Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2607.21991

Bias-Adjusted Attribution Estimation for Rainfall Enhancement Trials

Zhi Yang Tho·Raymond Chambers·A. H. Welsh
View original source ↗Read source document ↗Export metadata ↓

Abstract

Model-based analyses of rainfall enhancement trial data typically involve modelling log-transformed rainfall using linear mixed models to assess the effectiveness of enhancement methods under real-world conditions. This approach improves on traditional average-based analyses by allowing explicit control for the effects of meteorological and topographical covariates that may affect precipitation amounts. However, a key issue with such analyses is the bias that arises when back-transforming the log-rainfall to the original scale for estimating attribution, defined as the additional raw-scale rainfall attributable to the enhancement method. To address this issue, we propose a new attribution estimator that incorporates theoretically justified, observation-specific bias-adjustment terms. The proposed estimator improves upon existing estimators that rely on arbitrary adjustments, and satisfies a coherence property that ensures zero estimated attribution for observations without enhancement intervention. A proportional random effect block bootstrap is further used to conduct inference on the attribution quantities. Applying both the proposed estimator and an existing estimator to the Oman rainfall enhancement trial from 2013 to 2018, we find statistically significant positive effect of the ground-based ionization technology on downwind rainfall at the 5% significance level, with our proposed estimator indicating a smaller effect than the existing method. A simulation study further support the findings based on the proposed estimator, demonstrating its superior estimation accuracy and improved inferential performance of the associated bootstrap confidence intervals.

Explore related subjects

stat.MEstat.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zhi Yang Tho, Raymond Chambers, A. H. Welsh. 2026-07-24. Bias-Adjusted Attribution Estimation for Rainfall Enhancement Trials. https://arxiv.org/abs/2607.21991

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bias-Correction for Privacy-Protected Spatial Autoregressive Models with Application to Restaurant Network Analysis

Spatial autoregressive (SAR) models and their extensions are important tools for studying network effects. However, with an increasing emphasis on data privacy, data providers often implement protection measures that render standard SAR models inapplicable. In this study, we introduce a privacy-protected SAR model that incorporates noise into both the response and covariates to meet privacy requirements. With noise present in both components, the traditional quasi-maximum likelihood estimator becomes difficult to compute because the likelihood function cannot be directly formulated. To bypass this hurdle, we begin with a pseudo-likelihood approach, initially omitting the noise in the covariates. A Newton-Raphson algorithm is then applied to compute the estimator; however, the estimator is biased. To address this, we propose a bias-corrected Newton-Raphson-type algorithm that simultaneously accounts for noise in both the response and covariates. We further show, under appropriate regularity conditions, that the resulting estimator is consistent and asymptotically normal. To further enhance computational efficiency, we also develop a bias-corrected least squares estimator. Several extensions are discussed, and the finite-sample performance of the proposed methods is evaluated through extensive simulations. We apply the proposed methodology to restaurant transaction data from a third-party payment platform. Our method identifies a statistically significant competitive network effect among restaurants and further reveals meaningful restaurant-customer interaction patterns.

stat.ME↗
arXiv2026

A variational framework for modal estimation

Multivariate mode estimation arises in many statistical problems such as inverse problems, multimodal sampling, and density-based clustering, but becomes challenging in moderate to high dimensions, especially when the underlying density is not directly evaluable. We introduce GERVE (Gibbs-measure Entropy-Regularized Variational Estimation), a sample-based method for estimating multivariate modes by approximating Gibbs distributions directly from samples, without estimating or evaluating the density. GERVE uses Gaussian-mixture variational annealing and natural-gradient optimization, producing a mixture concentrated in high-density regions whose component responsibilities also provide a clustering of the observations. We prove theoretical guarantees in two regimes: as the Gibbs temperature goes to zero, the optimal variational mixture concentrates around the global modes of the population density; at fixed positive temperature, we prove existence, consistency, and asymptotic normality of empirical maximizers and propose a bootstrap procedure for uncertainty quantification. Simulations and a real-data experiment show that GERVE accurately recovers modes and produces meaningful clusters.

stat.ME↗
arXiv2026

Objective Model Prior Probabilities in Variable Selection

For many years it was routine to use equal model prior probabilities in Bayesian model uncertainty analysis. At least twenty years ago it became clear that this was problematic, leading to support of much too large models in the increasingly huge model spaces being considered in genomics and other fields. A popular replacement was to adopt a suggestion of Harold Jeffreys for the variable selection problem in which a total of $k$ possible variables are being considered for inclusion in the model: give the collection of all models containing $d$ variables ($d = 0, . . . , k$) prior probability $1/(k + 1)$ and then divide this prior probability equally among the models in the collection. Many other choices of model prior probabilities that impose severe parsimony have also been introduced. We begin by reviewing the problems with using equal model prior probabilities and then discuss some serious problems with the Jeffreys choice. Finally, we introduce and study a number of objective alternative choices of model prior probabilities, from both numerical and theoretical perspectives.

stat.ME↗