Search results for "Bay"
showing 10 items of 1187 documents
A New Technique of Invariant Statistical Embedding and Averaging in Terms of Pivots for Improvement of Statistical Decisions Under Parametric Uncerta…
2021
In this chapter, a new technique of invariant embedding of sample statistics in a decision criterion (performance index) and averaging this criterion via pivotal quantities (pivots) is proposed for intelligent constructing efficient (optimal, uniformly non-dominated, unbiased, improved) statistical decisions under parametric uncertainty. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, the technique of invariant statistical embedding and averaging in terms of pivotal quantities (ISE&APQ) is independent of the choice of priors and represents …
Bayesian adaptive estimation: The next dimension
2006
Abstract We propose a new psychometric model for two-dimensional stimuli, such as color differences, based on parameterizing the threshold of a one-dimensional psychometric function as an ellipse. The Ψ Bayesian adaptive estimation method applied to this model yields trials that vary in multiple stimulus dimensions simultaneously. Simulations indicate that this new procedure can be much more efficient than the more conventional procedure of estimating the psychometric function on one-dimensional lines independently, requiring only one-fourth or less the number of trials for equivalent performance in typical situations. In a real psychophysical experiment with a yes–no task, as few as 22 tri…
Stochastic Approach for Optimal Positioning of Pumps As Turbines (PATs)
2021
A generic water system consists of a series of works that allow the collection, conveyance, storage and finally the distribution of water in quantities and qualities such as to satisfy the needs of end users. In places characterized by high altitude differences between the intake works and inhabited centres, the potential energy of the water is very high. This energy is attributable to high pressures, which could compromise the functionality of the pipelines
Reference Priors in a Variance Components Problem
1992
The ordered group reference prior algorithm of Berger and Bernardo (1989b) is applied to the balanced variance components problem. Besides the intrinsic interest of developing good noninformative priors for the variance components problem, a number of theoretically interesting issues arise in application of the proposed procedure. The algorithm is described (for completeness) in an important special case, with a detailed heuristic motivation.
Hydrological post-processing based on approximate Bayesian computation (ABC)
2019
[EN] This study introduces a method to quantify the conditional predictive uncertainty in hydrological post-processing contexts when it is cumbersome to calculate the likelihood (intractable likelihood). Sometimes, it can be difficult to calculate the likelihood itself in hydrological modelling, specially working with complex models or with ungauged catchments. Therefore, we propose the ABC post-processor that exchanges the requirement of calculating the likelihood function by the use of some sufficient summary statistics and synthetic datasets. The aim is to show that the conditional predictive distribution is qualitatively similar produced by the exact predictive (MCMC post-processor) or …
The design of absorbing Bayesian pursuit algorithms and the formal analyses of their ε-optimality
2016
The fundamental phenomenon that has been used to enhance the convergence speed of learning automata (LA) is that of incorporating the running maximum likelihood (ML) estimates of the action reward probabilities into the probability updating rules for selecting the actions. The frontiers of this field have been recently expanded by replacing the ML estimates with their corresponding Bayesian counterparts that incorporate the properties of the conjugate priors. These constitute the Bayesian pursuit algorithm (BPA), and the discretized Bayesian pursuit algorithm. Although these algorithms have been designed and efficiently implemented, and are, arguably, the fastest and most accurate LA report…
Decomposition of Dynamic Single-Product and Multi-product Lotsizing Problems and Scalability of EDAs
2008
In existing theoretical and experimental work, Estimation of Distribution Algorithms (EDAs) are primarily applied to decomposable test problems. State-of-the-art EDAs like the Hierarchical Bayesian Optimization Algorithm (hBOA), the Learning Factorized Distribution Algorithm (LFDA) or Estimation of Bayesian Networks Algorithm (EBNA) solve these problems in polynomial time. Regarding this success, it is tempting to apply EDAs to real-world problems. But up to now, it has rarely been analyzed which real-world problems are decomposable. The main contribution of this chapter is twofold: (1) It shows that uncapacitated single-product and multi-product lotsizing problems are decomposable. (2) A s…
Reference point based multi-objective evolutionary algorithms for group decisions
2008
While in the past decades research on multi-objective evolutionary algorithms (MOEA) has aimed at finding the whole set of Pareto optimal solutions, current approaches focus on only those parts of the Pareto front which satisfy the preferences of the decision maker (DM). Therefore, they integrate the DM early on in the optimization process instead of leaving him/her alone with the final choice of one solution among the whole Pareto optimal set. In this paper, we address an aspect which has been neglected so far in the research on integrating preferences: in most real-world problems, there is not only one DM, but a group of DMs trying to find one consensus decision all participants are wille…
Invariant Embedding Technique and Its Applications for Improvement or Optimization of Statistical Decisions
2010
In the present paper, for improvement or optimization of statistical decisions under parametric uncertainty, a new technique of invariant embedding of sample statistics in a performance index is proposed. This technique represents a simple and computationally attractive statistical method based on the constructive use of the invariance principle in mathematical statistics. Unlike the Bayesian approach, an invariant embedding technique is independent of the choice of priors. It allows one to eliminate unknown parameters from the problem and to find the best invariant decision rule, which has smaller risk than any of the well-known decision rules. To illustrate the proposed technique, applica…
Bayesian model averaging and weighted-average least squares: Equivariance, stability, and numerical issues
2011
In this article, we describe the estimation of linear regression models with uncertainty about the choice of the explanatory variables. We introduce the Stata commands bma and wals, which implement, respectively, the exact Bayesian model-averaging estimator and the weighted-average least-squares estimator developed by Magnus, Powell, and Prüfer (2010, Journal of Econometrics 154: 139–153). Unlike standard pretest estimators that are based on some preliminary diagnostic test, these model-averaging estimators provide a coherent way of making inference on the regression parameters of interest by taking into account the uncertainty due to both the estimation and the model selection steps. Spec…