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Summary Tree graphs are used routinely in statistics. When estimating a Bayesian model with a tree component, sampling the posterior remains a core difficulty. Existing Markov chain Monte Carlo methods tend to rely on local moves, often leading to poor mixing. A promising approach is to instead directly sample spanning trees on an auxiliary graph. Current spanning tree samplers, such as the celebrated Aldous–Broder algorithm, rely predominantly on simulating random walks that are required to visit all the nodes of the graph. Such algorithms are prone to getting stuck in certain subgraphs. We formalize this phenomenon using the bottlenecks in the random walk’s transition probability matrix. We then propose a novel fast-forwarded cover algorithm that can break free from bottlenecks. The core idea is a marginalization argument that leads to a closed-form expression that allows for fast-forwarding to the event of visiting a new node. Unlike many existing approximation algorithms, our algorithm yields exact samples. We demonstrate the enhanced efficiency of the fast-forwarded cover algorithm, and illustrate its application in fitting a Bayesian dendrogram model on a Massachusetts crime and community dataset. 

The distance between homes and childcare providers serves as a crucial factor in evaluating accessibility and equity in early childhood education. Spatial mismatch between childcare demand and supply is suggested when families opt for facilities further than the nearest available options, a situation scarcely scrutinized in existing literature, especially among under-six children from economically disadvantaged backgrounds. To fill this research gap, this study leverages the excess commuting analysis to delve into the extent of extended travel undertaken by subsidized families to access childcare services. Utilizing real enrollment data from the Florida’s School Readiness program, it quantifies the disparity between actual and shortest possible commuting distances, investigating the tendencies of low-income families to forgo nearby providers for their young children. Furthermore, the research probes into age-related disparities in excess commuting, examining to what degree childcare facilities are more conveniently located for certain age groups compared to others. The analysis unveils substantial spatial mismatch in subsidized childcare, with a significant portion of low-income families choosing more distant providers, resulting in a 51.3% surplus in commuting distance. It also highlights a noticeable age- dependent trend in this mismatch: parents of infants face a dual disadvantage with longer commutes, compared to families with five-year-olds who have closer access to providers. The findings advocate for policy reforms that address these disparities, enhancing the efficiency and equity of childcare resource allocation. 

To mitigate the devastating impacts of hurricanes on people’s lives, communities, and societal infrastructures, disaster management would benefit considerably from a detailed understanding of evacuation, including the socio-demographics of the populations that evacuate, or remain, down to disaggregated geographic levels such as local neighborhoods. A detailed household evacuation prediction model for local neighborhoods requires both a robust household evacuation decision model and individual household data for small geographic units. This paper utilizes a recently pub- lished statistical meta-analysis for the first requirement and then conducts a rigorous population synthesis procedure for the second. Our model produces predicted non-evacuation rates for all US Census block groups for the Tampa-St. Petersburg-Clearwater Metropolitan Statistical Area for a Hurricane Irma-like storm along with their socio-demographic and hurricane impact risk profiles. Our model predictions indicate that non- evacuation rates are likely to vary considerably, even across neighboring block groups, driven by the variability in evacuation risk profiles. Our results also demonstrate how different predictors may come to the fore in influencing non-evacuation in different block groups, and that predictors which may have an outsize impact on individual household evacuation decisions, such as Race, are not necessarily associated with the greatest differentials in non-evacuation rates when we aggregate households to block group level and above. Our research is intended to provide a framework for the design of hurricane evacuation prediction tools that could be used in disaster management.