arXiv subjects

Anthony Almudevar

Publications and source records attributed to Anthony Almudevar.

7 recordsLinked to original sources

arXiv2026

Reproducibility and Statistical Methodology

In 2015 the Open Science Collaboration (OSC) (Nosek et al 2015) published a highly influential paper which claimed that a large fraction of published results in the psychological sciences were not reproducible. In this article we review this claim from several points of view. We first offer an extended analysis of the methods used in that study. We show that the OSC methodology induces a bias that is able by itself to explain the discrepancy between the OSC estimates of reproducibility and other more optimistic estimates made by similar studies. The article also offers a more general literature review and discussion of reproducibility in experimental science. We argue, for both scientific and ethical reasons, that a considered balance of false positive and false negative rates is preferable to a single-minded concentration on false positive rates alone.

stat.AP↗

arXiv2026

Using Artificial Neural Networks to Predict Claim Duration in a Work Injury Compensation Environment

Currently, work injury compensation boards in Canada track injury information using a standard system of codes (under the National Work Injury Statistics Program (NWISP)). These codes capture the medical nature and original cause of the injury in some detail, hence they potentially contain information which may be used to predict the severity of an injury and the resulting time loss from work. Claim duration easurements and forecasts are central to the operation of a work injury compensation program. However, due to the complexity of the codes traditional statistical modelling techniques are of limited value. We will describe an artificial neural network implementation of Cox proportional hazards regression due to Ripley (1998 thesis) which is used as the basis for a model for the prediction of claim duration within a work injury compensation environment. The model accepts as input the injury codes, as well as basic demographic and workplace information. The output consists of a claim duration prediction in the form of a distribution. The input represents information available when a claim is first filed, and may therefore be used in a claims management setting. We will describe the model selection procedure, as well as a procedure for accepting inputs with missing covariates.

stat.AP↗

arXiv2026

A Compound Logistic Regression Model for Binary Responses

Logistic regression is the most commonly used method for constructing predictive models for binary responses. One significant drawback to this approach, however, is that the asymptotes of the logistic response function are fixed at 0 and 1, and there are many applications for which this constraint is inappropriate. More flexible models have been proposed for this application, most proceeding by supplementing the logistic response function with additional parameters. In this article we extend these models to allow correlated responses and the inclusion of covariates. This is achieved through the \emph{compound logistic regression model}, for which the mean response is a function of several logistic regression functions. This permits a greater variety of models, while retaining the advantages of logistic regression.

stat.ME↗

arXiv2026

Revisiting the Lost Submarine Problem: A Decision Theoretic Approach

This article includes a discussion of the ``lost submarine problem", following Morey \emph{et al} (2016). As the title of that paper suggests (\emph{The fallacy of placing confidence in confidence intervals}), the example is intended to illustrate the futility of relying on the confidence interval as a formal inference statement. In the view of this author, the misgivings expressed in Morey \emph{et al} (2016) can be resolved using a decision theoretic approach. While it is true that a variety of statistical methods lead to a variety of confidence intervals, once we precisely define their purpose, a single optimal choice emerges. Furthermore, distinct purposes lead to distinct optimal choices. Therefore, that a variety of procedures exist is an advantage rather than a liability.

stat.OT↗

arXiv2023

Testing Sparsity Assumptions in Bayesian Networks

Bayesian network (BN) structure discovery algorithms typically either make assumptions about the sparsity of the true underlying network, or are limited by computational constraints to networks with a small number of variables. While these sparsity assumptions can take various forms, frequently the assumptions focus on an upper bound for the maximum in-degree of the underlying graph $\nabla_G$. Theorem 2 in Duttweiler et. al. (2023) demonstrates that the largest eigenvalue of the normalized inverse covariance matrix ($\Omega$) of a linear BN is a lower bound for $\nabla_G$. Building on this result, this paper provides the asymptotic properties of, and a debiasing procedure for, the sample eigenvalues of $\Omega$, leading to a hypothesis test that may be used to determine if the BN has max in-degree greater than 1. A linear BN structure discovery workflow is suggested in which the investigator uses this hypothesis test to aid in selecting an appropriate structure discovery algorithm. The hypothesis test performance is evaluated through simulations and the workflow is demonstrated on data from a human psoriasis study.

stat.ML↗

arXiv2022

Spectral Bayesian Network Theory

A Bayesian Network (BN) is a probabilistic model that represents a set of variables using a directed acyclic graph (DAG). Current algorithms for learning BN structures from data focus on estimating the edges of a specific DAG, and often lead to many `likely' network structures. In this paper, we lay the groundwork for an approach that focuses on learning global properties of the DAG rather than exact edges. This is done by defining the structural hypergraph of a BN, which is shown to be related to the inverse-covariance matrix of the network. Spectral bounds are derived for the normalized inverse-covariance matrix, which are shown to be closely related to the maximum indegree of the associated BN.

math.CO↗

arXiv2022

A Stochastic Contraction Mapping Theorem

In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive processes converge to zero $a.e.$ Extensions to multivariate processes are given. These properties may be used to model a number of important processes, including stochastic approximation and least-squares estimation of controlled linear models, with convergence properties derivable from a single theory. The approach has the advantage of not in general requiring analytical regularity properties such as continuity and differentiability.

math.PR↗