Semiparametric inference in mixture models with predictive recursion marginal likelihood

Abstract

Predictive recursion is an accurate and computationally efficient algorithm for nonparametric estimation of mixing densities in mixture models. In semiparametric mixture models, however, the algorithm fails to account for any uncertainty in the additional unknown structural parameter. As an alternative to existing profile likelihood methods, we treat predictive recursion as a filter approximation to fitting a fully Bayes model, whereby an approximate marginal likelihood of the structural parameter emerges and can be used for inference. We call this the predictive recursion marginal likelihood. Convergence properties of predictive recursion under model mis-specification also lead to an attractive construction of this new procedure. We show pointwise convergence of a normalized version of this marginal likelihood function. Simulations compare the performance of this new marginal likelihood approach that of existing profile likelihood methods as well as Dirichlet process mixtures in density estimation. Mixed-effects models and an empirical Bayes multiple testing application in time series analysis are also considered.

References in corpus (6)

• Microarrays, Empirical Bayes and the Two-Groups Model
• Bootstrap consistency for general semiparametric $M$-estimation
• Consistency of a recursive estimate of mixing distributions
• Stochastic Approximation and Newton's Estimate of a Mixing Distribution
• Nonparametric Bayesian multiple testing for longitudinal performance stratification
• Convergence rate for predictive recursion estimation of finite mixtures

Cited by in corpus (12)

• A nonparametric empirical Bayes framework for large-scale multiple testing
• On recursive Bayesian predictive distributions
• A semiparametric scale-mixture regression model and predictive recursion maximum likelihood
• Convergence rate for predictive recursion estimation of finite mixtures
• An approximate Bayesian marginal likelihood approach for estimating finite mixtures
• Permutation-based uncertainty quantification about a mixing distribution
• On nonparametric estimation of a mixing density via the predictive recursion algorithm
• Revisiting consistency of a recursive estimator of mixing distributions
• Estimating a mixing distribution on the sphere using predictive recursion
• Anytime valid and asymptotically optimal inference driven by predictive recursion
• A PRticle filter algorithm for nonparametric estimation of multivariate mixing distributions
• A deconvolution path for mixtures