arXiv subjects

Benjamin R. Baer

Publications and source records attributed to Benjamin R. Baer.

11 recordsLinked to original sources

arXiv2026

Capture history analysis for spatial wildlife surveys with detection times

Many wildlife surveys of species with individually identifiable animals are based on the analysis of the capture histories of individual animals. However, not many of these take account of both the animals' capture times and their capture locations. In this work, we develop a maximum likelihood estimator for surveys of individually identifiable animals using proximity detectors, multi-catch traps, single-catch traps, and traps that remove animals from the population, when capture times are known. We do this using the counting process theory at the foundation of event history (or survival) analysis. The work provides a unifying framework for such surveys, resolves open problems for single-catch traps and removal surveys, and introduces a new statistical method for multi-catch traps. We test the new methods by simulation and we present an analysis of possums in New Zealand caught with single-catch traps.

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arXiv2026

Fragility Measures For Typical Cases

The fragility index is a clinically motivated metric designed to supplement the $p$ value during hypothesis testing. The measure relies on two pillars: selecting cases to have their outcome modified and modifying the outcomes. The measure is interesting but the case selection suffers from a drawback which can hamper its interpretation. This work presents the drawback and a method, the stochastic generalized fragility indices, designed to remedy it. Two examples concerning electoral outcomes and the causal effect of smoking cessation illustrate the method.

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arXiv2025

On Causal Inference for the Survivor Function

In this expository paper, we consider the problem of causal inference and efficient estimation for the counterfactual survivor function. This problem has previously been considered in the literature in several papers, each relying on the imposition of conditions meant to identify the desired estimand from the observed data. These conditions, generally referred to as either implying or satisfying coarsening at random, are inconsistently imposed across this literature and, in all cases, fail to imply coarsening at random. We establish the first general characterization of coarsening at random, and also sequential coarsening at random, for this estimation problem. Other contributions include the first general characterization of the set of all influence functions for the counterfactual survival probability under sequential coarsening at random, and the corresponding nonparametric efficient influence function. These characterizations are general in that neither impose continuity assumptions on either the underlying failure or censoring time distributions. We further show how the latter compares to alternative forms recently derived in the literature, including establishing the pointwise equivalence of the influence functions for our nonparametric efficient estimator and that recently given in Westling et al (2024, Journal of the American Statistical Association).

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arXiv2025

Causal inference for the expected number of recurrent events in the presence of a terminal event

While recurrent event analyses have been extensively studied, limited attention has been given to causal inference within the framework of recurrent event analysis. We develop a multiply robust estimation framework for causal inference in recurrent event data with a terminal failure event. We define our estimand as the vector comprising both the expected number of recurrent events and the failure survival function evaluated along a sequence of landmark times. We show that the estimand can be identified under a weaker condition than conditionally independent censoring and derive the associated class of influence functions under general censoring and failure distributions (i.e., without assuming absolute continuity). We propose a particular estimator within this class for further study, conduct comprehensive simulation studies to evaluate the small-sample performance of our estimator, and illustrate the proposed estimator using a large Medicare dataset to assess the causal effect of PM$_{2.5}$ on recurrent cardiovascular hospitalization.

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arXiv2025

A foundation for the distance sampling methodology

The population size ("abundance") of wildlife species has central interest in ecological research and management. Distance sampling is a dominant approach to the estimation of wildlife abundance for many vertebrate animal species. One perceived advantage of distance sampling over the well-known alternative approach of capture-recapture is that distance sampling is thought to be robust to unmodelled heterogeneity in animal detection probability, via a conjecture known as "pooling robustness". Although distance sampling has been successfully applied and developed for decades, its statistical foundation is not complete: there are published proofs and arguments highlighting deficiency of the methodology. This work provides a statistical foundation for distance sampling that has attainable assumptions. In addition, because identification and consistency of the developed distance sampling abundance estimator is unaffected by detection heterogeneity, the pooling robustness conjecture is resolved.

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arXiv2024

On a theory of martingales for censoring

A theory of martingales for censoring is developed. The Doob-Meyer martingale is shown to be inadequate in general, and a repaired martingale is proposed with a non-predictable centering term. Associated martingale transforms, variation processes, and covariation processes are developed based on a measure of half-predictability that generalizes predictability. The development is applied to study the Kaplan Meier estimator.

math.ST↗

arXiv2024

Nonparametric assessment of regimen response curve estimators

Marginal structural models have been widely used in causal inference to estimate mean outcomes under either a static or a prespecified set of treatment decision rules. This approach requires imposing a working model for the mean outcome given a sequence of treatments and possibly baseline covariates. In this paper, we introduce a dynamic marginal structural model that can be used to estimate an optimal decision rule within a class of parametric rules. Specifically, we will estimate the mean outcome as a function of the parameters in the class of decision rules, referred to as a regimen-response curve. In general, misspecification of the working model may lead to a biased estimate with questionable causal interpretability. To mitigate this issue, we will leverage risk to assess "goodness-of-fit" of the imposed working model. We consider the counterfactual risk as our target parameter and derive inverse probability weighting and canonical gradients to map it to the observed data. We provide asymptotic properties of the resulting risk estimators, considering both fixed and data-dependent target parameters. We will show that the inverse probability weighting estimator can be efficient and asymptotic linear when the weight functions are estimated using a sieve-based estimator. The proposed method is implemented on the LS1 study to estimate a regimen-response curve for patients with Parkinson's disease.

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arXiv2023

On the Role of Volterra Integral Equations in Self-Consistent, Product-Limit, Inverse Probability of Censoring Weighted, and Redistribution-to-the-Right Estimators for the Survival Function

This paper reconsiders several results of historical and current importance to nonparametric estimation of the survival distribution for failure in the presence of right-censored observation times, demonstrating in particular how Volterra integral equations of the first kind help inter-connect the resulting estimators. The paper begins by considering Efron's self-consistency equation, introduced in a seminal 1967 Berkeley symposium paper. Novel insights provided in the current work include the observations that (i) the self-consistency equation leads directly to an anticipating Volterra integral equation of the first kind whose solution is given by a product-limit estimator for the censoring survival function; (ii) a definition used in this argument immediately establishes the familiar product-limit estimator for the failure survival function; (iii) the usual Volterra integral equation for the product-limit estimator of the failure survival function leads to an immediate and simple proof that it can be represented as an inverse probability of censoring weighted estimator (i.e., under appropriate conditions). Finally, we show that the resulting inverse probability of censoring weighted estimators, attributed to a highly influential 1992 paper of Robins and Rotnitzky, were implicitly introduced in Efron's 1967 paper in its development of the redistribution-to-the-right algorithm. All results developed herein allow for ties between failure and/or censored observations.

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arXiv2023

Confounding-adjustment methods for the causal difference in medians

With continuous outcomes, the average causal effect is typically defined using a contrast of expected potential outcomes. However, in the presence of skewed outcome data, the expectation may no longer be meaningful. In practice the typical approach is to either "ignore or transform" - ignore the skewness altogether or transform the outcome to obtain a more symmetric distribution, although neither approach is entirely satisfactory. Alternatively the causal effect can be redefined as a contrast of median potential outcomes, yet discussion of confounding-adjustment methods to estimate this parameter is limited. In this study we described and compared confounding-adjustment methods to address this gap. The methods considered were multivariable quantile regression, an inverse probability weighted (IPW) estimator, weighted quantile regression and two little-known implementations of g-computation for this problem. Motivated by a cohort investigation in the Longitudinal Study of Australian Children, we conducted a simulation study that found the IPW estimator, weighted quantile regression and g-computation implementations minimised bias when the relevant models were correctly specified, with g-computation additionally minimising the variance. These methods provide appealing alternatives to the common "ignore or transform" approach and multivariable quantile regression, enhancing our capability to obtain meaningful causal effect estimates with skewed outcome data.

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arXiv2021

Periodic Orbits on Obtuse Edge Tessellating Polygons

A periodic orbit on a frictionless billiard table is a piecewise linear path of a billiard ball that begins and ends at the same point with the same angle of incidence. The period of a primitive periodic orbit is the number of times the ball strikes a side of the table as it traverses its trajectory exactly once. In this paper we find and classify the periodic orbits on a billiard table in the shape of a 120-isosceles triangle, a 60-rhombus, a 60-90-120-kite, and a 30-right triangle. In each case, we use the edge tessellation (also known as tiling) of the plane generated by the figure to unfold a periodic orbit into a straight line segment and to derive a formula for its period in terms of the initial angle and initial position.

math.DS↗

arXiv2019

Fairness criteria through the lens of directed acyclic graphical models

A substantial portion of the literature on fairness in algorithms proposes, analyzes, and operationalizes simple formulaic criteria for assessing fairness. Two of these criteria, Equalized Odds and Calibration by Group, have gained significant attention for their simplicity and intuitive appeal, but also for their incompatibility. This chapter provides a perspective on the meaning and consequences of these and other fairness criteria using graphical models which reveals Equalized Odds and related criteria to be ultimately misleading. An assessment of various graphical models suggests that fairness criteria should ultimately be case-specific and sensitive to the nature of the information the algorithm processes.

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