A Bayesian model for longitudinal circular data based on the projected normal distribution

2014 ◽  
Vol 71 ◽  
pp. 506-519 ◽  
Author(s):  
Gabriel Nuñez-Antonio ◽  
Eduardo Gutiérrez-Peña
Keyword(s):  
Normal Distribution ◽  
Bayesian Model ◽  
Circular Data ◽  
Projected Normal Distribution

A Bayesian regression model for circular data based on the projected normal distribution

2011 ◽  
Vol 11 (3) ◽  
pp. 185-201 ◽  
Author(s):  
Gabriel Nuñez-Antonio ◽  
Eduardo Gutiérrez-Peña ◽  
Gabriel Escarela
Keyword(s):  
Regression Model ◽  
Normal Distribution ◽  
Bayesian Regression ◽  
Circular Data ◽  
Projected Normal Distribution

scholarly journals Modelling complex geological circular data with the projected normal distribution and mixtures of von Mises distributions

Solid Earth ◽  
2014 ◽  
Vol 5 (2) ◽  
pp. 631-639 ◽  
Author(s):  
R. M. Lark ◽  
D. Clifford ◽  
C. N. Waters
Keyword(s):  
Normal Distribution ◽  
Circular Data ◽  
Data Sets ◽  
Statistical Distributions ◽  
Data Set ◽  
Geological Interpretation ◽  
The Earth ◽  
Von Mises ◽  
Special Case ◽  
Projected Normal Distribution

Abstract. Circular data are commonly encountered in the earth sciences and statistical descriptions and inferences about such data are necessary in structural geology. In this paper we compare two statistical distributions appropriate for complex circular data sets: the mixture of von Mises and the projected normal distribution. We show how the number of components in a mixture of von Mises distribution may be chosen, and how one may choose between the projected normal distribution and the mixture of von Mises for a particular data set. We illustrate these methods with a few structural geological data, showing how the fitted models can complement geological interpretation and permit statistical inference. One of our data sets suggests a special case of the projected normal distribution which we discuss briefly.

scholarly journals Bayesian hidden Markov modelling using circular-linear general projected normal distribution

2015 ◽  
Vol 26 (2) ◽  
pp. 145-158 ◽  
Author(s):  
Gianluca Mastrantonio ◽  
Antonello Maruotti ◽  
Giovanna Jona-Lasinio
Keyword(s):  
Normal Distribution ◽  
Hidden Markov ◽  
Markov Modelling ◽  
Projected Normal Distribution

scholarly journals A clustering Bayesian approach for multivariate non-ordered circular data

2018 ◽  
Vol 19 (6) ◽  
pp. 595-616 ◽  
Author(s):  
Christophe Abraham ◽  
Rémi Servien ◽  
Nicolas Molinari
Keyword(s):  
Hierarchical Model ◽  
Bayesian Approach ◽  
Dirichlet Process ◽  
Bayesian Model ◽  
Theoretical Study ◽  
Real Data ◽  
Circular Data ◽  
Single Observation ◽  
Normal Distributions ◽  
X Ray

This article presents a Bayesian model for the clustering of non-ordered multivariate directional or circular data. The particular trait of our data is that each single observation is made up of [Formula: see text] non-ordered points on the circle. We introduce a hierarchical model that combines a symmetrization technique, projected normal distributions and a Dirichlet process. One parameter is introduced to model the non-ordered trait and another one to control the variability of the angles on the circle. An informative prior on the relative locations of the [Formula: see text] angles is also provided. The gain of the symmetrization is highlighted by a theoretical study. The parameters of the model are then inferred using a Metropolis–Hastings-within-Gibbs algorithm. Simulated datasets are analysed to study the sensitivity to hyperparameters. Then, the benefits of our approach are illustrated by clustering real data made up of the positions of five separate radiotherapy X-ray beams on a circle.

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