arXiv subjects

Bret Hanlon

Publications and source records attributed to Bret Hanlon.

4 recordsLinked to original sources

arXiv2023

Sampling distributions and estimation for multi-type Branching Processes

Consider a multi-dimensional supercritical branching process with offspring distribution in a parametric family. Here, each vector coordinate corresponds to the number of offspring of a given type. The process is observed under family-size sampling: a random sample is drawn, each individual reporting its vector of brood sizes. In this work, we show that the set in which no siblings are sampled (so that the sample can be considered independent) has probability converging to one under certain conditions on the sampling size. Furthermore, we show that the sampling distribution of the observed sizes converges to the product of identical distributions, hence developing a framework for which the process can be considered iid, and the usual methods for parameter estimation apply. We provide asymptotic distributions for the resulting estimators.

math.ST↗

arXiv2019

Asymptotic Seed Bias in Respondent-driven Sampling

Respondent-driven sampling (RDS) collects a sample of individuals in a networked population by incentivizing the sampled individuals to refer their contacts into the sample. This iterative process is initialized from some seed node(s). Sometimes, this selection creates a large amount of seed bias. Other times, the seed bias is small. This paper gains a deeper understanding of this bias by characterizing its effect on the limiting distribution of various RDS estimators. Using classical tools and results from multi-type branching processes (Kesten and Stigum, 1966), we show that the seed bias is negligible for the Generalized Least Squares (GLS) estimator and non-negligible for both the inverse probability weighted and Volz-Heckathorn (VH) estimators. In particular, we show that (i) above a critical threshold, VH converge to a non-trivial mixture distribution, where the mixture component depends on the seed node, and the mixture distribution is possibly multi-modal. Moreover, (ii) GLS converges to a Gaussian distribution independent of the seed node, under a certain condition on the Markov process. Numerical experiments with both simulated data and empirical social networks suggest that these results appear to hold beyond the Markov conditions of the theorems.

math.ST↗

arXiv2018

Chemo-Dynamical Clustering applied to APOGEE data: Re-Discovering Globular Clusters

We have developed a novel technique based on a clustering algorithm which searches for kinematically- and chemically-clustered stars in the APOGEE DR12 Cannon data. As compared to classical chemical tagging, the kinematic information included in our methodology allows us to identify stars that are members of known globular clusters with greater confidence. We apply our algorithm to the entire APOGEE catalog of 150,615 stars whose chemical abundances are derived by the Cannon. Our methodology found anti-correlations between the elements Al and Mg, Na and O, and C and N previously identified in the optical spectra in globular clusters, even though we omit these elements in our algorithm. Our algorithm identifies globular clusters without a priori knowledge of their locations in the sky. Thus, not only does this technique promise to discover new globular clusters, but it also allows us to identify candidate streams of kinematically- and chemically-clustered stars in the Milky Way.

astro-ph.SR↗

arXiv2017

Novel Sampling Design for Respondent-driven Sampling

Respondent-driven sampling (RDS) is a method of chain referral sampling popular for sampling hidden and/or marginalized populations. As such, even under the ideal sampling assumptions, the performance of RDS is restricted by the underlying social network: if the network is divided into communities that are weakly connected to each other, then RDS is likely to oversample one of these communities. In order to diminish the "referral bottlenecks" between communities, we propose anti-cluster RDS (AC-RDS), an adjustment to the standard RDS implementation. Using a standard model in the RDS literature, namely, a Markov process on the social network that is indexed by a tree, we construct and study the Markov transition matrix for AC-RDS. We show that if the underlying network is generated from the Stochastic Blockmodel with equal block sizes, then the transition matrix for AC-RDS has a larger spectral gap and consequently faster mixing properties than the standard random walk model for RDS. In addition, we show that AC-RDS reduces the covariance of the samples in the referral tree compared to the standard RDS and consequently leads to a smaller variance and design effect. We confirm the effectiveness of the new design using both the Add-Health networks and simulated networks.

stat.ME↗