2,320 research outputs found
Reference prior for Bayesian estimation of seismic fragility curves
One of the crucial quantities of probabilistic seismic risk assessment
studies is the fragility curve, which represents the probability of failure of
a mechanical structure conditional to a scalar measure derived from the seismic
ground motion. Estimating such curves is a difficult task because for most
structures of interest, few data are available, whether they come from complex
numerical simulations or experimental campaigns. For this reason, a wide range
of the methods of the literature rely on a parametric log-normal model.
Bayesian approaches allow for efficient learning of the model parameters.
However, for small data set sizes, the choice of the prior distribution has a
non-negligible influence on the posterior distribution, and therefore on any
resulting estimate. We propose a thorough study of this parametric Bayesian
estimation problem when the data are binary (i.e. data indicate the state of
the structure, failure or non-failure). Using the reference prior theory as a
support, we suggest an objective approach for the prior choice to simulate a
posteriori fragility curves. This approach leads to the Jeffreys prior and we
prove that this prior depends only of the ground motion characteristics, making
its calculation suitable for any equipment in an industrial installation
subjected to the same seismic hazard. Our proposal is theoretically and
numerically compared to those classically proposed in the literature by
considering three different case studies. The results show the robustness and
advantages of the Jeffreys prior in terms of regularization (no degenerate
estimations) and stability (no outliers of the parameters) for fragility curves
estimation
Reference Priors For Non-Normal Two-Sample Problems
The reference prior algorithm (Berger and Bernardo, 1992) is applied to locationscale models with any regular sampling density. A number of two-sample problems is analyzed in this general context, extending the dierence, ratio and product of Normal means problems outside Normality, while explicitly considering possibly dierent sizes for each sample. Since the reference prior turns out to be improper in all cases, we examine existence of the resulting posterior distribution and its moments under sampling from scale mixtures of Normals. In the context of an empirical example, it is shown that a reference posterior analysis is numerically feasible and can display some sensitivity to the actual sampling distributions. This illustrates the practical importance of questioning the Normality assumption.Behrens-Fisher problem;Fieller-Creasy problem;Gibbs sampling;Jeffreys' prior;location-scale model;posterior existence;product of means;scale mixtures of normals;skewness
Fuzzy sets in nonparametric Bayes regression
A simple Bayesian approach to nonparametric regression is described using
fuzzy sets and membership functions. Membership functions are interpreted as
likelihood functions for the unknown regression function, so that with the help
of a reference prior they can be transformed to prior density functions. The
unknown regression function is decomposed into wavelets and a hierarchical
Bayesian approach is employed for making inferences on the resulting wavelet
coefficients.Comment: Published in at http://dx.doi.org/10.1214/074921708000000084 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
A Comparison of Empirical Bayes and Reference Prior Methods for Spatio-Temporal Data Analysis
AbstractIn Bayesian analysis of spatio-temporal data, the problem of selecting prior distribution for model parameters is of great demand. This paper considers two most popular approaches, empirical Bayes and reference prior, for Bayesian inference. We then use simulation to compare the frequentist properties of these two methods. Since, posterior propriety of the reference prior is only established under separable correlation models, this comparison is concentrated on this case
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