A circular-linear dependence measure under Johnson-Wehrly distributions and its application in Bayesian networks. (English) Zbl 1454.62161
Summary: Circular data jointly observed with linear data are common in various disciplines. Since circular data require different techniques than linear data, it is often misleading to use usual dependence measures for joint data of circular and linear observations. Moreover, although a mutual information measure between circular variables exists, the measure has drawbacks in that it is defined only for a bivariate extension of the wrapped Cauchy distribution and has to be approximated using numerical methods. In this paper, we introduce two measures of dependence, namely, (i) circular-linear mutual information as a measure of dependence between circular and linear variables and (ii) circular-circular mutual information as a measure of dependence between two circular variables. It is shown that the expression for the proposed circular-linear mutual information can be greatly simplified for a subfamily of Johnson-Wehrly distributions. We apply these two dependence measures to learn a circular-linear tree-structured Bayesian network that combines circular and linear variables. To illustrate and evaluate our proposal, we perform experiments with simulated data. We also use a real meteorological data set from different European stations to create a circular-linear tree-structured Bayesian network model.
MSC:
| 62H11 | Directional data; spatial statistics |
| 62M30 | Inference from spatial processes |
| 94A17 | Measures of information, entropy |
Keywords:
circular-linear mutual information; tree-structured Bayesian network; dependence measures; directional statisticsReferences:
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