arXiv subjects

Kenichiro McAlinn

Publications and source records attributed to Kenichiro McAlinn.

At least 19 recordsLinked to original sources

arXiv2026

Fast boundary-aware spatial intensity estimation on complex domains

Spatial intensity maps are routinely used to summarize point patterns on geographically constrained regions, such as islands, coastlines, watersheds, ecological reserves, and administrative areas with physical barriers. In these settings, the domain is not a nuisance feature-- it determines where probability mass may be assigned and which locations should be smoothed together. Standard kernel density estimators can place mass outside the study region and smooth according to Euclidean distance, while diffusion-based estimators respect the geometry but are costly to recompute when the data subset, bandwidth, or evaluation grid changes. Motivated by repeated hotspot mapping of theft and larceny incidents on Oahu, Hawaii, we propose the projected diffusion kernel density estimator (PDKDE). PDKDE expands the Neumann diffusion kernel in a truncated Laplacian eigenbasis, so that the geometry of a fixed domain is computed once and subsequent density estimates are obtained through explicit spectral coefficients. The resulting estimator preserves the boundary-aware and geometry-respecting behavior of diffusion smoothing while making repeated estimation and least-squares cross-validation computationally practical. For the exact projected estimator, we prove MISE consistency and pointwise consistency up to the boundary. Controlled simulations show that PDKDE reduces boundary and barrier artifacts relative to Euclidean kernels and is substantially faster than the geometry-aware comparators considered after the one-time domain computation. In the Oahu application, the method produces coastline-constrained descriptive maps across time windows in seconds, illustrating its intended fixed-domain, changing-data use case.

stat.ME↗

arXiv2026

An Entropy-Energy Identity for Predictive Kullback-Leibler Regret in Infinitely Divisible Location Models

We consider predictive density estimation under logarithmic score for $d$-dimensional infinitely divisible location models. Taking the formal Bayes predictive density under the Lebesgue prior as a benchmark, we study the Kullback-Leibler regret of competing Bayes predictive densities. Our main contribution is an exact entropy-energy identity: the integrated regret of a Bayes predictive density $\hat{p}^π$ under prior $π$ relative to the benchmark admits an exact representation as the Dirichlet-form energy of the square-rooted marginal distribution $\sqrt{M^π}$ for the symmetric Markov semigroup induced by the benchmark kernel. This converts regret comparisons into a potential-theoretic problem and yields a sharp recurrence/transience characterization of when the benchmark predictive density can or cannot be uniformly improved. We introduce an $\mathcal{A}$-harmonic class of improper priors -- defined through the generator $\mathcal{A}$ of the induced process -- and give explicit tail conditions -- an integral test on the induced marginal, equivalent to power-law prior decay in heavy-tailed models -- that guarantee admissibility of the resulting Bayes predictive density. We illustrate the theory with new results for several distributions.

math.ST↗

arXiv2026

Predictive Synthesis under Sporadic Participation: Evidence from Inflation Density Surveys

Central banks rely on density forecasts from professional surveys to assess inflation risks and communicate uncertainty. A central challenge in using these surveys is irregular participation: forecasters enter and exit, skip rounds, and reappear after long gaps. In the European Central Bank's Survey of Professional Forecasters, turnover and missingness vary substantially over time, causing the set of submitted predictions to change from quarter to quarter. Standard aggregation rules -- such as equal-weight pooling, renormalization after dropping missing forecasters, or ad hoc imputation -- can generate artificial jumps in combined predictions driven by panel composition rather than economic information, complicating real-time interpretation and obscuring forecaster performance. We develop coherent Bayesian updating rules for forecast combination under sporadic participation that maintain a well-defined latent predictive state for each forecaster even when their forecast is unobserved. Rather than relying on renormalization or imputation, the combined predictive distribution is updated through the implied conditional structure of the panel. This approach isolates genuine performance differences from mechanical participation effects and yields interpretable dynamics in forecaster influence. In the ECB survey, it improves predictive accuracy relative to equal-weight benchmarks and delivers smoother and better-calibrated inflation density forecasts, particularly during periods of high turnover.

stat.AP↗

arXiv2026

When Is Generalized Bayes Bayesian? A Decision-Theoretic Characterization of Loss-Based Updating

Loss-based updating, including generalized Bayes, Gibbs, and quasi-posteriors, replaces likelihoods by a user-chosen loss and produces a posterior-like distribution via exponential tilt. We give a decision-theoretic characterization that separates \emph{belief posteriors} -- conditional beliefs justified by the foundations of Savage and Anscombe-Aumann under a joint probability mode l-- from \emph{decision posteriors} -- randomized decision rules justified by preferences over decision rules. We make explicit that a loss-based posterior coincides with ordinary Bayes if and only if the loss is, up to scale and a data-only term, negative log-likelihood. We then show that generalized marginal likelihood is not evidence for decision posteriors, and Bayes factors are not well-defined without additional structure. In the decision posterior regime, non-degenerate posteriors require nonlinear preferences over decision rules. Under sequential coherence and separability, these lead to an entropy-penalized variational representation yielding generalized Bayes as the optimal rule.

stat.ME↗

arXiv2026

Optimal Hold-Out Size in Cross-Validation

Cross-validation (CV) is routinely used across the sciences to select models and tune parameters, and the resulting choices are often interpreted as substantive scientific conclusions (e.g., which variables, mechanisms, or risk factors are ``supported by the data''). A key part of the CV procedure -- the hold-out size, or equivalently the fold count $K$ -- is typically set by convention (e.g., 80/20, $K=5$) rather than by a principled criterion. Central to the issue is the tradeoff between training and testing: increasing the training sample size improves model accuracy, while sacrificing certainty around the accuracy itself. We formalize the tradeoff by targeting predictive performance and explicitly penalizing evaluation uncertainty, which cannot be identified from the data without additional assumptions. We derive finite-sample expressions of this evaluation uncertainty under symmetric errors and general upper bounds under broader error conditions, yielding a transparent utility-based rule for selecting the hold-out size as a function of an irreducible-noise parameter. Empirical analyses with linear regression and random forests across multiple domains, and a high-dimensional genomics application, show that (i) the choice of $K$ is dependent on the data and model. (ii) the optimal $K$ varies based on the assumption on the irreducible error, and (iii) the implied inferential conclusions can change materially as the irreducible error, and thus $K$, varies. The resulting framework replaces a one-size-fits-all convention with a context-specific, assumption-explicit choice of $K$, enabling more reliable model comparisons and downstream scientific inference.

stat.ME↗

arXiv2026

Dynamic causal inference with time series data

We generalize the potential outcome framework to time series with an intervention by defining causal effects on stochastic processes. Interventions in dynamic systems alter not only outcome levels but also evolutionary dynamics -- changing persistence and transition laws. Our framework treats potential outcomes as entire trajectories, enabling causal estimands, identification conditions, and estimators to be formulated directly on path space. The resulting Dynamic Average Treatment Effect (DATE) characterizes how causal effects evolve through time and reduces to the classical average treatment effect under one period of time. For observational data, we derive a dynamic inverse-probability weighting estimator that is unbiased under dynamic ignorability and positivity. When treated units are scarce, we show that conditional mean trajectories underlying the DATE admit a linear state-space representation, yielding a dynamic linear model implementation. Simulations demonstrate that modeling time as intrinsic to the causal mechanism exposes dynamic effects that static methods systematically misestimate. An empirical study of COVID-19 lockdowns illustrates the framework's practical value for estimating and decomposing treatment effects.

stat.ME↗

arXiv2025

Bayesian Spatial Predictive Synthesis

Due to spatial dependence -- often characterized as complex and non-linear -- model misspecification is a prevalent and critical issue in spatial data analysis and prediction. As the data, and thus model performance, is heterogeneous, typical model selection and ensemble methods that assume homogeneity are not suitable. We address the issue of model uncertainty for spatial data by proposing a novel Bayesian ensemble methodology that captures spatially-varying model uncertainty and performance heterogeneity of multiple spatial predictions, and synthesizes them for improved predictions, which we call Bayesian spatial predictive synthesis. Our proposal is defined by specifying a latent factor spatially-varying coefficient model as the synthesis function, which enables spatial characteristics of each model to be learned and ensemble coefficients to vary over regions to achieve flexible predictions. We derive our method from the theoretically best approximation of the data generating process, and show that it provides a finite sample theoretical guarantee for its predictive performance, specifically that the predictions are exact minimax. Two MCMC strategies are implemented for full uncertainty quantification, as well as a variational inference strategy for fast point inference. We also extend the estimation strategy for general responses. Through simulation examples and two real data applications in real estate and ecology, our proposed Bayesian spatial predictive synthesis outperforms standard spatial models and ensemble methods, and advanced machine learning methods, in terms of predictive accuracy and uncertainty quantification, while maintaining interpretability of the prediction mechanism.

stat.ME↗

arXiv2024

Ensemble Doubly Robust Bayesian Inference via Regression Synthesis

The doubly robust estimator, which models both the propensity score and outcomes, is a popular approach to estimate the average treatment effect in the potential outcome setting. The primary appeal of this estimator is its theoretical property, wherein the estimator achieves consistency as long as either the propensity score or outcomes is correctly specified. In most applications, however, both are misspecified, leading to considerable bias that cannot be checked. In this paper, we propose a Bayesian ensemble approach that synthesizes multiple models for both the propensity score and outcomes, which we call doubly robust Bayesian regression synthesis. Our approach applies Bayesian updating to the ensemble model weights that adapt at the unit level, incorporating data heterogeneity, to significantly mitigate misspecification bias. Theoretically, we show that our proposed approach is consistent regarding the estimation of both the propensity score and outcomes, ensuring that the doubly robust estimator is consistent, even if no single model is correctly specified. An efficient algorithm for posterior computation facilitates the characterization of uncertainty regarding the treatment effect. Our proposed approach is compared against standard and state-of-the-art methods through two comprehensive simulation studies, where we find that our approach is superior in all cases. An empirical study on the impact of maternal smoking on birth weight highlights the practical applicability of our proposed method.

stat.ME↗

arXiv2024

Bayesian Causal Synthesis for Meta-Inference on Heterogeneous Treatment Effects

The estimation of heterogeneous treatment effects in the potential outcome setting is biased when there exists model misspecification or unobserved confounding. As these biases are unobservable, what model to use when remains a critical open question. In this paper, we propose a novel Bayesian methodology to mitigate misspecification and improve estimation via a synthesis of multiple causal estimates, which we call Bayesian causal synthesis. Our development is built upon identifying a synthesis function that correctly specifies the heterogeneous treatment effect under no unobserved confounding, and achieves the irreducible bias under unobserved confounding. We show that our proposed method results in consistent estimates of the heterogeneous treatment effect; either with no bias or with irreducible bias. We provide a computational algorithm for fast posterior sampling. Several benchmark simulations and an empirical study highlight the efficacy of the proposed approach compared to existing methodologies, providing improved point and density estimation of the heterogeneous treatment effect, even under unobserved confounding.

stat.ME↗

arXiv2023

Inadmissibility and Transience

We discuss the relation between the statistical question of inadmissibility and the probabilistic question of transience. Brown (1971) proved the mathematical link between the admissibility of the mean of a Gaussian distribution and the recurrence of a Brownian motion, which holds for $\mathbb{R}^{2}$ but not for $\mathbb{R}^{3}$ in Euclidean space. We extend this result to symmetric, non-Gaussian distributions, without assuming the existence of moments. As an application, we prove that the relation between the inadmissibility of the predictive density of a Cauchy distribution under a uniform prior and the transience of the Cauchy process differs from dimensions $\mathbb{R}^{1}$ to $\mathbb{R}^{2}$. We also show that there exists an extreme model that is inadmissible in $\mathbb{R}^{1}$.

math.ST↗

arXiv2023

Equivariant online predictions of non-stationary time series

We discuss the finite sample theoretical properties of online predictions in non-stationary time series under model misspecification. To analyze the theoretical predictive properties of statistical methods under this setting, we first define the Kullback-Leibler risk, in order to place the problem within a decision theoretic framework. Under this framework, we show that a specific class of dynamic models -- random walk dynamic linear models -- produce exact minimax predictive densities. We first show this result under Gaussian assumptions, then relax this assumption using semi-martingale processes. This result provides a theoretical baseline, under both non-stationary and stationary time series data, for which other models can be compared against. We extend the result to the synthesis of multiple predictive densities. Three topical applications in epidemiology, climatology, and economics, confirm and highlight our theoretical results.

math.ST↗

arXiv2022

Learning Causal Models from Conditional Moment Restrictions by Importance Weighting

We consider learning causal relationships under conditional moment restrictions. Unlike causal inference under unconditional moment restrictions, conditional moment restrictions pose serious challenges for causal inference, especially in high-dimensional settings. To address this issue, we propose a method that transforms conditional moment restrictions to unconditional moment restrictions through importance weighting, using a conditional density ratio estimator. Using this transformation, we successfully estimate nonparametric functions defined under conditional moment restrictions. Our proposed framework is general and can be applied to a wide range of methods, including neural networks. We analyze the estimation error, providing theoretical support for our proposed method. In experiments, we confirm the soundness of our proposed method.

econ.EM↗

arXiv2022

Dynamic Bayesian Predictive Synthesis in Time Series Forecasting

We discuss model and forecast combination in time series forecasting. A foundational Bayesian perspective based on agent opinion analysis theory defines a new framework for density forecast combination, and encompasses several existing forecast pooling methods. We develop a novel class of dynamic latent factor models for time series forecast synthesis; simulation-based computation enables implementation. These models can dynamically adapt to time-varying biases, miscalibration and inter-dependencies among multiple models or forecasters. A macroeconomic forecasting study highlights the dynamic relationships among synthesized forecast densities, as well as the potential for improved forecast accuracy at multiple horizons.

stat.ME↗

arXiv2021

Policy Choice and Best Arm Identification: Asymptotic Analysis of Exploration Sampling

We consider the "policy choice" problem -- otherwise known as best arm identification in the bandit literature -- proposed by Kasy and Sautmann (2021) for adaptive experimental design. Theorem 1 of Kasy and Sautmann (2021) provides three asymptotic results that give theoretical guarantees for exploration sampling developed for this setting. We first show that the proof of Theorem 1 (1) has technical issues, and the proof and statement of Theorem 1 (2) are incorrect. We then show, through a counterexample, that Theorem 1 (3) is false. For the former two, we correct the statements and provide rigorous proofs. For Theorem 1 (3), we propose an alternative objective function, which we call posterior weighted policy regret, and derive the asymptotic optimality of exploration sampling.

econ.EM↗

arXiv2021

The Adaptive Doubly Robust Estimator for Policy Evaluation in Adaptive Experiments and a Paradox Concerning Logging Policy

The doubly robust (DR) estimator, which consists of two nuisance parameters, the conditional mean outcome and the logging policy (the probability of choosing an action), is crucial in causal inference. This paper proposes a DR estimator for dependent samples obtained from adaptive experiments. To obtain an asymptotically normal semiparametric estimator from dependent samples with non-Donsker nuisance estimators, we propose adaptive-fitting as a variant of sample-splitting. We also report an empirical paradox that our proposed DR estimator tends to show better performances compared to other estimators utilizing the true logging policy. While a similar phenomenon is known for estimators with i.i.d. samples, traditional explanations based on asymptotic efficiency cannot elucidate our case with dependent samples. We confirm this hypothesis through simulation studies.

cs.LG↗

arXiv2021

Controlling False Discovery Rates under Cross-Sectional Correlations

We consider controlling the false discovery rate for testing many time series with an unknown cross-sectional correlation structure. Given a large number of hypotheses, false and missing discoveries can plague an analysis. While many procedures have been proposed to control false discovery, most of them either assume independent hypotheses or lack statistical power. A problem of particular interest is in financial asset pricing, where the goal is to determine which ``factors" lead to excess returns out of a large number of potential factors. Our contribution is two-fold. First, we show the consistency of Fama and French's prominent method under multiple testing. Second, we propose a novel method for false discovery control using double bootstrapping. We achieve superior statistical power to existing methods and prove that the false discovery rate is controlled. Simulations and a real data application illustrate the efficacy of our method over existing methods.

stat.ME↗

arXiv2021

Convergence of Computed Dynamic Models with Unbounded Shock

This paper studies the asymptotic convergence of computed dynamic models when the shock is unbounded. Most dynamic economic models lack a closed-form solution. As such, approximate solutions by numerical methods are utilized. Since the researcher cannot directly evaluate the exact policy function and the associated exact likelihood, it is imperative that the approximate likelihood asymptotically converges -- as well as to know the conditions of convergence -- to the exact likelihood, in order to justify and validate its usage. In this regard, Fernandez-Villaverde, Rubio-Ramirez, and Santos (2006) show convergence of the likelihood, when the shock has compact support. However, compact support implies that the shock is bounded, which is not an assumption met in most dynamic economic models, e.g., with normally distributed shocks. This paper provides theoretical justification for most dynamic models used in the literature by showing the conditions for convergence of the approximate invariant measure obtained from numerical simulations to the exact invariant measure, thus providing the conditions for convergence of the likelihood.

econ.EM↗

arXiv2019

Mean-shift least squares model averaging

This paper proposes a new estimator for selecting weights to average over least squares estimates obtained from a set of models. Our proposed estimator builds on the Mallows model average (MMA) estimator of Hansen (2007), but, unlike MMA, simultaneously controls for location bias and regression error through a common constant. We show that our proposed estimator-- the mean-shift Mallows model average (MSA) estimator-- is asymptotically optimal to the original MMA estimator in terms of mean squared error. A simulation study is presented, where we show that our proposed estimator uniformly outperforms the MMA estimator.

econ.EM↗