Related papers: Canonical insurance models: stochastic equations a…

The log-Lindley distribution was recently introduced in the literature as a viable alternative to the Beta distribution. This distribution has a simple structure and possesses useful theoretical properties relevant in insurance. Classical…

People often deviate from expected utility theory when making risky and intertemporal choices. While the effects of probabilistic risk and time delay have been extensively studied in isolation, their interplay and underlying theoretical…

In this paper, we consider a wide class of time-varying multivariate causal processes which nests many classic and new examples as special cases. We first prove the existence of a weakly dependent stationary approximation for our model…

A new class of generalized backward doubly stochastic differential equations (GBDSDEs in short) driven by Teugels martingales associated with L\'evy process are investigated. We establish a comparison theorem which allows us to derive an…

Typical Bayesian methods for models with latent variables (or random effects) involve directly sampling the latent variables along with the model parameters. In high-level software code for model definitions (using, e.g., BUGS, JAGS, Stan),…

Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…

In proof theory the notion of canonical proof is rather basic, and it is usually taken for granted that a canonical proof of a sentence must be unique up to certain minor syntactical details (such as, e.g., change of bound variables). When…

In this work we mainly prove the existence and pathwise uniqueness of solutions to general backward doubly stochastic differential equations with jumps appearing in both forward and backward integral parts. Several comparison theorems under…

Contrastive explanations clarify why an event occurred in contrast to another. They are more inherently intuitive to humans to both produce and comprehend. We propose a methodology to produce contrastive explanations for classification…

We introduce methodology to bridge scenario analysis and model-based risk forecasting, leveraging their respective strengths in policy settings. Our Bayesian framework addresses the fundamental challenge of reconciling judgmental narrative…

We study counting statistics of number of transitions in a stochastic process. For mesoscopic systems, a path integral formulation for the counting statistics has already been derived. We here show that it is also possible to derive the…

Canonical correlation analysis is a family of multivariate statistical methods for the analysis of paired sets of variables. Since its proposition, canonical correlation analysis has for instance been extended to extract relations between…

Statistical models can involve implicitly defined quantities, such as solutions to nonlinear ordinary differential equations (ODEs), that unavoidably need to be numerically approximated in order to evaluate the model. The approximation…

Difference-in-differences (DiD) identification relies mainly on a parallel trends assumption about untreated potential outcomes. Researchers often relax this assumption by assuming conditional parallel trends within units with the same…

We introduce two simple models of forward-backward stochastic differential equations with a singular terminal condition and we explain how and why they appear naturally as models for the valuation of CO2 emission allowances. Single phase…

Discrimination and calibration represent two important properties of survival analysis, with the former assessing the model's ability to accurately rank subjects and the latter evaluating the alignment of predicted outcomes with actual…

The usual homogeneous form of equality type in Martin-L\"of Type Theory contains identifications between elements of the same type. By contrast, the heterogeneous form of equality contains identifications between elements of possibly…

A probabilistic model describes a system in its observational state. In many situations, however, we are interested in the system's response under interventions. The class of structural causal models provides a language that allows us to…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

In clinical trials, studies often present longitudinal data or clustered data. These studies are commonly analyzed using linear mixed models (LMMs), usually considering Gaussian assumptions for random effect and error terms. Recently,…