Abstract. This paper clarifies the generalization errors of Bayes and Gibbs estimations in non-identifiable statistical models based on algebraic geometry and empirical process theory. First, the concrete results are proven for statistical models with normal crossing singularities. Second, they are generalized for all models by using Hironaka’s desingularization theorem. The Bayes generalizatio...

The hierarchical normal-normal model considered. Standard Empirical Bayes methods underestimate variability because they ignore uncertainty about the hyperparameters. Bayes' theorem solves this problem. We provide fast, exact inference that requires only a simple, univariate numerical integration to obtain the posterior distribution of the means. However, when standard, scale-invariant, vague p...

The paper proposes to combine stochastic frontier models and linear programming methods by using DEA measures as priors of efficiency in the stochastic frontier model. These prior measures are revised to obtain posterior measures using Bayes theorem. Monte Carlo methods are developed to perform empirical Bayes inference in the new model. The methods are organized around Gibbs sampling with data...

Let Γ = (V,E) be a reflexive relation having a transitive group of automorphisms and let v ∈ V. Let F be a subset of V with F ∩Γ−(v) = {v}. (i) If F is finite, then |Γ(F ) \ F | ≥ |Γ(v)| − 1. (ii) If F is cofinite, then |Γ(F ) \ F | ≥ |Γ−(v)| − 1. In particular, let G be group, B be a finite subset of G and let F be a finite or a cofinite subset of G such that F ∩ B = {1}. Then |(FB) \ F | ≥ |B...

OBJECTIVES China has experienced a sharply increasing rate of human brucellosis in recent years. Effective spatial monitoring of human brucellosis incidence is very important for successful implementation of control and prevention programmes. The purpose of this paper is to apply exploratory spatial data analysis (ESDA) methods and the empirical Bayes (EB) smoothing technique to monitor county-...

Studies involving the use of probabilistic record linkage are becoming increasingly common. However, the methods underpinning probabilistic record linkage are not widely taught or understood, and therefore these studies can appear to be a 'black box' research tool. In this article, we aim to describe the process of probabilistic record linkage through a simple exemplar. We first introduce the c...

Using computer simulations, we investigate the time evolution of the (Boltzmann) entropy of a dense fluid not in local equilibrium. The macrovariables M describing the system are the (empirical) particle density f=[f(x,v)] and the total energy E. We find that S(f(t),E) is a monotone increasing in time even when its kinetic part is decreasing. We argue that for isolated Hamiltonian systems monot...

We prove a version of the quantum de Finetti theorem: permutation-invariant quantum states are well approximated as a probabilistic mixture of multifold product states. The approximation is measured by distinguishability under measurements that are implementable by fully-one-way local operations and classical communication (LOCC). Our result strengthens Brandão and Harrow's de Finetti theorem w...