arXiv subjects

Gursharn Kaur

Publications and source records attributed to Gursharn Kaur.

9 recordsLinked to original sources

arXiv2026

EpiFlow: A framework for improving the utility of wastewater signals for disease forecasting

Wastewater-based surveillance is an effective tool for disease monitoring and can provide early warning of outbreaks. Although wastewater viral loads (WVL) correlate with disease burden, their utility for improving real-time forecasting remains under investigation. During the early phases of an epidemic, many indicators can effectively monitor disease spread, but their reliability may decline because of reporting fatigue and low prevalence. Hospital burden can vary substantially even during low-prevalence periods, making accurate forecasting of burden indicators essential for minimizing disease impacts. In this paper, we present principled approaches for processing wastewater data, characterizing its relationship with burden indicators, and generating real-time forecasts. We assess the predictability of WVL using entropy measures. We analyze the relationship between WVL and burden indicators using causality tests that capture temporal dynamics and the leading-indicator behavior of WVL. We incorporate these insights into a time-varying forecasting model that accounts for the evolving relationship between the signals. We also evaluate the effects of delays in WVL reporting through simulations. We test the utility of our methods by forecasting COVID-19 hospital admissions across Virginia and its health regions during periods of varying disease prevalence. Incorporating WVL improves forecast accuracy relative to baseline models, particularly during critical epidemic phases, and results in a 20 percentage point improvement in forecast coverage. Our results demonstrate that WVL signals can improve infectious disease forecasting even under conditions of low prevalence or delayed reporting.

cs.LG↗

arXiv2025

Interacting Urns on Directed Networks with Node-Dependent Sampling and Reinforcement

We consider interacting urns on a finite directed network, where both sampling and reinforcement processes depend on the nodes of the network. This extends previous research by incorporating node-dependent sampling and reinforcement. We classify the sampling and reinforcement schemes, as well as the networks on which the proportion of balls of either colour in each urn converges almost surely to a deterministic limit. We also investigate conditions for achieving synchronisation of the colour proportions across the urns and analyse fluctuations under specific conditions on the reinforcement scheme and network structure.

math.PR↗

arXiv2024

Wastewater-based Epidemiology for COVID-19 Surveillance and Beyond: A Survey

The pandemic of COVID-19 has imposed tremendous pressure on public health systems and social economic ecosystems over the past years. To alleviate its social impact, it is important to proactively track the prevalence of COVID-19 within communities. The traditional way to estimate the disease prevalence is to estimate from reported clinical test data or surveys. However, the coverage of clinical tests is often limited and the tests can be labor-intensive, requires reliable and timely results, and consistent diagnostic and reporting criteria. Recent studies revealed that patients who are diagnosed with COVID-19 often undergo fecal shedding of SARS-CoV-2 virus into wastewater, which makes wastewater-based epidemiology for COVID-19 surveillance a promising approach to complement traditional clinical testing. In this paper, we survey the existing literature regarding wastewater-based epidemiology for COVID-19 surveillance and summarize the current advances in the area. Specifically, we have covered the key aspects of wastewater sampling, sample testing, and presented a comprehensive and organized summary of wastewater data analytical methods. Finally, we provide the open challenges on current wastewater-based COVID-19 surveillance studies, aiming to encourage new ideas to advance the development of effective wastewater-based surveillance systems for general infectious diseases.

stat.AP↗

arXiv2021

Distributions of cherries and pitchforks for the Ford model

We study two fringe subtree counting statistics, the number of cherries and that of pitchforks for Ford's $α$ model, a one-parameter family of random phylogenetic tree models that includes the uniform and the Yule models, two tree models commonly used in phylogenetics. Based on a nonuniform version of the extended Pólya urn models in which negative entries are permitted for their replacement matrices, we obtain the strong law of large numbers and the central limit theorem for the joint distribution of these two count statistics for the Ford model. Furthermore, we derive a recursive formula for computing the exact joint distribution of these two statistics. This leads to exact formulas for their means and higher order asymptotic expansions of their second moments, which allows us to identify a critical parameter value for the correlation between these two statistics. That is, when $n$ is sufficiently large, they are negatively correlated for $0\le α\le 1/2$ and positively correlated for $1/2<α<1$.

math.PR↗

arXiv2021

Higher-order fluctuations in dense random graph models

Our main results are quantitative bounds in the multivariate normal approximation of centred subgraph counts in random graphs generated by a general graphon and independent vertex labels. We are interested in these statistics because they are key to understanding fluctuations of regular subgraph counts -- a cornerstone of dense graph limit theory. We also identify the resulting limiting Gaussian stochastic measures by means of the theory of generalised $U$-statistics and Gaussian Hilbert spaces, which we think is a suitable framework to describe and understand higher-order fluctuations in dense random graph models. With this article, we believe we answer the question "What is the central limit theorem of dense graph limit theory?". We complement the theory with some statistical applications to illustrate the use of centred subgraph counts in network modelling.

math.PR↗

arXiv2021

Interacting Urns on a Finite Directed Graph

We introduce a general two colour interacting urn model on a finite directed graph, where each urn at a node, reinforces all the urns in its out-neighbours according to a fixed, non-negative and balanced reinforcement matrix. We show that the fraction of balls of either colour converges almost surely to a deterministic limit if either the reinforcement is not of Pólya type or if the graph is such that every vertex with non-zero in-degree can be reached from some vertex with zero in-degree. We also obtain joint central limit theorems, with appropriate scaling, around the vector of limiting proportion. Further, in the remaining case when there are no vertices with zero in-degree and the reinforcement is of Pólya type, we restrict our analysis to a regular graph and show that the fraction of balls of either colour converges almost surely to a finite random limit, which is the same across all the urns.

math.PR↗

arXiv2021

On asymptotic joint distributions of cherries and pitchforks for random phylogenetic trees

Tree shape statistics provide valuable quantitative insights into evolutionary mechanisms underpinning phylogenetic trees, a commonly used graph representation of evolution systems ranging from viruses to species. By developing limit theorems for a version of extended Pólya urn models in which negative entries are permitted for their replacement matrices, we present strong laws of large numbers and central limit theorems for asymptotic joint distributions of two subtree counting statistics, the number of cherries and that of pitchforks, for random phylogenetic trees generated by two widely used null tree models: the proportional to distinguishable arrangements (PDA) and the Yule-Harding-Kingman (YHK) models. Our results indicate that the limiting behaviour of these two statistics, when appropriately scaled, are independent of the initial trees used in the tree generating process.

math.PR↗

arXiv2018

Negatively Reinforced Balanced Urn Schemes

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 $w$ is a non-increasing function. Under certain assumptions on the replacement matrix $R$ and weight function $w$, such as, $w$ is differentiable and $w(0) < \infty$, we obtain almost sure convergence of the random configuration of the urn model. In particular, we show that if $R$ is doubly stochastic the random configuration of the urn converges to the uniform vector, and asymptotic normality holds, if the number of colours in the urn are sufficiently large.

math.PR↗

arXiv2018

Generalized Pólya Urn Schemes with Negative but Linear Reinforcements

In this paper, we consider a new type of urn scheme, where the selection probabilities are proportional to a weight function, which is linear but decreasing in the proportion of existing colours. We refer to it as the \emph{negatively reinforced} urn scheme. We establish almost sure limit of the random configuration for any \emph{balanced} replacement matrix $R$. In particular, we show that the limiting configuration is uniform on the set of colours, if and only if, $R$ is a \emph{doubly stochastic} matrix. We further establish almost sure limit of the vector of colour counts and prove central limit theorems for the random configuration, as well as, for the colour counts.

math.PR↗