A Simple Predictive Density Function

Lejeune, Michel; Faulkenberry, G. David

doi:10.2307/2287730

Cited by 23 publications

(15 citation statements)

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“…Foremost in this work is the problem that it does not take into account the parameter variability for each of the maximizations of the joint likelihood function required (Bjornstad, 1990, Lindsey, 1996. Lejeune & Faulkenberry (1982) propose a similar predictive likelihood, but include a normalizing function.…”

Section: Predictive Likelihoodmentioning

confidence: 99%

A review of probabilistic methods of assessment of load effects in bridges

O’Brien

Schmidt²,

Hajializadeh

et al. 2015

Structural Safety

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This paper reviews a range of statistical approaches to illustrate the influence of data quality and quantity on the probabilistic modelling of traffic load effects. It also aims to demonstrate the importance of long-run simulations in calculating characteristic traffic load effects. The popular methods of Peaks Over Threshold and Generalized Extreme Value are considered but also other methods including the Box-Cox approach, fitting to a Normal distribution and the Rice formula. For these five methods, curves are fitted to the tails of the daily maximum data.Bayesian Updating and Predictive Likelihood are also assessed, which require the entire data for fittings. The accuracy of each method in calculating 75-year characteristic values and probability of failure, using different quantities of data, is assessed. The nature of the problem is first introduced by a simple numerical example with a known theoretical answer. It is then extended to more realistic problems, where long-run simulations are used to provide benchmark results, against which each method is compared. Increasing the number of data in the sample results in higher accuracy of approximations but it is not able to completely eliminate the uncertainty associated with the extrapolation. Results also show that the accuracy of estimations of characteristic value and probabilities of failure are more a function of data quality than extrapolation technique. This highlights the importance of long-run simulations as a means of reducing the errors associated with the extrapolation process.

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Section: Predictive Likelihoodmentioning

confidence: 99%

A review of probabilistic methods of assessment of load effects in bridges

O’Brien

Schmidt²,

Hajializadeh

et al. 2015

Structural Safety

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show abstract

“…This pseudo prediction density does not reflect the uncertainty in parameter estimates. A "large sample" maximum likelihood prediction density (MLPD) for z = log(d), as proposed by Lejeune and Faulkenberry (1982) is…”

Section: Prediction Density For Future Outcomesmentioning

confidence: 99%

Statistical Analysis of Data with Non-Detectable Values

Frome¹

2004

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“…As already mentioned in the introduction, one naive but simple way to make predictions is to consider the pro®le predictive likelihood (Fisher, 1959, pp. 128±33, Lejeune andFaulkenberry, 1982):…”

Section: Likelihood Prediction Envelopesmentioning

confidence: 99%

“…Similarly, p% likelihood prediction interval could be de®ned as fz X LzaL z b p%g The classical likelihood extension in this context is based on the relative likelihood described in Fisher (1959, pp. 128±33) and in Lejeune and Faulkenberry (1982). It consists of two parts: the ®rst is the contribution to the likelihood made by the observed data, as provided, for example, by the GARM; the second is related to the observation to come.…”

Section: Introductionmentioning

confidence: 99%

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Predictions in Overdispersed Series of Counts Using an Approximate Predictive Likelihood

Lambert

1997

J. Forecast.

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The generalized autoregression model or GARM, originally used to model series of non-negative data measured at irregularly spaced time points (Lambert, 1996a), is considered in a count data context. It is ®rst shown how the GARM can be expressed as a GLM in the special case of a linear model for some transform of the location parameter. The Butler approximate predictive likelihood (Butler, 1986, Rejoinder) is then used to de®ne likelihood prediction envelopes. The width of these intervals is shown to be slightly wider than the Fisher (1959, pp. 128±33) and Lejeune and Faulkenberry (1982) predictive likelihood-based envelopes which assume that the parameters have ®xed known values (equal to their maximum likelihood estimates). The method is illustrated on a small count data set showing overdispersion. # 1997 by John Wiley and Sons, Ltd.

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A Simple Predictive Density Function

Cited by 23 publications

References 0 publications

A review of probabilistic methods of assessment of load effects in bridges

A review of probabilistic methods of assessment of load effects in bridges

Statistical Analysis of Data with Non-Detectable Values

Predictions in Overdispersed Series of Counts Using an Approximate Predictive Likelihood

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