Prediction of categorical spatial data via Bayesian updating

ABSTRACT

This study introduces a transition probability-based Bayesian updating (BU) approach for spatial classification through expert system. Transition probabilities are interpreted as expert opinions for updating the prior marginal probabilities of categorical response variables. The main objective of this paper is to provide a spatial categorical variable prediction method which has a solid theoretical foundation and yields relatively higher classification accuracy compared with conventional ones. The basic idea is to first build a linear Bayesian updating (LBU) model that corresponds to an application of Bayes’ theorem. Since the linear opinion pool is intrinsically suboptimal and underconfident, the beta-transformed Bayesian updating (BBU) model is proposed to overcome this limitation. Another type of BU approach, conditional independent Bayesian updating (CIBU), is derived based on conditional independent experts. It is shown that traditional Markovian-type categorical prediction (MCP) is equivalent to a particular CIBU model with specific parameters. As three variants of the BU method, these techniques are illustrated in synthetic and real-world case studies, comparison results with both the LBU and MCP favor the BBU model.

KEYWORDS:

• Bayesian updating
• beta transform
• expert opinion
• transition probability

Acknowledgments

The authors are indebted to Wuyue Shen for her critical review of the paper. Finally, the authors gratefully thank the associate editor and three anonymous reviewers for their constructive comments and suggestions, which has profoundly improved the composition of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This study was funded by National Science and Technology Major Project of China [No. 2011ZX05002-005-006].