On Quantifying Expert Opinion about Multinomial Models that Contain Covariates

Elfadaly, Fadlalla G.; Garthwaite, Paul H.

doi:10.1111/rssa.12546

Cited by 5 publications

(7 citation statements)

References 23 publications

(24 reference statements)

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“…The focus is the task of eliciting a prior distribution for a multinomial logistic regression model, in which there are more than two categories and a generalised linear regression model that links covariates to the membership probabilities. Elfadaly and Garthwaite (2019) develop a new elicitation method for this task that quantifies opinion as a multivariate normal prior distribution on the regression coefficients. They first address the simpler case where there are no covariates and represent opinion as a logistic normal distribution.…”

Section: Eliciting Prior Distributions For Multinomial Models That Co...mentioning

confidence: 99%

“…The benefit of the logistic normal distribution is that it can be extended in a natural way to form a prior distribution that is appropriate for a multinomial logistic regression model. Moreover, the elicitation method that yields the parameters of a logistic normal distribution can be expanded to elicit the parameters of the corresponding multivariate normal prior distribution (Elfadaly and Garthwaite, 2019). The elicitation method is implemented in interactive software that is freely available on the web at http://statistics.open.ac.uk/elicitation.…”

Section: Eliciting Prior Distributions For Multinomial Models That Co...mentioning

confidence: 99%

“…(ii) On a bar-chart similar to that in Figure 9, the expert assesses the lower (upper) quartiles, L * 2 (U * 2 ) for the probability ratio r 2 . This gives the variance of Y 2 as (Elfadaly and Garthwaite, 2019)…”

Section: Eliciting Priors For Multinomial Models Without Covariatesmentioning

confidence: 99%

“…. , k. These conditional quartile assessments are used to encode the conditional variances (Elfadaly and Garthwaite, 2019)…”

Section: Eliciting Priors For Multinomial Models Without Covariatesmentioning

confidence: 99%

See 3 more Smart Citations

Recent Advances in the Elicitation of Uncertainty Distributions from Experts for Multinomial Probabilities

Wilson

Elfadaly

Garthwaite

et al. 2021

International Series in Operations Research &Amp; Management Science

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In this chapter we consider the problem of the elicitaton and specification of an uncertainty distribution based on expert judgements, which may be a subjective prior distribution in a Bayesian analysis, for a set of probabilities which are constrained to sum to one. A typical context for this is as a prior distribution for the probabilities in a multinomial model. The Dirichlet distribution has long been advocated as a natural way to represent the uncertainty distribution over the probabilities in this context. The relatively small number of parameters allow for specification based on relatively few elicited quantities but at the expense of a very restrictive structure. We detail recent advances in elicitation for the Dirichlet distribution and recently proposed alternative approaches, which offer greater flexibility at the expense of added complexity. In order of increasing flexibility, they are the generalised Dirichlet distribution, multivariate copulas and vines. An extension to multinomial models containing covariates is discussed.

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Section: Eliciting Prior Distributions For Multinomial Models That Co...mentioning

confidence: 99%

Section: Eliciting Prior Distributions For Multinomial Models That Co...mentioning

confidence: 99%

Section: Eliciting Priors For Multinomial Models Without Covariatesmentioning

confidence: 99%

“…. , k. These conditional quartile assessments are used to encode the conditional variances (Elfadaly and Garthwaite, 2019)…”

Section: Eliciting Priors For Multinomial Models Without Covariatesmentioning

confidence: 99%

See 2 more Smart Citations

Recent Advances in the Elicitation of Uncertainty Distributions from Experts for Multinomial Probabilities

Wilson

Elfadaly

Garthwaite

et al. 2021

International Series in Operations Research &Amp; Management Science

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“…The operation mechanism of container liners is very similar to above research objects, which greatly inspires us. Therefore, we performed a specialized analysis and statistical verification (Elfadaly & Garthwaite, 2020) on the deviation law of container liner ships to explore its regularity.…”

Section: Introductionmentioning

confidence: 99%

On Probability Distributions of the Time Deviation Law of Container Liner Ships Under Interference Uncertainty

Song

Wang

2020

Journal of the Royal Statistical Society Series A: Statistics in Society

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Container liner shipping is a kind of transportation mode that is operated according to a schedule. Although the goal is to operate container liner ships on time, the actual arrival time and handling time often deviate from the schedule due to uncertain factors. The identification of a proper probability distribution to describe time deviation law will have a significant impact on accurately recognizing the uncertainty of the operation of container liner ships. In view of this problem, this paper discusses the basic characteristics of container liner ships’ operation time, analyses the properties of relevant probability distributions, and selects representative container ports around the world to collect data on the container liner ships’ operation time for statistical verification. The results show that under schedule constraints and interference uncertainty, the time deviation presents a specific state between a fixed length and random distribution that conforms to the properties of an Erlang distribution. Given that container liner shipping follows the same operation rules worldwide, it is reasonable to deduce that the time deviation law could be generalized to other container ports. Finally, the practical value of this study is demonstrated through quantitative evaluation of port congestion degree under various probabilistic models.

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Elicitation of Priors

Garthwaite¹,

Elfadaly²

2021

Wiley StatsRef: Statistics Reference Online

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Prior distributions provide a formal mechanism for including an expert's background knowledge in a statistical analysis. To exploit this knowledge, the expert is questioned through carefully chosen assessment tasks, and answers are encoded in a prior distribution that hopefully captures the main features of the expert's opinion. The procedure that does this is called an elicitation method . This article gives an overview of elicitation methods, paying particular attention to assessment tasks and the sampling models that have attracted most attention.

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On Quantifying Expert Opinion about Multinomial Models that Contain Covariates

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Cited by 5 publications

References 23 publications

Recent Advances in the Elicitation of Uncertainty Distributions from Experts for Multinomial Probabilities

Recent Advances in the Elicitation of Uncertainty Distributions from Experts for Multinomial Probabilities

On Probability Distributions of the Time Deviation Law of Container Liner Ships Under Interference Uncertainty

Elicitation of Priors

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