arXiv subjects

Duncan A. Clark

Publications and source records attributed to Duncan A. Clark.

5 recordsLinked to original sources

arXiv2026

Sensitivity Bounds and Conservative Inference for Contagion under Latent Homophily

Whether connected units are similar because influence spreads across ties or because similar units form ties is a long standing problem. We study a fixed network with two waves of nodal outcomes. Rather than positing a parametric model for network formation, we consider identification of contagion under latent homophily as a selection bias problem. We define a focal component controlled direct effect (CDE) that holds a tie present, changes one alter's lagged outcome, and permits dependence on the remaining fixed network background. We show that the gap between the CDE and the observed connected dyad risk ratio is governed by how strongly a latent variable shifts the composition of connected dyads. Under stated mean exchangeability and sensitivity restrictions, we develop interpretable nonparametric bounds for the primary naturally connected target. For inference conditional on the observed network and baseline outcomes, heterogeneous dyad specific means can invalidate the usual inclusion exclusion variance estimator; we establish asymptotically conservative one sided limits under conditional actor dissociation and stated regularity conditions. A simulation study characterizes the bounds' error control and power. We apply the framework to the 2008 U.S. House votes on the Troubled Asset Relief Program. The connected contrast among legislators suggests vote contagion and survives mild latent homophily and outcome susceptibility.

stat.AP↗

arXiv2026

Causal inference for spatiotemporal point processes in the presence of outcome spillover and carryover

We develop a framework for causal inference with continuous spatiotemporal point-process outcomes under cell-level interventions and outcome spillover. Potential outcomes are indexed by full treatment allocations, and the observed post-treatment process is represented as an unlabelled superposition of latent control and treatment components. On the observed design support, expected post-treatment event counts in any spacetime region under a given treatment allocation are identified under consistency, exchangeability, and positivity; off-support contrasts are identified relative to a regime-stable structural point-process model. Estimation is likelihood-based and implemented with stochastic EM. To understand when this is feasible, we analyse a predictable blockwise hard-EM surrogate and show nonasymptotic contraction of estimation error to a statistical floor governed by locally ambiguous regions. This yields plug-in guarantees for cell-level and global causal functionals, and clarifies the additional array conditions needed for unnormalised growing-window contrasts. The framework covers history dependent spatiotemporal point processes including Poisson and Hawkes models, with applications to settings such as epidemiology, seismology, and finance. We provide an application assessing the causal effect of injecting wastewater into the ground on seismic activity in Oklahoma.

stat.ME↗

arXiv2022

An Approach to Causal Inference over Stochastic Networks

Claiming causal inferences in network settings necessitates careful consideration of the often complex dependency between outcomes for actors. Of particular importance are treatment spillover or outcome interference effects. We consider causal inference when the actors are connected via an underlying network structure. Our key contribution is a model for causality when the underlying network is unobserved and the actor covariates evolve stochastically over time. We develop a joint model for the relational and covariate generating process that avoids restrictive separability assumptions and deterministic network assumptions that do not hold in the majority of social network settings of interest. Our framework utilizes the highly general class of Exponential-family Random Network models (ERNM) of which Markov Random Fields (MRF) and Exponential-family Random Graph models (ERGM) are special cases. We present potential outcome based inference within a Bayesian framework, and propose a simple modification to the exchange algorithm to allow for sampling from ERNM posteriors. We present results of a simulation study demonstrating the validity of the approach. Finally, we demonstrate the value of the framework in a case-study of smoking over time in the context of adolescent friendship networks.

stat.ME↗

arXiv2021

On the Goodwillie derivatives of the identity in structured ring spectra

The aim of this paper is three-fold: (i) we construct a naturally occurring highly homotopy coherent operad structure on the derivatives of the identity functor on structured ring spectra which can be described as algebras over an operad $\mathcal{O}$ in spectra, (ii) we prove that every connected $\mathcal{O}$-algebra has a naturally occurring left action of the derivatives of the identity, and (iii) we show that there is a naturally occurring weak equivalence of highly homotopy coherent operads between the derivatives of the identity on $\mathcal{O}$-algebras and the operad $\mathcal{O}$. Along the way, we introduce the notion of $\mathbf{N}$-colored operads with levels which -- by construction -- provides a precise algebraic framework for working with and comparing highly homotopy coherent operads, operads, and their algebras.

math.AT↗

arXiv2020

The partition poset complex and the Goodwillie derivatives of the identity in spaces

We produce a canonical highly homotopy-coherent operad structure on the derivatives of the identity functor in spaces via a pairing of cosimplicial objects, providing a new description of an operad structure on such objects first described by Ching. We prove that the two structures agree: both are restrictions of a single algebra over an operad of windowed cut systems on weighted trees, whose component spaces are contractible, along maps of structuring operads which are all levelwise weak equivalences. In addition, we show the derived primitives of a commutative coalgebra in spectra form an algebra over this operad.

math.AT↗