIVa, the JDMSVM runs best under 9 out of 15 situations and averagely outperforms counterparts by 10.1%, 9.5%, 3.2% and 1.7%, respectively. For GigaDataset, JDMSVM runs best under 8 of 12 conditions. It averagely outperforms its counterparts by 10.4%, 5.3%, 2.7% and 2.4%, respectively. The experiments demonstrate that the proposed algorithm is effective and competitive for cross-subject BCI.

Do wages underestimate the inequality in workers' rewards? The joint distribution of job quality and wages across occupations

AbstractInformation on both wages and job quality is needed in order to understand the occupational dispersion of wellbeing. We analyse subjective wellbeing in a large UK sample to construct a measure of ‘overall reward’, the sum of wages and the value of job quality, in 90 different occupations. If only wages are included, then labour market inequality is underestimated: the dispersion of overall rewards is one‐third larger than the dispersion of wages. Our findings are similar, and stronger, in data on US workers. We find a positive correlation between job quality and wages in all specifications, both between individuals in the cross‐section and within individuals in panel data. The gender and ethnic gaps in the labour market are larger than those in wages alone, and the overall rewards to education on the labour market are underestimated by earnings differentials alone.

A Joint Probability Distribution for Multivariate Wind-Wave Conditions and Discussions on Uncertainties

Abstract This article presents a joint statistical model, which is needed in probabilistic design and structural risk assessment, that has been fitted to data of wind and wave conditions for an offshore location off South Brittany. The data are from a numerical model and contain hourly values for several wind and wave variables over a period of 32 years. The joint distribution presented in this article considers the variables wind direction, mean wind speed, significant wave height, wave direction, and peak period. A conditional model for turbulence given wind speed is introduced to yield an additional variable for the joint model. The joint model is constructed as a product of marginal and conditional models for the various variables. Additionally, the fitted models will be used to construct environmental contours for some of the variables. For significant wave height, various models are used to obtain different extreme value estimates, illustrating the uncertainties involved in extrapolating statistical models beyond the support of the data, and a discussion on the use of nonparametric copulas for the joint distribution is presented. Moreover, bootstrap has been performed to estimate the uncertainty in estimated model parameters from sampling variability. The effect of changing which variable to model as the marginal in a conditional model is illustrated by switching from wind speed to significant wave height. Such joint distribution models are important inputs for design of offshore structures, and in particular for offshore wind turbines, and the influence of the joint model in design is illustrated by a simple case study. This article is an extension of the conference paper by Vanem et al. (2023, “A Joint Probability Distribution Model for Multivariate Wind and Wave Conditions,” 42nd International Conference on Ocean, Offshore and Arctic Engineering).

Considering Uncertainty of Historical Ice Jam Flood Records in a Bayesian Frequency Analysis for the Peace‐Athabasca Delta

AbstractThe Peace‐Athabasca Delta in Alberta, Canada has numerous perched basins that are primarily recharged after large ice jams cause floods (an ecological benefit). Previous studies have estimated that such large floods are likely to decrease in frequency under various climate projections. However, there is a sizable uncertainty range in these predicted flood probabilities, in part due to the short 60‐year systematic record that contained few large ice jam floods. An additional 50 years of historical data are available from various sources, with expert‐interpreted flood categories; however, these categorizations are uncertain in magnitude and occurrence. We developed a Bayesian framework that considers magnitude and occurrence uncertainties within a logistic regression model that predicts the annual probability of a large flood. The Bayesian regression estimates the joint distribution of parameters describing the effects of climatic factors and parameters that describe the probability that historical flood magnitudes were recorded as large (or not) when a truly large (or not) flood occurred. We compare four models for hindcasting and projecting large ice jam flood probabilities in future climates. The models consider: (a) historical data uncertainty, (b) no historical data uncertainty, (c) only the systematic record, and (d) the systematic record with a different model. Neglecting historical data uncertainty provides inaccurate estimates, while using only the systematic record provides wider prediction intervals than considering the full record with uncertain historical data. Thus, we demonstrate that including uncertain historical information can effectively extend the record length and make flood frequency analyses more accurate and precise.

Inference for partial correlations of a multivariate Gaussian time series

Abstract We derive an asymptotic joint distribution and novel covariance estimator for the partial correlations of a multivariate Gaussian time series under mild regularity conditions. Using our derived asymptotic distribution, we develop a Wald confidence interval and testing procedure for inference of individual partial correlations for time series data. Through simulation we demonstrate that our proposed confidence interval attains higher coverage rates and our testing procedure achieves false positive rates closer to the nominal levels than approaches that assume independent observations when autocorrelation is present.

A Dirichlet process mixture regression model for the analysis of competing risk events

We develop a regression model for the analysis of competing risk events. The joint distribution of the time to these events is flexibly characterized by a random effect which follows a discrete probability distribution drawn from a Dirichlet Process, explaining their variability. This entails an additional layer of flexibility of this joint model, whose inference is robust with respect to the misspecification of the distribution of the random effects. The model is analysed in a fully Bayesian setting, yielding a flexible Dirichlet Process Mixture model for the joint distribution of the time to events. An efficient MCMC sampler is developed for inference. The modelling approach is applied to the empirical analysis of the surrending risk in a US life insurance portfolio previously analysed by Milhaud and Dutang (2018). The approach yields an improved predictive performance of the surrending rates.

Emergent invariance and scaling properties in the collective return dynamics of a stock market.

A key metric to determine the performance of a stock in a market is its return over different investment horizons (τ). Several works have observed heavy-tailed behavior in the distributions of returns in different markets, which are observable indicators of underlying complex dynamics. Such prior works study return distributions that are marginalized across the individual stocks in the market, and do not track statistics about the joint distributions of returns conditioned on different stocks, which would be useful for optimizing inter-stock asset allocation strategies. As a step towards this goal, we study emergent phenomena in the distributions of returns as captured by their pairwise correlations. In particular, we consider the pairwise (between stocks i, j) partial correlations of returns with respect to the market mode, ci,j(τ), (thus, correcting for the baseline return behavior of the market), over different time horizons (τ), and discover two novel emergent phenomena: (i) the standardized distributions of the ci,j(τ)'s are observed to be invariant of τ ranging from from 1000min (2.5 days) to 30000min (2.5 months); (ii) the scaling of the standard deviation of ci,j(τ)'s with τ admits good fits to simple model classes such as a power-law τ-λ or stretched exponential function [Formula: see text] (λ, β > 0). Moreover, the parameters governing these fits provide a summary view of market health: for instance, in years marked by unprecedented financial crises-for example 2008 and 2020-values of λ (scaling exponent) are substantially lower. Finally, we demonstrate that the observed emergent behavior cannot be adequately supported by existing generative frameworks such as single- and multi-factor models. We introduce a promising agent-based Vicsek model that closes this gap.

Metocean conditions at two Norwegian sites for development of offshore wind farms

This paper examines metocean data from NORA3, a state-of-the-art wind and wave hindcast dataset for Northern Europe. Two offshore Norwegian areas, Utsira Nord (UN) and Sørlige Nordsjø II (SN2), are investigated. Both areas offer significant potential for the offshore wind sector. UN is situated in deep-sea water, suitable for floating offshore wind turbines. In contrast, SN2 lies in intermediate waters and ranks among the North Sea’s most promising regions allocated for offshore wind. Data from NORA3, originally on a 3-km resolution grid, are resampled into unstructured grids spanning from 1982 to 2022. This refined dataset offers a climatology time scale with superior spatial and temporal resolution compared to most other hindcast and reanalysis databases. The study examines mean wind speed and direction across seven levels, ranging from 10 m to 750 m above the surface. Analyses of extreme wind and wave conditions have been conducted. Results reveal that UN experiences higher extreme wave heights than SN2 while the extreme wind speeds may be substantially larger at SN2 than UN. Moreover, this study establishes joint distribution models that encompass several parameters, including mean wind speed, significant wave height, wave spectral peak period, and direction difference between wind and waves. Thus, this metocean data is valuable for designing and analyzing floating wind farms over their lifecycles.