Theory &amp; Methods: An Empirical Bayes Inference for the von Mises Distribution

Rodrigues, Josemar; Leite, José Galvâo; Milan, Luís Aparecido

doi:10.1111/1467-842x.00140

Cited by 11 publications

(13 citation statements)

References 13 publications

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“…Although the induced estimator of the location parameter is not always of linear form, we will find that a type of linearity is observed in all the cases. Rodrigues et al (2000) noted this fact in the von Mises case.…”

Section: Introductionmentioning

confidence: 88%

“…Our prior density for M(1) is also in M(1). The von Mises prior density was employed in Guttorp and Lockhart (1988), Bagchi (1994) and Rodrigues et al (2000). We obtain…”

Section: Example 45 Von-mises Family M(1);mentioning

confidence: 99%

“…There are a considerable number of existing works on Bayesian analysis of the location family, which include Mardia and El-Atoum (1976), Diaconis and Ylvisaker (1985), Spiegelhalter (1985), Polson (1991), Bischoff (1993), Angers (1996), Garvan and Ghosh (1997), Leblanc and Angers (1999), Rodrigues et al (2000) and Ohnishi and Yanagimoto (2003). Among them, Diaconis and Ylvisaker (1985) is one which discussed formally a conjugate prior for the location family.…”

Section: Introductionmentioning

confidence: 99%

“…Their paper, however, concentrated on the analytical aspect; no explicit form of a conjugate prior density was given. Mardia and El-Atoum (1976) noted that a von Mises prior density is conjugate for a von Mises sampling density, which was followed by Rodrigues et al (2000).…”

Section: Introductionmentioning

confidence: 99%

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Conjugate Location-Dispersion Families

Ohnishi

Yanagimoto

2007

JJSS

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We make a conjugate analysis for the five location-dispersion families including the normal, the transformed gamma and the von Mises distributions. The five families are introduced through the requirement for the existence of conjugate prior densities. We show in a unified way that a Pythagorean relationship holds with respect to posterior risks, which clarifies the optimality of the posterior mode under a KullbackLeibler loss. An explicit form of the posterior mode is given, and a type of linearity is observed. We construct an empirical Bayes estimator of a location vector explicitly.

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Section: Introductionmentioning

confidence: 88%

“…Our prior density for M(1) is also in M(1). The von Mises prior density was employed in Guttorp and Lockhart (1988), Bagchi (1994) and Rodrigues et al (2000). We obtain…”

Section: Example 45 Von-mises Family M(1);mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Conjugate Location-Dispersion Families

Ohnishi

Yanagimoto

2007

JJSS

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“…Additionally, the parameters of the disturbance distributions are better defined when scedasticity is accounted for. It is worth mentioning that both the normal distribution and the von Mises-Fisher distribution have a complete range of analytical or approximated solutions for both posterior and posterior predictive distributions (Rodrigues et al, 2000;Bagchi and Figure 5. Distribution of errors for the cases described in Fig.…”

Section: Measurement Scedasticitymentioning

confidence: 99%

Monte Carlo simulation for uncertainty estimation on structural data in implicit 3-D geological modeling, a guide for disturbance distribution selection and parameterization

et al. 2018

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Abstract. Three-dimensional (3-D) geological structural modeling aims to determine geological information in a 3-D space using structural data (foliations and interfaces) and topological rules as inputs. This is necessary in any project in which the properties of the subsurface matters; they express our understanding of geometries in depth. For that reason, 3-D geological models have a wide range of practical applications including but not restricted to civil engineering, the oil and gas industry, the mining industry, and water management. These models, however, are fraught with uncertainties originating from the inherent flaws of the modeling engines (working hypotheses, interpolator's parameterization) and the inherent lack of knowledge in areas where there are no observations combined with input uncertainty (observational, conceptual and technical errors). Because 3-D geological models are often used for impactful decision-making it is critical that all 3-D geological models provide accurate estimates of uncertainty. This paper's focus is set on the effect of structural input data measurement uncertainty propagation in implicit 3-D geological modeling. This aim is achieved using Monte Carlo simulation for uncertainty estimation (MCUE), a stochastic method which samples from predefined disturbance probability distributions that represent the uncertainty of the original input data set. MCUE is used to produce hundreds to thousands of altered unique data sets. The altered data sets are used as inputs to produce a range of plausible 3-D models. The plausible models are then combined into a single probabilistic model as a means to propagate uncertainty from the input data to the final model. In this paper, several improved methods for MCUE are proposed.The methods pertain to distribution selection for input uncertainty, sample analysis and statistical consistency of the sampled distribution. Pole vector sampling is proposed as a more rigorous alternative than dip vector sampling for planar features and the use of a Bayesian approach to disturbance distribution parameterization is suggested. The influence of incorrect disturbance distributions is discussed and propositions are made and evaluated on synthetic and realistic cases to address the sighted issues. The distribution of the errors of the observed data (i.e., scedasticity) is shown to affect the quality of prior distributions for MCUE. Results demonstrate that the proposed workflows improve the reliability of uncertainty estimation and diminish the occurrence of artifacts.

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Circular data

Lee

2010

WIREs Computational Stats

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The special nature of circular data means that conventional methods suitable for the analysis of linear data do not apply. In this article, we survey a range of methods that have been developed over the last 50 years to handle the special characteristics of data consisting of angular measurements. We discuss summary statistics and graphical methods, methods for the analysis of single and multiple samples of circular data, circular correlation, regression methods, and time series. We discuss the standard probability models on which these analyses are based, and give several examples of the application of these methods. A reasonably comprehensive bibliography is provided .

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Theory & Methods: An Empirical Bayes Inference for the von Mises Distribution

Cited by 11 publications

References 13 publications

Conjugate Location-Dispersion Families

Conjugate Location-Dispersion Families

Monte Carlo simulation for uncertainty estimation on structural data in implicit 3-D geological modeling, a guide for disturbance distribution selection and parameterization

Circular data

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