composite likelihood estimation

This work addresses the challenge of efficiently estimating and optimizing the marginal likelihood and its functionals in models with high-dimensional parameters and low-dimensional continuous hyperparameters. The authors propose a smooth functional estimation framework based on posterior samples, which integrates Bayesian posterior sampling, function interpolation, and functional estimation techniques. By leveraging posterior samples evaluated at a finite set of grid points, the method constructs a globally smooth estimator of the marginal likelihood. Notably, it unifies sequential Monte Carlo, Gibbs sampling, and Monte Carlo maximum likelihood approaches within a single theoretical framework and establishes estimation consistency under both fixed and dense grid designs. Empirical evaluations on Gaussian process regression and classification, as well as cross-effects models, demonstrate that the approach accurately estimates the marginal likelihood and its associated functionals—including derivatives and integrals.

This study addresses the high computational cost associated with parameter estimation in fractional Gaussian processes by proposing an efficient composite likelihood–based estimation method. By deriving analytical expressions for the Fisher and Godambe information of fractional Brownian motion and fractional Gaussian noise, the authors design a sequential strategy to select optimal subsets of observations that maximize Godambe information. This approach substantially reduces computational burden while enhancing estimation accuracy. Simulation studies demonstrate superior performance compared to conventional moment-based methods and maximum likelihood estimation. The efficacy of the proposed method is further corroborated through empirical analyses of stock index volatility and wind speed time series.

Traditional hybrid experimental designs struggle to robustly control the frequentist operating characteristics of Bayesian decisions under model misspecification and lack efficient sample size determination methods applicable to generalized posteriors. This work proposes a computationally efficient experimental design framework that requires simulations at only two sample sizes and leverages extrapolation modeling of posterior summary functions to infer performance across the entire sample size space. This approach enables identification of the minimal sample size and decision rule satisfying desired operating characteristics. It represents the first general and scalable method for sample size planning under generalized posteriors, substantially reducing computational burden while enhancing robustness to model misspecification. The method’s validity and broad applicability within Bayesian M-estimation–type experiments are demonstrated through the redesign of an adaptive clinical trial with time-to-event outcomes.

This paper studies semiparametric identification of continuous-outcome learning models featuring three types of unobservables: known heterogeneity, initially unknown heterogeneity gradually revealed over time, and transitory shocks. Identification is achieved using only short-panel data on choices and outcomes. Methodologically, the approach integrates semiparametric identification theory, sieve maximum likelihood estimation, and profile likelihood inference to rigorously establish both point identification of structural parameters and distributional identification of all three unobservable components. Crucially, no parametric distributional assumptions are imposed on the initially unknown heterogeneity. The paper’s key contribution lies in being the first to jointly identify all three unobservable components within a short-panel framework—without requiring functional-form restrictions on the latent heterogeneity structure. Asymptotic properties of the proposed estimators are derived, and Monte Carlo simulations demonstrate excellent finite-sample performance.

This work addresses the computational inefficiency in Bayesian semiparametric regression arising from complex design matrix structures. To mitigate this challenge, the authors propose an orthogonalization preprocessing step applied to the design日晚间 matrix prior to iterative inference, combined with a hybrid algorithm integrating Gibbs sampling and coordinate ascent variational inference. This approach reduces computational complexity to quadratic in the number of covariates, substantially accelerating both model fitting and posterior inference. Empirical evaluations across diverse experimental settings demonstrate speedups ranging from 5× to 60× compared to conventional methods, effectively alleviating the computational bottleneck induced by high-dimensional covariates.

This study addresses the unreliability of finite population inference from nonprobability samples, which often hinges on the unverifiable missing-at-random (MAR) assumption. The authors propose a design-based sequential sampling framework that treats the nonprobability sample as a deterministic stratum and draws a probability sample from its complement. Within this framework, they construct two classes of generalized regression estimators that guarantee design consistency without imposing any assumptions on the nonprobability selection mechanism—even under not-missing-at-random (NMAR) scenarios. Under stronger modeling assumptions such as coefficient homogeneity, the estimators achieve Isaki–Fuller asymptotic optimality. Simulations demonstrate that the proposed approach yields approximately unbiased estimates under both MAR and NMAR conditions and outperforms propensity score adjustment. Empirical analysis further reveals that separate regression is preferable when heterogeneity is strong, whereas combined regression offers modest efficiency gains under homogeneity.

This work addresses the lack of explicit confidence modeling for various sources of uncertainty in Bayesian inference by proposing a general extension framework that, for the first time, explicitly incorporates confidence in key uncertainty components—such as the prior and likelihood—into Bayesian modeling. The framework not only introduces a novel regularization mechanism but also provides a unified approach to inducing model sparsity. Without compromising theoretical rigor, the method achieves controllable sparsity across diverse models, including linear regression, logistic regression, and Bayesian neural networks, thereby significantly enhancing both interpretability and generalization performance.