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The use of Bayes factors for model selection in structural reliability
 In: Proc. of 8th Int. Conf. on Structural Safety and Reliability (ICOSSAR). June 2001
, 2001
"... ABSTRACT: Probabilistic design of structures is usually based on estimates of a design load with a high average return period. Design loads are often estimated using classical statistical methods. A shortcoming of this approach is that statistical uncertainties are not taken into account. In this pa ..."
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ABSTRACT: Probabilistic design of structures is usually based on estimates of a design load with a high average return period. Design loads are often estimated using classical statistical methods. A shortcoming of this approach is that statistical uncertainties are not taken into account. In this paper, a method based on Bayesian statistics is presented. Using Bayes ’ theorem, the prior distribution representing information about the uncertainty of the statistical parameters can be updated to the posterior distribution as soon as data becomes available. Seven predictive probability distributions are considered for determining extreme quantiles of loads: the exponential, Rayleigh, normal, lognormal, gamma, Weibull and Gumbel. The Bayesian method has been successfully applied to estimate the design discharge of the river Rhine while taking account of the statistical uncertainties involved. As a prior the noninformative Jeffreys prior was chosen. The Bayes estimates are compared to the classical maximumlikelihood estimates. Furthermore, socalled Bayes factors are used to determine weights corresponding to how well a probability distribution fits the observed data; that is, the better the fit, the higher the weighting. 1
Empirical evaluation of a prior for Bayesian phylogenetic inference
"... The Bayesian method of phylogenetic inference often produces high posterior probabilities (PPs) for trees or clades, even when the trees are clearly incorrect. The problem appears to be mainly due to large sizes of molecular datasets and to the largesample properties of Bayesian model selection and ..."
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The Bayesian method of phylogenetic inference often produces high posterior probabilities (PPs) for trees or clades, even when the trees are clearly incorrect. The problem appears to be mainly due to large sizes of molecular datasets and to the largesample properties of Bayesian model selection and its sensitivity to the prior when several of the models under comparison are nearly equally correct (or nearly equally wrong) and are of the same dimension. A previous suggestion to alleviate the problem is to let the internal branch lengths in the tree become increasingly small in the prior with the increase in the data size so that the bifurcating trees are increasingly starlike. In particular, if the internal branch pffiffiffi lengths are assigned the exponential prior, the prior mean m0 should approach zero faster than 1 = n but more slowly than 1/n, where n is the sequence length. This paper examines the usefulness of this data sizedependent prior using a dataset of the mitochondrial proteincoding genes from the baleen whales, with the prior mean fixed at m0Z0.1n K2/3. In this dataset, phylogeny reconstruction is sensitive to the assumed evolutionary model, species sampling and the type of data (DNA or protein sequences), but Bayesian inference using the default prior attaches high PPs for conflicting phylogenetic relationships. The data sizedependent prior alleviates the problem to some extent, giving weaker support for unstable relationships. This prior may be useful in reducing apparent conflicts in the results of Bayesian analysis or in making the method less sensitive to model violations.
Bayes estimates of flood quantiles using the generalised gamma distribution
 System and Bayesian Reliability; Essays in Honor of Professor Richard E. Barlow on His 70th Birthday
, 2001
"... In this paper, a Bayesian approach is proposed to estimate flood quantiles while taking statistical uncertainties into account. Predictive exceedance probabilities of annual maximum discharges are obtained using the three and fourparameter generalised gamma distribution (without and with location p ..."
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Cited by 1 (1 self)
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In this paper, a Bayesian approach is proposed to estimate flood quantiles while taking statistical uncertainties into account. Predictive exceedance probabilities of annual maximum discharges are obtained using the three and fourparameter generalised gamma distribution (without and with location parameter respectively). The parameters of this distribution are assumed to be random quantities rather than deterministic quantities and to have a prior joint probability distribution. On the basis of observations, this prior joint distribution is then updated to the posterior joint distribution by using Bayes ’ theorem. An advantage is that the generalised gamma distribution fits well with the stagedischarge rating curve being an approximate power law between water level and discharge. Furthermore, since the generalised gamma distribution has three or four parameters, it is flexible in fitting data. Many wellknown probability distributions which are commonly used to estimate quantiles of hydrological random quantities are special cases of the generalised gamma distribution. As an example, a Bayesian analysis of annual maximum discharges of the Rhine River at Lobith is performed to determine flood quantiles including their uncertainty intervals. The generalised gamma distribution can also be applied in lifetime and reliability analysis. Keywords Bayesian analysis; generalised gamma distribution; flood quantiles;
Ministry of Transport, Public Works, and Water Management,
"... eights. 1 Introduction Probabilistic design of river dikes is usually based on estimates of the design discharge. In The Netherlands, the design discharge is defined as an extreme discharge with an average return period of 1,250 years. Extreme quantiles, such as the design discharge are usually det ..."
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eights. 1 Introduction Probabilistic design of river dikes is usually based on estimates of the design discharge. In The Netherlands, the design discharge is defined as an extreme discharge with an average return period of 1,250 years. Extreme quantiles, such as the design discharge are usually determined by fitting various probability distributions to the available observations. [See for example DH & EACRAND (1993), Castillo (1988), and Van Gelder (1999)]. Probability plots and goodnessoffit tests (such as chisquare and KolmogorovSmirnov) are commonly used to select an appropriate distribution. A major practical difficulty in fitting probability distributions is that there is often a limited amount of data for determining extreme quantiles. The associated return period is large compared with the length of the period of observation. In The Netherlands, observed flood discharges are available for a period of 98 years only. There is a large statistical uncertainty involved in estim
Specification of prior distributions under model uncertainty
, 2008
"... We consider the specification of prior distributions for Bayesian model comparison, focusing on regressiontype models. We propose a particular joint specification of the prior distribution across models so that sensitivity of posterior model probabilities to the dispersion of prior distributions fo ..."
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We consider the specification of prior distributions for Bayesian model comparison, focusing on regressiontype models. We propose a particular joint specification of the prior distribution across models so that sensitivity of posterior model probabilities to the dispersion of prior distributions for the parameters of individual models (Lindley’s paradox) is diminished. We illustrate the behavior of inferential and predictive posterior quantities in linear and loglinear regressions under our proposed prior densities with a series of simulated and real data examples.
Bayesian estimation of design loads
"... Probabilistic design of structures is usually based on estimates of design loads with a large average return period. Design loads are often estimated using classical statistical methods. A shortcoming of this approach is that statistical uncertainties are not taken into account. In this paper, a met ..."
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Probabilistic design of structures is usually based on estimates of design loads with a large average return period. Design loads are often estimated using classical statistical methods. A shortcoming of this approach is that statistical uncertainties are not taken into account. In this paper, a method based on Bayesian statistics is presented. Using Bayes ’ theorem, the prior distribution representing information about the uncertainty of the statistical parameters can be updated to the posterior distribution as soon as data becomes available. Nine predictive probability distributions are considered for determining extreme quantiles of loads: the exponential, Rayleigh, normal, lognormal, gamma, Weibull, Gumbel, generalised gamma and generalised extremevalue. The Bayesian method has been successfully applied to estimate the discharge of the rivers Rhine and Meuse with an average return period of 1,250 years while taking account of the statistical uncertainties involved. In order that the observations ‘speak for themselves’, the noninformative Jeffreys priors were chosen as priors. The Bayes estimates are compared to the classical maximumlikelihood estimates. Furthermore, socalled Bayes factors are used to determine weights corresponding to how well a probability distribution fits the observed data; that is, the better the fit, the higher the weighting.