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Causal inference is widely used in various fields, such as biology, psychology and economics, etc. In observational studies, we need to balance the covariates before estimating causal effect. This study extends the one-dimensional entropy…
Hazard ratios are ubiquitously used in time to event analysis to quantify treatment effects. Although hazard ratios are invaluable for hypothesis testing, other measures of association, both relative and absolute, may be used to fully…
We study methods for simultaneous analysis of many noisy experiments in the presence of rich covariate information. The goal of the analyst is to optimally estimate the true effect underlying each experiment. Both the noisy experimental…
In economic program evaluation, it is common to obtain panel data in which outcomes are indicators that an individual has reached an absorbing state. For example, they may indicate whether an individual has exited a period of unemployment,…
Many research questions involve time-to-event outcomes that can be prevented from occurring due to competing events. In these settings, we must be careful about the causal interpretation of classical statistical estimands. In particular,…
The paper aims to emphasise how switched systems can be analysed with elementary techniques which require only undergraduate-level linear algebra and differential equations. It is also emphasised how math software can become useful for…
Average-case analysis computes the complexity of an algorithm averaged over all possible inputs. Compared to worst-case analysis, it is more representative of the typical behavior of an algorithm, but remains largely unexplored in…
Kaplan-Meier estimate, commonly known as product limit method (PLM), and maximum likelihood estimate (MLE) methods in general are often cited as means of stochastic highway capacity estimation. This article discusses their unsuitability for…
Probabilistic load forecasts provide comprehensive information about future load uncertainties. In recent years, many methodologies and techniques have been proposed for probabilistic load forecasting. Forecast combination, a widely…
A priori error bounds have been derived for different balancing-related model reduction methods. The most classical result is a bound for balanced truncation and singular perturbation approximation that is applicable for asymptotically…
Prediction algorithms that quantify the expected benefit of a given treatment conditional on patient characteristics can critically inform medical decisions. Quantifying the performance of treatment benefit prediction algorithms is an…
Using three hypergeometric identities, we evaluate the harmonic measure of a finite interval and of its complementary for a strictly stable real L{\'e}vy process. This gives a simple and unified proof of several results in the literature,…
Unmeasured confounding is a key threat to reliable causal inference based on observational studies. Motivated from two powerful natural experiment devices, the instrumental variables and difference-in-differences, we propose a new method…
When the Stable Unit Treatment Value Assumption is violated and there is interference among units, there is not a uniquely defined Average Treatment Effect, and alternative estimands may be of interest. Among these are average unit-level…
This paper describes prediction methods for the number of future events from a population of units associated with an on-going time-to-event process. Examples include the prediction of warranty returns and the prediction of the number of…
This paper reexamines Abadie and Imbens (2016)'s work on propensity score matching for average treatment effect estimation. We explore the asymptotic behavior of these estimators when the number of nearest neighbors, $M$, grows with the…
A concentration index, a standardized covariance between a health variable and relative income ranks, is often used to quantify income-related health inequalities. There is a lack of formal approach to study the effect of an exposure, e.g.,…
Investigating the causal relationship between exposure and the time-to-event outcome is an important topic in biomedical research. Previous literature has discussed the potential issues of using the hazard ratio as a marginal causal effect…
This paper studies the mean-field Markov decision process (MDP) with the centralized stopping under the non-exponential discount. The problem differs fundamentally from most existing studies on mean-field optimal control/stopping due to its…
We observed that safety arguments are prone to stay too abstract, e.g. solutions refer to large packages, argument strategies to complex reasoning steps, contexts and assumptions lack traceability. These issues can reduce the confidence we…