Coherent and robust Bayesian inference under informative sampling via sample-level weight models
Year: 2026
Type: preprint
Abstract: We develop two complementary Bayesian procedures for analytic inference under informative sampling. The first constructs a coherent likelihood by modeling the sample-level distribution of the design weight given the study variable and recovering the conditional inclusion probability through the identity of Sverchkov and Pfeffermann (2004); it is the Bayesian counterpart of a recently proposed conditional-likelihood estimator, attains the model-based efficiency bound under the correctly specified sample-level joint model, and can be biased otherwise. The second uses the same weight model only as input to a Neyman-orthogonalized analog of the design-weighted score and applies the loss-likelihood bootstrap; the resulting credible intervals are asymptotically sandwich-correct under Poisson sampling, and the posterior remains centered at the truth under misspecification of the weight model, although the working model can still affect the first-order variance. A beta regression on the population-level inclusion probability, inducing a beta prime sample-level weight distribution, serves as the parametric default. A data-adaptive implementation of the second procedure estimates the efficient factor $\barπ(x,y)=1/E_p(W\mid x,y)$ by a design-weighted Gamma/log-link regression and uses it in a joint one-step loss-likelihood bootstrap for the analytic parameter; its validity requires no rate conditions on the nuisance fit. We illustrate both procedures with simulations and Canadian Workforce data.
Source: arXiv (Cornell University)
Authors: Morikawa, Kosuke, Kim, Jae Kwang, Chang, Won
Institutions: Iowa State University, Seoul National University
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1337118460, G162450102, 特異な傾向スコアを用いた統計的推測：傾向スコアの境界値問題への対処, G3004754169, G3339155827, G3707054632, G3812690899, Construction of the foundations of statistical earthquake prediction research, G4308274077, Developing Statistical Tools for Data integration and Data Fusion for Finite Population Inference, Mathematical Foundation for Seismic Modeling Pioneered by Information Statistics, G7701761691
OpenAlex ID: W7213437129