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Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer ''what-iF'' questions. Existing causal inference approaches typically consider regular, discrete-time…

This PhD thesis contains several contributions to the field of statistical causal modeling. Statistical causal models are statistical models embedded with causal assumptions that allow for the inference and reasoning about the behavior of…

We propose a goodness-of-fit test for degree-corrected stochastic block models (DCSBM). The test is based on an adjusted chi-square statistic for measuring equality of means among groups of $n$ multinomial distributions with $d_1,\dots,d_n$…

Recently, high-dimensional heterogeneous data have attracted a lot of attention and discussion. Under heterogeneity, semiparametric regression is a popular choice to model data in statistics. In this paper, we take advantages of expectile…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

This paper introduces an Ordinary Differential Equation (ODE) notion for survival analysis. The ODE notion not only provides a unified modeling framework, but more importantly, also enables the development of a widely applicable, scalable,…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Most unsupervised anomaly detection methods based on representations of normal samples to distinguish anomalies have recently made remarkable progress. However, existing methods only learn a single decision boundary for distinguishing the…

In statistical modeling we strive to specify models that resemble data collected in studies or observed from processes. Consequently, distributional specification and parameter estimation are central to parametric models. Graphical…

Neural Ordinary Differential Equations (NODEs) have proven successful in learning dynamical systems in terms of accurately recovering the observed trajectories. While different types of sparsity have been proposed to improve robustness, the…

Pearson's chi-squared test is widely used to test the goodness of fit between categorical data and a given discrete distribution function. When the number of sets of the categorical data, say $k$, is a fixed integer, Pearson's chi-squared…

In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests…

Ordinary differential equations have been used to model dynamical systems in a broad range. Model checking for parametric ordinary differential equations is a necessary step to check whether the assumed models are plausible. In this paper…

Machine learning methods such as deep neural networks (DNNs), despite their success across different domains, are known to often generate incorrect predictions with high confidence on inputs outside their training distribution. The…

The generalized linear model is widely used in all areas of applied statistics and while correct asymptotic inference can be achieved under misspecification of the distributional assumptions, a correctly specified mean structure is crucial…

Detecting out-of-distribution (OOD) samples for trusted medical image segmentation remains a significant challenge. The critical issue here is the lack of a strict definition of abnormal data, which often results in artificial problem…

In industrial settings, surface defects on steel can significantly compromise its service life and elevate potential safety risks. Traditional defect detection methods predominantly rely on manual inspection, which suffers from low…

Out-of-distribution (OOD) detection is essential for determining when a supervised model encounters inputs that differ meaningfully from its training distribution. While widely studied in classification, OOD detection for regression and…

This paper is about learning the parameter-to-solution map for systems of partial differential equations (PDEs) that depend on a potentially large number of parameters covering all PDE types for which a stable variational formulation (SVF)…

Recently, the use of Polynomial Chaos Expansion (PCE) has been increasing to study the uncertainty in mathematical models for a wide range of applications and several extensions of the original PCE technique have been developed to deal with…