Related papers: Analyzing Generalized P\'olya Urn Models using Mar…
Many applications in genetic analyses utilize sampling distributions, which describe the probability of observing a sample of DNA sequences randomly drawn from a population. In the one-locus case with special models of mutation such as the…
Consider an urn filled with balls, each labeled with one of several possible collective decisions. Now, let a random voter draw two balls from the urn and pick her more preferred as the collective decision. Relabel the losing ball with the…
The gambler's ruin problem for correlated random walks (CRW), both with and without delays, is addressed using the Optional Stopping Theorem for martingales. We derive closed-form expressions for the ruin probabilities and the expected game…
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…
Maximum entropy random walks (MERWs) are maximally dispersing and play a key role in optimizing information spreading in various contexts. However, building MERWs comes at the cost of knowing beforehand the global structure of the network,…
Mutations sometimes increase contagiousness for evolving pathogens. During an epidemic, scientists use viral genome data to infer a shared evolutionary history and connect this history to geographic spread. We propose a model that directly…
We consider P\'olya urns with infinitely many colours that are of a random walk type, in two related version. We show that the colour distribution a.s., after rescaling, converges to a normal distribution, assuming only second moments on…
Computational models for the simulation of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) epidemic evolution would be extremely useful to support authorities in designing healthcare policies and lockdown measures to…
We study the distribution of entries of a random permutation matrix under a "randomized basis," i.e., we conjugate the random permutation matrix by an independent random orthogonal matrix drawn from Haar measure. It is shown that under…
Mendelian randomization (MR) is a powerful method that uses genetic variants as instrumental variables (IVs) to infer the causal effect of a modifiable exposure on an outcome. Although recent years have seen many extensions of basic MR…
In Mendelian randomization (MR) studies, genetic variants are used as instrumental variables (IVs) to investigate causal relationships between exposures and outcomes based on observational data. However, numerous genetic studies have shown…
The inverse probability weighting (IPW) method is used to handle attrition in association analyses derived from cohort studies. It consists in weighting the respondents at a given follow-up by their inverse probability to participate.…
We describe an new algorithm for visualizing an alignment of biological sequences according to a probabilistic model of evolution. The resulting data array is readily interpreted by the human eye and amenable to digital image techniques. We…
We calculate the probability distribution of repetitions of ancestors in a genealogical tree for simple neutral models of a closed population with sexual reproduction and non-overlapping generations. Each ancestor at generation g in the…
Randomized smoothing (RS) is one of the prominent techniques to ensure the correctness of machine learning models, where point-wise robustness certificates can be derived analytically. While RS is well understood for classification, its…
We consider the problem of model building for rare events prediction in longitudinal follow-up studies. In this paper, we compare several resampling methods to improve standard regression models on a real life example. We evaluate the…
We consider weighted negatively reinforced urn schemes with finitely many colours. An urn scheme is called negatively reinforced, if the selection probability for a colour is proportional to the weight $w$ of the colour proportion, where…
In this note, we show how the penalization method, introduced in order to describe some non-trivial changes of the Wiener measure, can be applied to the study of some simple polymer models such as the pinning model. The bulk of the analysis…
Micro-randomized trials are commonly conducted for optimizing mobile health interventions such as push notifications for behavior change. In analyzing such trials, causal excursion effects are often of primary interest, and their estimation…
The numerical stochastic perturbation method based on Parisi-Wu quantisation is applied to a suite of simple models to test its validity at high orders. Large deviations from normal distribution for the basic estimators are systematically…