Problems in Identification and Estimation: Algorithms for Pathogen, Ancestral, and Rashomon Analysis

Abstract

This dissertation answers three questions on identifiability and estimability that arise in policy-making and causal discovery. First, we study contact tracing as a tool to prevent the spread of infectious diseases. We show how to substantially improve the efficiency of contact tracing using multi-armed bandits that leverage heterogeneity in how infectious a sick person is. We propose to test contacts of infected persons to ascertain whether they are likely to be a "high infector" and to find additional infections only if it is likely to be highly fruitful. Using administrative COVID-19 contact tracing datasets, we show that an easily implementable strategy in the field performs at nearly optimal levels. Second, we robustly estimate heterogeneities in the outcome of interest with respect to a factorial feature space. We partition this factorial space into "pools" of feature combinations where the outcome differs only across the pools. We fully enumerate the Rashomon Partition Set (RPS), a collection of all partitions with sufficiently high posterior density. Using the L0 prior, which we show is minimax optimal, we calculate approximation error relative to the entire posterior and bound the size of the RPS. In three empirical settings (charitable giving, chromosomal structure, and microfinance), we highlight robust conclusions, including affirmations and reversals of extant literature findings. Third, we restrict Markov equivalence classes of causal maximal ancestral graphs (MAGs) that agree with expert knowledge in the form of edge orientations. We can uniquely represent this equivalence class using its essential graph. We revise two previously described graphical orientation rules and present a novel rule to add expert knowledge. We provide an algorithm for adding expert knowledge and show that it is complete for edge marks in the circle component of the essential graph. We also provide an algorithm for verifying completeness in the general case.