Simultaneous prediction of independent Poisson observables

独立泊松观测量的近极小极大经验贝叶斯预测

Nearly minimax empirical Bayesian prediction of independent Poisson observables

本研究提出一类经验贝叶斯预测分布，用于独立泊松观测量，在K-L损失下优于Jeffreys先验贝叶斯预测，且风险小于极小极大下界的1.04倍。

Simultaneous prediction for independent Poisson processes with different durations

Simultaneous predictive densities for independent Poisson observables are investigated. The observed data and the target variables to be predicted are independently distributed according to different Poisson distributions parametrized by the same parameter. The performance of predictive densities is evaluated by the Kullback-Leibler divergence. A class of prior distributions depending on the objective of prediction is introduced. A Bayesian predictive density based on a prior in this class dominates the Bayesian predictive density based on the Jeffreys prior.

在库尔贝克-莱布勒损失下独立泊松过程的改进近极小极大预测

Improved nearly minimax prediction for independent Poisson processes under Kullback-Leibler loss

研究独立泊松过程预测分布，基于先验超调和性改进贝叶斯预测分布，给出充分条件及满足条件的例子，如点和子空间收缩先验，证明改进预测的K-L风险小于极小极大下界的1.04倍。

Compound Poisson Processes, Latent Shrinkage Priors and Bayesian Nonconvex Penalization

In this paper we discuss Bayesian nonconvex penalization for sparse learning problems. We explore a nonparametric formulation for latent shrinkage parameters using subordinators which are one-dimensional Lévy processes. We particularly study a family of continuous compound Poisson subordinators and a family of discrete compound Poisson subordinators. We exemplify four specific subordinators: Gamma, Poisson, negative binomial and squared Bessel subordinators. The Laplace exponents of the subordinators are Bernstein functions, so they can be used as sparsity-inducing nonconvex penalty functions.…

Bayesian Poisson Log-normal Model with Regularized Time Structure for Mortality Projection of Multi-population

The improvement of mortality projection is a pivotal topic in the diverse branches related to insurance, demography, and public policy. Motivated by the thread of Lee-Carter related models, we propose a Bayesian model to estimate and predict mortality rates for multi-population. This new model features in information borrowing among populations and properly reflecting variations of data. It also provides a solution to a long-time overlooked problem: model selection for dependence structures of population-specific time parameters. By introducing a Dirac spike function, simultaneous model select…