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We introduce and study a fractional version of the Skellam process of order $k$ by time-changing it with an independent inverse stable subordinator. We call it the fractional Skellam process of order $k$ (FSPoK). An integral representation…
The semiparametric accelerated failure time model is not as widely used as the Cox relative risk model mainly due to computational difficulties. Recent developments in least squares estimation and induced smoothing estimating equations…
We introduce new approaches for forecasting IBNR (Incurred But Not Reported) frequencies by leveraging individual claims data, which includes accident date, reporting delay, and possibly additional features for every reported claim. A key…
We use the Fokker Planck equation as a starting point for studying the orientational probability distribution of an Active Brownian Particle (ABP) in $(d+1)$ dimensions. This Fokker Planck equation admits an exact solution in series form…
In epidemiological studies of time-to-event data, a quantity of interest to the clinician and the patient is the risk of an event given a covariate profile. However, methods relying on time matching or risk-set sampling (including Cox…
The analysis of multiple time-to-event outcomes in a randomised controlled clinical trial can be accomplished with exisiting methods. However, depending on the characteristics of the disease under investigation and the circumstances in…
Common deep learning approaches for antibody engineering focus on modeling the marginal distribution of sequences. By treating sequences as independent samples, however, these methods overlook affinity maturation as a rich and largely…
Survival analysis often relies on Cox models, assuming both linearity and proportional hazards (PH). This study evaluates machine and deep learning methods that relax these constraints, comparing their performance with penalized Cox models…
Since survival data occur over time, often important covariates that we wish to consider also change over time. Such covariates are referred as time-dependent covariates. Quantile regression offers flexible modeling of survival data by…
We study the Heston model, where the stock price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance. We solve the corresponding Fokker-Planck equation exactly and, after integrating out the…
In survival analysis it often happens that some subjects under study do not experience the event of interest; they are considered to be `cured'. The population is thus a mixture of two subpopulations: the one of cured subjects, and the one…
In healthcare, risk assessment of patient outcomes has been based on survival analysis for a long time, i.e. modeling time-to-event associations. However, conventional approaches rely on data from a single time-point, making them suboptimal…
Empirical determination of the scaling properties and exponents of time series presents a formidable challenge in testing, and developing, a theoretical understanding of turbulence and other out-of-equilibrium phenomena. We discuss the…
Survival analysis models the distribution of time until an event of interest, such as discharge from the hospital or admission to the ICU. When a model's predicted number of events within any time interval is similar to the observed number,…
Two Cox-based multistate modeling approaches are compared for analyzing a complex multicohort event history process. The first approach incorporates cohort information as a fixed covariate, thereby providing a direct estimation of the…
The relationship between a time-dependent covariate and survival times is usually evaluated via the Cox model. Time-dependent covariates are generally available as longitudinal data collected regularly during the course of the study. A…
We derive confidence intervals and confidence sequences for causal effects in situations where the back-door or front-door criteria are applicable. Our tightest confidence intervals hold in the standard setting where the training data…
Over the past several decades there has been a proliferation of epidemiological models with ordinary derivatives replaced by fractional derivatives in an an-hoc manner. These models may be mathematically interesting but their relevance is…
Modern macroeconometrics often relies on time series models for which it is time-consuming to evaluate the likelihood function. We demonstrate how Bayesian computations for such models can be drastically accelerated by reweighting and…
The question of how individual patient data from cohort studies or historical clinical trials can be leveraged for designing more powerful, or smaller yet equally powerful, clinical trials becomes increasingly important in the era of…