Communicating Uncertainties in Bi- and Multivariate Distributions

Multivariate distributions are useful in modeling several dependent random variables. It is difficult to develop a unique multivariate skewed distribution. There are different forms to the same distribution are available. For this reason, the research is ongoing into ways to construct multivariate families from univariate margins. In this paper, we have proposed a generalization of univariate cubic transmuted family to a multivariate family named a multivariate cubic transmuted (MCT) family. This new family applied to (p) baseline Weibull variables named multivariate cubic transmuted Weibull distribution (CTPW). Statistical properties of (CTPW) have been studied, and the parameters have been estimated by maximum likelihood (ML) method. A real data set for bone density test by photon absorption in the peripheral bones of olderly women fitted by (CTpW), trivariate transmuted Weibull (T3W) and FGMW distributions. The important theoretical conclusions are, the marginal distributions belong to multivariate cubic family with dimension less than p, joint moments of any order depend on raw moments of each baseline variable and moments of the largest order statistics of random samples of sizes two and three drawn from each baseline distribution. In real application, the (CT3W) is a better fit to bone density data.

A distribution P 0 of a random vector X = ( X 1 ,..., X n ) is said to be linear exponential in a parameter θ = ( θ 1 ,..., θ n ) if [Formula: see text]. A multivariate linear exponential distribution is binomial if and only if its univariate marginals are binomial.

Lampreys (Petromyzontiformes) are an ancient group of fishes with complex life histories. We created a life cycle model that includes an R Shiny interactive web application interface to simulate abundance by life stage. This will allow scientists and managers to connect available demographic information in a framework that can be applied to questions regarding lamprey biology and conservation. We used Pacific lamprey (Entosphenus tridentatus) as a case study to highlight the utility of this model. We applied a global sensitivity analysis to explore the importance of individual life stage parameters to overall population size, and to better understand the implications of existing gaps in knowledge. We also provided example analyses of selected management scenarios (dam passage, fish translocations, and hatchery additions) influencing Pacific lamprey in fresh water. These applications illustrate how the model can be applied to inform conservation efforts. This tool will provide new capabilities for users to explore their own questions about lamprey biology and conservation. Simulations can hone hypotheses and predictions, which can then be empirically tested in the real world.

In Bayesian decision theory, stochastic simulation techniques have been widely used by decision makers. The Markov chain Monte Carlo method (MCMC) plays a key role in stochastic simulation within the framework of Bayesian statistics. The notion of "slice sampling", or employing auxiliary variables in sampling, has been recently suggested in the literature for improving the efficiency of the traditional MCMC methods. In the existing literature, the one dimensional slice sampler has been extensively studied, yet the literature on the multidimensional case is sparse. In this study, we utilize multiple auxiliary variables in our sampling algorithms for multivariate normal distributions, which adapt better to the local properties of the target probability distributions. We show that these methods are flexible enough to allow for truncation to rectangular regions and/or the exclusion of any n dimensional hyper-quadrant. We compare these algorithms for both efficiency and accuracy via simulation experiments. Our results show that our new sampling techniques are accurate and more effective than the traditional single auxiliary variable slice sampler, especially for truncated multivariate distributions. Further, we extend our methods to general multivariate distributions including multivariate student t distributions, multivariate elliptical distributions, multivariate skew normal distributions, multivariate skew t distributions and a general class of multivariate skew elliptical distributions. We also discuss and outline some applications of our algorithms in the real business world, especially in the production and operations management and the finance areas. With regard to production and operations management, we find that the proposed multivariate normal slice sampler can be implemented in a stochastic optimization process for finding the optimal fulfillment rate of an assembly system. This system consists of n components, from which m products are assembled via a periodic review control policy. In finance area, we show that multivariate slice samplers can be used to update model parameters and predict future asset returns in a higher moments Bayesian portfolio optimization model, which is based on a general class of multivariate skew t distributions. The application of a multivariate slice sampler improves the model's ability of handling large data sets and saves computation time for deriving complicated posterior probability distributions.

Multivariate probability distributions with given marginals are considered, along with linear functionals, to be minimized or maximized, acting on them. The functionals are supposed to satisfy the Monge or inverse Monge or some higher order convexity property, and they may be only partially known. Existing results in connection with Monge arrays are reformulated and extended in terms of linear programming dual feasible bases. Lower and upper bounds are given for the optimum value as well as for unknown coefficients of the objective function, based on the knowledge of some dual feasible bases and corresponding objective function coefficients. In the two- and three-dimensional cases dual feasible bases are obtained for the problem, where not only the univariate marginals but also the covariances of the pairs of random variables are known.

Exploratory data analysis refers to the existing data to explore under the assumption of less as far as possible, through drawing, tabulation, calculation methods to explore characteristics of data structure and regularity of a kind of analysis method. However, exploratory data by calculation method is a very general method to find the key of data. In this paper, we introduce a correlation measure for exploratory analysis based on maximal information coefficient. First, we briefly introduce the traditional data analysis methods and features, expound the necessity of exploring analysis and content. Then, correlation measurement which used commonly are expounded, summarized their characteristics and models. Therefore, we propose a weighted measure based on Maximal Information Coefficient to improve effectiveness of exploratory analysis. Then we get eigenvalues of the Maximal Information Coefficient and Pearson correlation coefficient in linear and nonlinear function of plus noise. Finally, explore analysis display visualization of the results by test dataset, emphasis direction of further research.

Copulas have become an important analytic tool for characterizing multivariate distributions and dependence. One is often interested in simulating data from copula estimates. The process can be analytically and computationally complex and usually involves steps that are unique to a given parametric copula. We describe an alternative approach that uses \probability{proportional{to{size" (PPS) random sampling with weights formed from the copula likelihood function. The method is flexible and can be applied to parametric and nonparametric marginal density estimates. The precision of the simulation can be calibrated by adjusting the density of the multidimensional grid used in the simulation process. The approach is fully transparent to any copula function with continuous random variables. An example evaluates a number of goodness-of-fit criteria and provides strong support for the validity and practicality of the method.

Copula-based conditional tail indices

Digital twins (DT) offer a low-overhead evaluation platform and the ability to generate rich datasets for training machine learning (ML) models before actual deployment. Specifically, for the scenario of ML-aided millimeter wave (mmWave) links between moving vehicles to roadside units, we show how DT can create an accurate replica of the real world for model training and testing. The contributions of this paper are twofold: First, we propose a framework to create a multimodal Digital Twin (DT), where synthetic images and LiDAR data for the deployment location are generated along with RF propagation measurements obtained via ray-tracing. Second, to ensure effective domain adaptation, we leverage <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">meta-learning</i>, specifically <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Model-Agnostic Meta-Learning</i> (MAML), with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">transfer learning</i> (TL) serving as a baseline validation approach. The proposed framework is validated using a comprehensive dataset containing both real and synthetic LiDAR and image data for mmWave V2X beam selection. It also enables the investigation of how each sensor modality impacts domain adaptation, taking into account the unique requirements of mmWave beam selection. Experimental results show that models trained on synthetic data using transfer learning and meta-learning, followed by minimal fine-tuning with real-world data, achieve up to 4.09× and 14.04× improvements in accuracy, respectively. These findings highlight the potential of synthetic data and meta-learning to bridge the domain gap and adapt rapidly to real-world beamforming challenges.

Estimated cardiac deaths associated with treating chronic lymphocytic leukemia with ibrutinib versus zanubrutinib in the United States

Deep learning models require vast amounts of annotated training data. Gathering and annotating the data from the real world is an expensive and time-consuming process. Thus, synthetically generated data is being researched more and more. This paper tries to answer the question of whether and to what extent synthetically generated data can help in developing the advanced driver-assistance system (ADAS) algorithms for autonomous vehicles, for the object detection task based on deep learning. Two state-of-the-art deep learning object detectors were trained on various combinations of real-world and synthetic data. A total of 12 detectors were tested on real-world test images. Results show that synthetic data can contribute to better detector performance until a certain ratio between real-world and synthetic data is reached.

Recently, an increasing number of Artificial Intelligence services have been developed for a variety of domains. Machine Learning and especially Deep Learning services require a large amount of data to provide their functionality. Since data collection is typically complex and difficult, there is often not enough data available. Machine learning services such as anomaly detection or disaggregation algorithms are also being developed in the smart living domain. In practice, however, only a few energy datasets are publicly available, as the collection of such data is expensive and time-consuming due to the equipment required. One way to generate more smart meter data is to use a simulation. Developing such a simulation that is capable of generating meaningful data is a complex task. Therefore, in this paper, we present the Synthetic Time Series Data Generator (SynTiSeD), a multi-agent-based simulation tool that generates meaningful synthetic energy data based on real-world data. Furthermore, SynTiSeD allows generating data of critical situations, which are important for the development of such services, but which cannot be provoked in the real world. For transferability, we demonstrate that Nonintrusive Load Monitoring algorithms trained on synthetic data generated by SynTiSeD provide meaningful results that are even better than those of models trained on real data.

The dual hesitant fuzzy sets (DHFSs) were proposed by Zhu et al. (2012), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Correlation measures analysis is an important research topic. In this paper, we define the correlation measures for dual hesitant fuzzy information and then discuss their properties in detail. One numerical example is provided to illustrate these correlation measures. Then we present a direct transfer algorithm with respect to the problem of complex operation of matrix synthesis when reconstructing an equivalent correlation matrix for clustering DHFSs. Furthermore, we prove that the direct transfer algorithm is equivalent to transfer closure algorithm, but its asymptotic time complexity and space complexity are superior to the latter. Another real world example, that is, diamond evaluation and classification, is employed to show the effectiveness of the association coefficient and the algorithm for clustering DHFSs.

Generation of realistic synthetic data has garnered considerable attention in recent years, particularly in the health research domain due to its utility in, for instance, sharing data while protecting patient privacy or determining optimal clinical trial design. While much work has been concentrated on synthetic image generation, generation of realistic and complex synthetic tabular data of the type most commonly encountered in classic epidemiological or clinical studies is still lacking, especially with regard to generating data for randomized controlled trials (RCTs). There is no consensus regarding the best way to generate synthetic tabular RCT data such that the underlying multivariate data distribution is preserved. Motivated by an RCT in the treatment of Human Immunodeficiency Virus, we empirically compared the ability of several strategies and three generation techniques (two machine learning, the other a more classical statistical method) to faithfully reproduce realistic data. Our results suggest that using a sequential generation approach with an R-vine copula model to generate baseline variables, followed by a simple random treatment allocation to mimic the RCT setting, and subsequent regression models for variables post-treatment allocation (such as the trial outcome) is the most effective way to generate synthetic tabular RCT data that capture important and realistic features of the real data.

Introduction 1.1 Advancements of AI in HealthcareArtificial intelligence has rapidly advanced in the last decade for applications in healthcare from diagnostic tools to predictive analytics.Machine learning, a subset of the wide range of AI tools undergoing implementation, uses its sophisticated abilities to recognize patterns in subsequent data sets to help enable the early detection of chronic illnesses like Alzheimer's disease. Alzheimer's Disease and the Need for Early DiagnosisAlzeihemer's, "a type of dementia that affects memory, thinking and behavior" (Alzheimer's Association, 2025), affects millions worldwide and remains a significant challenge in public health.Early diagnosis is vital to allowing opportunities for intervention in the early growth activity of the disease, which could slow disease progression and improve patient outcomes.However, a tenacious challenge persists in the reliance of real world data, when developing machine learning models, raising ethical concerns over privacy, security, and bias. The Role of Synthetic Data and ChatbotsSynthetic data offers a potential solution by mimicking real-world medical datasets while avoiding privacy issues.Traditional approaches rely on statistical analytics and simulations to generate viable data sets, unlike this research, which will be proposing a new source of data generation: ChatGPT.Chatbots such as ChatGPT utilize conversational AI techniques like natural language processing systems to understand user questions and simulate responses to them (IBM, 2025).This can provide the edge of the implementations of conversational, contextual, and behavioral aspects onto the data generated, making the model increasingly authentic.This study investigates the viable use of AI generated synthetic data in effectively training machine learning models to predict the future onset of Alzheimer's disease.It specifically seeks to answer if synthetic data from AI chatbots can produce accurate and reliable predictive models with further investigation into methods that can validate these models' effectiveness and barriers that might prevent their adoption in real-world healthcare settings. Research Significance and Future ImplicationsThe desire of advancing this research topic originates from a fascination with AI's potential in predictive analytics within healthcare.Since the public debut of ChatGPT, AI has been implemented into various domains with a wide breadth of exploration of its applications, including health care.However, chatbots are generally utilized in website management, its true potential remaining unexamined.This interest is personally further driven by an aspiration to merge computer science and healthcare, through observing the challenges and opportunities within the healthcare field through familial connections.This research dives into uncharted territory, with the exploration of the intersection of natural language processing and predictive machine learning models, leveraging synthetic data generated by AI chatbots to train machine learning models for predicting the onset of Alzheimer's disease.This new approach seeks to plug the existing gaps in healthcare technology with emphasis on current ethical dilemmas on the usage of patient data.Exploring AI-generated synthetic data shows promise for a future in enhanced early diagnostic capabilities, and if successful, goes far beyond Alzheimer's.My research shows the possibilities of AI in healthcare developments, where it is further magnified for a maximized psychosocial