Objective priors for the number of degrees of freedom of a multivariate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml352" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>t</mml:mi></mml:math> distribution and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml353" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>t</mml:mi></mml:math>-copula

Villa, Cristiano; Rubio, Francisco J.

doi:10.1016/j.csda.2018.03.010

Cited by 19 publications

(10 citation statements)

References 36 publications

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“…Obviously, alternative priors can be considered. As has been observed elsewhere, objective priors for discrete parameters are starting to be considered both in the univariate scenario [15] and in the multivariate case [16]. This constitutes an interesting line of research for future investigation.…”

Section: Discussionmentioning

confidence: 85%

Bayesian Inference in Auditing with Partial Prior Information Using Maximum Entropy Priors

Martel–Escobar

Polo

Hernández-Bastida

2018

Entropy

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Problems in statistical auditing are usually one–sided. In fact, the main interest for auditors is to determine the quantiles of the total amount of error, and then to compare these quantiles with a given materiality fixed by the auditor, so that the accounting statement can be accepted or rejected. Dollar unit sampling (DUS) is a useful procedure to collect sample information, whereby items are chosen with a probability proportional to book amounts and in which the relevant error amount distribution is the distribution of the taints weighted by the book value. The likelihood induced by DUS refers to a 201–variate parameter p but the prior information is in a subparameter θ linear function of p , representing the total amount of error. This means that partial prior information must be processed. In this paper, two main proposals are made: (1) to modify the likelihood, to make it compatible with prior information and thus obtain a Bayesian analysis for hypotheses to be tested; (2) to use a maximum entropy prior to incorporate limited auditor information. To achieve these goals, we obtain a modified likelihood function inspired by the induced likelihood described by Zehna (1966) and then adapt the Bayes’ theorem to this likelihood in order to derive a posterior distribution for θ . This approach shows that the DUS methodology can be justified as a natural method of processing partial prior information in auditing and that a Bayesian analysis can be performed even when prior information is only available for a subparameter of the model. Finally, some numerical examples are presented.

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Section: Discussionmentioning

confidence: 85%

Bayesian Inference in Auditing with Partial Prior Information Using Maximum Entropy Priors

Martel–Escobar

Polo

Hernández-Bastida

2018

Entropy

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“…Our work enhances Bayesian optimization by showing STP ( = 5) ERM outperforms GP ERM on three popular synthetic problems [12] and one real-world application [9] in mathematical optimization. Rather than choosing = 5 [8], future work will consider STP ERM with prior chosen using Kullback-Leibler divergence [21].…”

Section: Discussionmentioning

confidence: 99%

Expected Regret Minimization for Bayesian Optimization with Student's-t Processes

Clare¹,

Hawe²,

McClean³

2020

Proceedings of the 2020 3rd International Conference on Artificial Intelligence and Pattern Recognition

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“…There are several ways to estimate degrees of freedom. Suggested methods for multivariate Student t-test are the maximum likelihood estimation and method of moments [41]. Both methods are estimating the parameters of the statistical model.…”

Section: Standard Normal Probability Density Function (Pdf)mentioning

confidence: 99%

Investigating the Viability of Applying a Lower Bound Risk Metric for Altman’s z-Score

Holpus¹,

Alqatan²,

Arslan³

2021

Accounting and Finance Innovations

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The study aimed to build a risk metric for finding the lower boundary limits for Altman’s z-score bankruptcy model. The new metric included a volatility of Altman’s variables and predicted the riskiness of a firm bankrupting in adverse situations. The research examined whether the new risk metric is feasible and whether it provides satisfying outcomes compared to Altman’s z-score values during the same period. The methods to conduct the analysis were based on Value at Risk methodology. The main tools used in constructing the model were Monte Carlo simulation, Lehmer random number generator, normal and t-distribution, matrices and Cholesky decomposition. The sample firms were selected from FTSE 250 index. The important variables used in the analysis were all Altman’s z-score variables, and the period under observation was 2001–2007. The selected risk horizon was the first quarter of 2008. The first results were promising and showed that the model does work to the specified extent. The research demonstrated that Altman’s z-score does not provide a full and accurate overview. Therefore, the lower bound risk metric developed in this research, produces valuable supplementary information for a well-informed decision making. To verify the model, it must be back- and forward tested, neither of which was carried out in this research. Furthermore, the research elaborated on limitations and suggested further improvement options for the model.

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Objective priors for the number of degrees of freedom of a multivariate t distribution and the t-copula

Cited by 19 publications

References 36 publications

Bayesian Inference in Auditing with Partial Prior Information Using Maximum Entropy Priors

Bayesian Inference in Auditing with Partial Prior Information Using Maximum Entropy Priors

Expected Regret Minimization for Bayesian Optimization with Student's-t Processes

Investigating the Viability of Applying a Lower Bound Risk Metric for Altman’s z-Score

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