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Consider a parametric statistical model, P (dx|θ), and an improper prior distribution, ν(dθ), that together yield a (proper) formal posterior distribution, Q(dθ|x). The prior is called strongly admissible if the generalized Bayes estimator of every bounded function of θ is admissible under squared error loss. Eaton [5] used the Blyth-Stein Lemma to develop… (More)

Consider the problem of estimating a parametric function when the loss is quadratic. Given an improper prior distribution, there is a formal Bayes estimator for the parametric function. Associated with the estimation problem and the improper prior is a symmetric Markov chain. It is shown that if the Markov chain is recurrent, then the formal Bayes estimator… (More)

- Lawrence D. Brown, Morris L. Eaton, +4 authors Martin T. Wells
- 1999

This paper is a discussion of Census 2000, focusing on planned use of sampling techniques for adjustment. Past experience with similar adjustment methods suggests that the design for Census 2000 is quite risky. Adjustment was the focus of litigation in the census of 1980 and 1990. The planned use of sampling to obtain population counts for apportionment was… (More)

We consider evaluation of proper posterior distributions obtained from improper prior distributions. Our context is estimating a bounded function φ of a parameter when the loss is quadratic. If the posterior mean of φ is admissible for all bounded φ the posterior is strongly admissible. In this paper, we present sufficient conditions for strong… (More)

Abstract: In this expository paper we describe a relatively elementary method of establishing the existence of a Dutch book in a simple multivariate normal prediction setting. The method involves deriving a nonstandard predictive distribution that is motivated by invariance. This predictive distribution satisfies an interesting identity which in turn yields… (More)

Let X rv Np(O, E), the p-variate normal distribution with mean °and positive definite covariance matrix .E. Anderson (1955) showed that if .E2 .E1 is positive semidefinite then PEl (C) 2: P E2(C) for every centrally symmetric (-C = convex set C ~ RP. Fefferman, Jodeit, and Perlman (1972) extended this result to elliptically contoured distributions. In the… (More)

- Morris L. Eaton
- Genetic testing
- 1999

Genetic tests are commercially available for the purpose of aiding in the differential diagnosis of Alzheimer disease among patients with dementia. Such patients often lack the mental capacity to consent to or reject such testing. If genetic testing is to be undertaken, it is important legally and ethically to consider who should participate in the decision… (More)

- James M. Dickey, Morris L. Eaton, William D. Sudderth
- Notre Dame Journal of Formal Logic
- 2009

The logical consistency of a collection of assertions about events can be viewed as a special case of coherent probability assessments in the sense of de Finetti.

- Morris L. Eaton
- 2005

In a simple multivariate normal prediction setting, derivation of a predictive distribution can flow from formal Bayes arguments as well as pivoting arguments. We look at two special cases and show that the classical invariant predictive distribution is based on a pivot that does not have a parameter free distribution – that is, is not an ancillary… (More)

This paper is motivated by the following observation. Take a 3 × 3 random (Haar distributed) orthogonal matrix Γ, and use it to “rotate” the north pole, x0 say, on the unit sphere in R . This then gives a point u = Γx0 that is uniformly distributed on the unit sphere. Now use the same orthogonal matrix to transform u, giving v = Γu = Γx0. Simulations… (More)