arXiv subjects

Easton Huch

Publications and source records attributed to Easton Huch.

4 recordsLinked to original sources

arXiv2026

Stable Central Limit Theorems for Discrete-Time Lag Martingale Difference Arrays: Applications to Dynamic Causal Inference

Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain lagged filtrations but not given the natural filtration. We formalize this class of stochastic processes and prove stable central limit theorems (CLTs) via martingale-coboundary decomposition, leveraging the classical martingale CLT. We develop a variety of sufficient conditions, including conditions under which the limiting variance has a simple form that depends on variances and covariances of neighboring variates. We demonstrate the application of these results to inference for time-averaged treatment effects in switchback designs and present a simulation study supporting their validity. The CLTs enable various extensions to existing methodology for design-based approaches to dynamic causal inference, including time-lagged effects, random limiting variances, cross-unit dependence, and vector-valued estimands.

math.ST↗

arXiv2026

Amortized Inference for Correlated Discrete Choice Models via Equivariant Neural Networks

Discrete choice models are fundamental tools in management science, economics, and marketing for understanding and predicting decision-making. Logit-based models are dominant in applied work, largely due to their convenient closed-form expressions for choice probabilities. However, they impose restrictive assumptions on the stochastic utility component, constraining our ability to capture realistic substitution patterns. We propose an amortized inference approach that relies on a neural network emulator to approximate choice probabilities for general error distributions, including those with correlated errors. We develop a specialized neural network architecture designed to respect the invariance properties of discrete choice models. We provide group-theoretic foundations for the architecture, including a proof of universal approximation given a minimal set of invariant features. Once trained, the emulator enables rapid likelihood evaluation and gradient computation. We use Sobolev training, augmenting the likelihood loss with a gradient-matching penalty, so that the emulator learns both choice probabilities and their derivatives. We show that emulator-based maximum likelihood estimators are consistent and asymptotically normal under mild approximation conditions, and we provide sandwich standard errors that remain valid for a psuedo-true parameter even with imperfect likelihood approximation. Simulations show significant gains over the GHK simulator in accuracy and speed.

stat.ME↗

arXiv2025

Robust Bayesian Inference of Causal Effects via Randomization Distributions

We present a general framework for Bayesian inference of causal effects that delivers provably robust inferences founded on design-based randomization of treatments. The framework involves fixing the observed potential outcomes and forming a likelihood based on the randomization distribution of a statistic. The method requires specification of a treatment effect model; in many cases, however, it does not require specification of marginal outcome distributions, resulting in weaker assumptions compared to Bayesian superpopulation-based methods. We show that the framework is compatible with posterior model checking in the form of posterior-averaged randomization tests. We prove several theoretical properties for the method, including a Bernstein-von Mises theorem and large-sample properties of posterior expectations. In particular, we show that the posterior mean is asymptotically equivalent to Hodges-Lehmann estimators, which provides a bridge to many classical estimators in causal inference, including inverse-probability-weighted estimators and Hájek estimators. We evaluate the theory and utility of the framework in simulation and a case study involving a nutrition experiment. In the latter, our framework uncovers strong evidence of effect heterogeneity despite a lack of evidence for moderation effects. The basic framework allows numerous extensions, including the use of covariates, sensitivity analysis, estimation of assignment mechanisms, and generalization to nonbinary treatments.

stat.ME↗

arXiv2024

Data integration methods for micro-randomized trials

Existing statistical methods for the analysis of micro-randomized trials (MRTs) are designed to estimate causal excursion effects using data from a single MRT. In practice, however, researchers can often find previous MRTs that employ similar interventions. In this paper, we develop data integration methods that capitalize on this additional information, leading to statistical efficiency gains. To further increase efficiency, we demonstrate how to combine these approaches according to a generalization of multivariate precision weighting that allows for correlation between estimates, and we show that the resulting meta-estimator possesses an asymptotic optimality property. We illustrate our methods in simulation and in a case study involving two MRTs in the area of smoking cessation.

stat.ME↗