The Statistics and Data Science Research Group conducts interdisciplinary research spanning theoretical statistics, modern data science, machine learning, and statistical computing. Our research aims to develop novel methodologies with strong mathematical foundations and impactful real-world applications.
Copula modelling is one of the flagship research areas of the Statistics and Data Science Research Group. Our research focuses on developing flexible copula families for modelling complex dependence structures between random variables beyond traditional correlation measures. We investigate the construction of novel bivariate and multivariate copulas, probability generating function-based copulas, FGM-type extensions, and copula models with enhanced dependence characteristics. We also develop copula-based regression methodologies, semiparametric and nonparametric estimation techniques, and causal inference methods for dependent data. Particular emphasis is placed on statistical inference, goodness-of-fit testing, parameter estimation, and computational algorithms for copula models. Applications of our research include reliability engineering, financial risk modelling, survival analysis, environmental statistics, epidemiology, insurance, and healthcare analytics. Our recent contributions include new copula families with wider dependence ranges, copula-based regression methods in the presence of outliers, and estimation of causal effects using copula models. Through both theoretical developments and practical applications, our work advances modern dependence modelling and provides powerful statistical tools for analysing complex multivariate datasets.
Our research lies at the intersection of Statistics, Data Science, Machine Learning, and Deep Learning, focusing on the development of robust, scalable, and interpretable data-driven methodologies for solving complex real-world problems. We integrate statistical inference, optimization, computational algorithms, and artificial intelligence to address prediction, classification, regression, clustering, feature learning, visualization, and intelligent decision support. Our work encompasses support vector machines, twin support vector machines, randomized neural networks, broad learning systems, deep neural networks, robust loss functions, and probability-based learning algorithms, with particular emphasis on noisy, imbalanced, uncertain, incomplete, and high-dimensional data. We also investigate statistical computing, feature engineering, uncertainty quantification, computer vision, medical image analysis, and pattern recognition. Our research has broad applications in healthcare, medical diagnosis, finance, reliability engineering, environmental science, and other scientific and industrial domains, advancing accurate, efficient, reliable, and interpretable intelligent systems.
Estimation Theory has been one of the foundational research areas of our group for more than a decade. Our research focuses on developing efficient statistical estimation procedures for a wide range of probability distributions and stochastic models. We investigate point estimation, interval estimation, Bayesian estimation, shrinkage estimation, estimation after selection, and estimation under asymmetric loss functions. Particular emphasis is placed on record values, generalized order statistics, stress-strength reliability models, lifetime distributions, exponential, Weibull, Pareto, Gamma, and other reliability distributions. We study the theoretical properties of estimators including unbiasedness, admissibility, consistency, asymptotic behaviour, and minimum risk under various decision frameworks. Our work also addresses estimation problems in selected populations, common parameter estimation, multicomponent systems, and reliability analysis. These methodologies have broad applications in engineering, industrial quality control, biostatistics, healthcare, and risk assessment, providing statistically efficient solutions for complex inference problems.
Information Theory provides a rigorous mathematical framework for quantifying uncertainty, information, and statistical dependence. Our research explores the application of entropy measures, divergence functions, information-based learning principles, and probabilistic modelling in modern statistics and machine learning. We investigate information-theoretic approaches for feature selection, uncertainty quantification, model comparison, statistical inference, and intelligent decision-making. Information measures are incorporated into optimization and learning algorithms to improve robustness, interpretability, and predictive performance. We are particularly interested in the interaction between information theory and statistical learning, where entropy-based methods contribute to robust classification, probabilistic modelling, and high-dimensional data analysis. Our research aims to establish strong theoretical foundations while addressing practical challenges arising in artificial intelligence, data science, pattern recognition, and computational statistics. These developments support efficient knowledge extraction from complex datasets under uncertainty.
Ranking and Selection deals with identifying the best population, treatment, process, or competing alternative based on observed experimental data. Our research investigates statistically optimal procedures for ranking populations and selecting superior alternatives under uncertainty. We study estimation after selection, selection under asymmetric loss functions, decision-theoretic approaches, ranking methodologies, multiple comparison procedures, and optimal allocation strategies. Theoretical developments are complemented by practical applications in industrial experimentation, reliability engineering, quality assurance, healthcare, agricultural experiments, manufacturing systems, and operations research. By combining probability theory, statistical inference, and optimization, our research develops efficient methodologies that support evidence-based decision-making in complex stochastic environments.
Time Series Analysis focuses on modelling, analysing, and forecasting data collected over time. Our research develops statistical techniques for understanding temporal dependence, trend behaviour, seasonal variation, and stochastic dynamics in sequential observations. We investigate classical forecasting methods such as ARIMA, exponential smoothing, and Holt-Winters models together with modern statistical approaches for predictive analytics. Applications include forecasting inflation, gold prices, economic indicators, infectious disease outbreaks, public health surveillance, environmental monitoring, and financial markets. We also study model selection, forecast evaluation, uncertainty quantification, and computational techniques for large temporal datasets. Our research aims to provide reliable forecasting tools that support evidence-based planning, policy formulation, and strategic decision-making across scientific, economic, and industrial domains.