Minimax prediction of the difference of sample distribution functions
Modelos para la asignación de tratamiento.
In this paper the problem of treatment allocation is studied from the predictive decision theoretical point of view. The utility of obtaining some final characteristics y when a treatment a is applied to a person with initial facet x is assumed to be known. The problem is then reduced to the derivation of the expected utility of a given x, by means of either prognostic or diagnostic distributions.To find prognostic distributions, regression models and appropriate partitions of the population, according...
Monotonicity of Bayes estimators
Let X=(X₁,..., Xₙ) be a sample from a distribution with density f(x;θ), θ ∈ Θ ⊂ ℝ. In this article the Bayesian estimation of the parameter θ is considered. We examine whether the Bayes estimators of θ are pointwise ordered when the prior distributions are partially ordered. Various cases of loss function are studied. A lower bound for the survival function of the normal distribution is obtained.
Neural network realizations of Bayes decision rules for exponentially distributed data
For general Bayes decision rules there are considered perceptron approximations based on sufficient statistics inputs. A particular attention is paid to Bayes discrimination and classification. In the case of exponentially distributed data with known model it is shown that a perceptron with one hidden layer is sufficient and the learning is restricted to synaptic weights of the output neuron. If only the dimension of the exponential model is known, then the number of hidden layers will increase...
Neymann-Pearson type test of hypotheses about random parameters
Node assignment problem in Bayesian networks
This paper deals with the problem of searching for the best assignments of random variables to nodes in a Bayesian network (BN) with a given topology. Likelihood functions for the studied BNs are formulated, methods for their maximization are described and, finally, the results of a study concerning the reliability of revealing BNs' roles are reported. The results of BN node assignments can be applied to problems of the analysis of gene expression profiles.
Objective Bayesian point and region estimation in location-scale models.
Point and region estimation may both be described as specific decision problems. In point estimation, the action space is the set of possible values of the quantity on interest; in region estimation, the action space is the set of its possible credible regions. Foundations dictate that the solution to these decision problems must depend on both the utility function and the prior distribution. Estimators intended for general use should surely be invariant under one-to-one transformations, and this...
On generalized entropies, Bayesian decisions and statistical diversity
On maximum entropy priors and a most likely likelihood in auditing.
There are two basic questions auditors and accountants must consider when developing test and estimation applications using Bayes' Theorem: What prior probability function should be used and what likelihood function should be used. In this paper we propose to use a maximum entropy prior probability function MEP with the most likely likelihood function MLL in the Quasi-Bayesian QB model introduced by McCray (1984). It is defined on an adequate parameter. Thus procedure only needs an expected value...
On minimax estimation of the parameter in the Pólya urn scheme
On optimal credibility premiums in multiperiod insurance
This paper focuses on the problem of optimal arrangement of a stream of premiums in a multiperiod credibility model. On the basis of a given claim history (screening) and some individual information unknown to the insurance company (signaling), we derive the optimal streams in the case when the coverage period is not necessarily fixed, e.g., because of lapses, renewals, deaths, total losses, etc.
On perturbations of strongly admissible prior distributions
On the experience utilization in statistical decisions
On the foundations of statistics and decision theory.
An elementary axiomatic foundation for decision theory is presented at a general enough level to cover standard applications of Bayesian methods. The intuitive meaning of both axioms and results is stressed. It is argued that statistical inference is a particular decision problem to which the axiomatic argument fully applies.
On the Natural Selection Rule in General Linear Models.
On the optimum sequential test of two hypotheses for statistically dependent observations
Optimal alternative robustness in Bayesian Decision Theory.
In Martin et al (2003), we suggested an approach to general robustness studies in Bayesian Decision Theory and Inference, based on ε-contamination neighborhoods. In this note, we generalise the results considering neighborhoods based on norms, specifically, the supremum norm for utilities and the total variation norm for probability distributions. We provide tools to detect changes in preferences between alternatives under perturbations of the prior and/or the utility and the most sensitive direction....
Optimal Regression Designs for Prediction when Prior Knowledge is Available.
Optimal sequential multiple hypothesis tests
This work deals with a general problem of testing multiple hypotheses about the distribution of a discrete-time stochastic process. Both the Bayesian and the conditional settings are considered. The structure of optimal sequential tests is characterized.
Optimal sequential procedures with Bayes decision rules
In this article, a general problem of sequential statistical inference for general discrete-time stochastic processes is considered. The problem is to minimize an average sample number given that Bayesian risk due to incorrect decision does not exceed some given bound. We characterize the form of optimal sequential stopping rules in this problem. In particular, we have a characterization of the form of optimal sequential decision procedures when the Bayesian risk includes both the loss due to incorrect...