Search results for " Probability"
showing 10 items of 2176 documents
Geometric characterization and simulation of planar layered elastomeric fibrous biomaterials
2015
An important class of biomaterials is composed of layered networks of elastomeric fibers. While there is a growing interest in modeling and simulation of the mechanical response of these biomaterials, a theoretical foundation for such simulations has yet to be firmly established. The present work addresses this issue in two ways. First, using methods of geometric probability we develop theoretical estimates for the linear and areal fiber intersection densities for two-dimensional fibrous networks. These are expressed in terms of the fiber density and orientation distribution function, both of which are relatively easy to measure properties. Secondly, we develop a random walk algorithm for g…
Statistical prediction of corrosion front penetration
1997
A statistical method to predict the stochastic evolution of corrosion fronts has been developed. The method is based on recording material loss and maximum front depth. In this paper we introduce the method and test its applicability. In the absence of experimental data we use simulation data from a three-dimensional corrosion model for this test. The corrosion model simulates localized breakdown of a protective oxide layer, hydrolysis of corrosion product and repassivation of the exposed surface. In the long time limit of the model, pits tend to coalesce. For different model parameters the model reproduces corrosion patterns observed in experiment. The statistical prediction method is base…
Bayesian estimation of edge orientations in junctions
1999
Abstract Junctions, defined as those points of an image where two or more edges meet, play a significant role in many computer vision applications. Junction detection is a widely treated problem, and some detectors can provide even the directions of the edges that meet in a junction. The main objective of this paper is the precise estimation of such directions. It is supposed that the junction point has been previously found by some detector. Also, it is assumed that samples, possibly noisy, of orientations of the edges found in a circular window surrounding the point are available. A mixture of von Mises distributions is assumed for these data, and then a Bayesian methodology is applied to…
Inventory Control Under Parametric Uncertainty of Underlying Models
2013
A large number of problems in inventory control, production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty of underlying models. In the present paper we consider the case, where it is known that the underlying distribution belongs to a parametric family of distributions. The problem of determining an optimal decision rule in the absence of complete information about the underlying distribution, i.e., when we specify only the functional form of the distribution and leave some or all of its parameters unspecified, is seen to be a standard problem of statistical estimation. Unfortunately, the clas…
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 …
Generalized Multitarget Linear Regression with Output Dependence Estimation
2019
Multitarget regression has recently received attention in the context of modern, large-scale problems in which finding good enough solutions in a timely manner is crucial. Different proposed alternatives use a combination of regularizers that lead to different ways of solving the problem. In this work, we introduce a general formulation with several regularizers. This leads to a biconvex minimization problem and we use an alternating procedure with accelerated proximal gradient steps to solve it. We show that our formulation is equivalent but more efficient than some previously proposed approaches. Moreover, we introduce two new variants. The experimental validation carried out, suggests th…
A new strategy for effective learning in population Monte Carlo sampling
2016
In this work, we focus on advancing the theory and practice of a class of Monte Carlo methods, population Monte Carlo (PMC) sampling, for dealing with inference problems with static parameters. We devise a new method for efficient adaptive learning from past samples and weights to construct improved proposal functions. It is based on assuming that, at each iteration, there is an intermediate target and that this target is gradually getting closer to the true one. Computer simulations show and confirm the improvement of the proposed strategy compared to the traditional PMC method on a simple considered scenario.
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…
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.
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…