Bayesian Multiperiod Forecasting for Arma Model under Jeffrey's Prior

Reference Prior for ARMA(1,1) Model

Jeffreys ’ prior is asymptotically least favorable under entropy risk

We provide a rigorous proof that Jeffreys’ prior asymptotically maximizes Shannon’s mutual information between a sample of size n and the parameter. This was conjectured by Bernard0 (1979) and, despite the absence of a proof, forms the basis of the reference prior method in Bayesian statistical analysis. Our proof rests on an examination of large sample decision theoretic properties associated ...

Adaptive Sparseness Using Jeffreys Prior

In this paper we introduce a new sparseness inducing prior which does not involve any (hyper)parameters that need to be adjusted or estimated. Although other applications are possible, we focus here on supervised learning problems: regression and classification. Experiments with several publicly available benchmark data sets show that the proposed approach yields state-of-the-art performance. I...

Nonparametric Bayesian Estimation of a Bivariate Copula Using the Jeffreys Prior SIMON GUILLOTTE and FRANÇOIS PERRON

ABSTRACT. A bivariate distribution with continuous margins can be uniquely decomposed via a copula and its marginal distributions. We consider the problem of estimating the copula function and adopt a nonparametric Bayesian approach. On the space of copula functions, we construct a finite dimensional approximation subspace which is parameterized by a doubly stochastic matrix. A major problem he...

Exchangeability Characterizes Optimality of Sequential Normalized Maximum Likelihood and Bayesian Prediction with Jeffreys Prior

We study online prediction of individual sequences under logarithmic loss with parametric constant experts. The optimal strategy, normalized maximum likelihood (NML), is computationally demanding and requires the length of the game to be known. We consider two simpler strategies: sequential normalized maximum likelihood (SNML), which computes the NML forecasts at each round as if it were the la...