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Targeted or lagged walk sampling for estimation of finite-order graph parameters

23 September 2021
Location: Virtual

IASS webinar

Please register for the IASS Webinar here.

A pure random walk in a graph is a probabilistic depth-first search algorithm where, at any given time step, a move is made randomly over one of the out-edges from the current node. More generally, a walk is said to be targeted if the transition probabilities from the current node are also subject to other choices, including the possibility and manner of taking random jumps. Targeted random walk (with jumps) has applications in many fields, such as Goolge’s PageRank. Uniform and degree+1 walks are two examples of targeted walks, which involve acceptance-rejection mechanisms for the proposed moves in addition. Finally, a walk is said to be lagged, if the transition probabilities depend on not only the current node but also a given number of previous nodes, such that it is not ‘memoryless’ like either pure or targeted random walks. Let individuals and contacts between them be the nodes and edges of a graph. Let y indicate whether a node belongs to a certain community, such as a group of pathogen carriers or a fraternal society. Let θ be the total number of triangles where all the three nodes belong the community, and let θ’ be that of the other triangles. The larger the ratio between θ and θ’ is, the higher is the transitivity among the community members compared to the overall transitivity in the graph. Until recently, sampling theory for targeted or lagged walks in graphs has only dealt with the estimation of 1st-order (node) graph parameters, such as the mean of a y-value associated with all the nodes, but not other kinds of graph parameters such as the ratio of two triangle totals above.

This talk presents a novel approach for estimating finite-order graph parameters based on targeted or lagged walk sampling.

Biography of Speaker

Li-Chun Zhang is Professor of Social Statistics at University of Southampton, Senior Researcher at Statistics Norway, and Professor of Official Statistics at University of Oslo. His research interests include finite population sampling design and coordination, finite graph sampling, sample survey estimation, non-response, measurement errors, small area estimation, index number calculations, editing and imputation, register-based statistics, statistical matching, record linkage. His involvement in research projects include the EU framework projects EURAREA, DACSEIS, RISQ and BLUE-ETS; the ESSnet projects Small Area Estimation, Data Integration and Quality of Multisource Statistics; the H2020-project InGRID-2; the ESRC-projects ADRCE, NCRM-SAE.

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