Minimax prediction of the difference of sample distribution functions
Minimax state estimation for linear stochastic systems with an uncertain parameter
Misclassified multinomial data: a Bayesian approach.
In this paper, the problem of inference with misclassified multinomial data is addressed. Over the last years there has been a significant upsurge of interest in the development of Bayesian methods to make inferences with misclassified data. The wide range of applications for several sampling schemes and the importance of including initial information make Bayesian analysis an essential tool to be used in this context. A review of the existing literature followed by a methodological discussion is...
Model selection with vague prior information
In the Bayesian approach, the Bayes factor is the main tool for model selection and hypothesis testing. When prior information is weak, "default" or "automatic" priors, which are typicaIly improper, are commonly used but, unfortunately, the Bayes factor is defined up to a multiplicative constant. In this paper we revise some recent but already popular methodologies, intrinsic and lractional, to deal with improper priors in model selection and hypothesis testing. Special attention is paid to the...
Model-free objective Bayesian prediction.
Modeling biased information seeking with second order probability distributions
Updating probabilities by information from only one hypothesis and thereby ignoring alternative hypotheses, is not only biased but leads to progressively imprecise conclusions. In psychology this phenomenon was studied in experiments with the “pseudodiagnosticity task”. In probability logic the phenomenon that additional premises increase the imprecision of a conclusion is known as “degradation”. The present contribution investigates degradation in the context of second order probability distributions....
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 networks using Bayesian training
Bayesian probability theory provides a framework for data modeling. In this framework it is possible to find models that are well-matched to the data, and to use these models to make nearly optimal predictions. In connection to neural networks and especially to neural network learning, the theory is interpreted as an inference of the most probable parameters for the model and the given training data. This article describes an application of Neural Networks using the Bayesian training to the problem...
Neymann-Pearson type test of hypotheses about random parameters
Nonquadratic stabilization of continuous-time systems in the Takagi-Sugeno form
This paper presents a relaxed scheme for controller synthesis of continuous- time systems in the Takagi-Sugeno form, based on non-quadratic Lyapunov functions and a non-PDC control law. The relaxations here provided allow state and input dependence of the membership functions’ derivatives, as well as independence on initial conditions when input constraints are needed. Moreover, the controller synthesis is attainable via linear matrix inequalities, which are efficiently solved by commercially available...
Numerical realization of the Bayesian inversion accelerated using surrogate models
The Bayesian inversion is a natural approach to the solution of inverse problems based on uncertain observed data. The result of such an inverse problem is the posterior distribution of unknown parameters. This paper deals with the numerical realization of the Bayesian inversion focusing on problems governed by computationally expensive forward models such as numerical solutions of partial differential equations. Samples from the posterior distribution are generated using the Markov chain Monte...
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 a family of bayesian estimators and predictors for a Gumbel model based on the kth lower records
Bayesian estimation for the two parameters of a Gumbel distribution are obtained based on kth lower record values. Prediction, either point or interval, for future kth lower record values is also presented from a Bayesian view point. Some of the results of [4] can be obtained as special cases of our results (k=1).
On a famous problem of induction.
A Bayesian solution is provided to the problem of testing whether an entire finite population shows a certain characteristic, given that all the elements of a random sample are observed to have it. This is obtained as a direct application of existing theory and, it is argued, improves upon Jeffrey's solution.
On Bayesian estimation in an exponential distribution under random censorship
The paper gives some basic ideas of both the construction and investigation of the properties of the Bayesian estimates of certain parametric functions of the parent exponential distribution under the model of random censorship assuming the Koziol–Green model. Various prior distributions are investigated and the corresponding estimates are derived. The stress is put on the asymptotic properties of the estimates with the particular stress on the Bayesian risk. Small sample properties are studied...
On Bayesian Optimum Allocation in Some Two Phase Sampling Problems.
On conditional independence and the relationship between sufficiency and invariance under the Bayesian point of view.
On empirical Bayes estimation of multivariate regression coefficient.
On Least Favourable Two Point Priors and Minimax Estimators Under Absolute Error Loss.
On minimax estimation of the parameter in the Pólya urn scheme