Bayesian data fusion in a spatial prediction context: a general formulation

Abstract

In spite of the exponential growth in the amount of data that one may expect to provide greater modeling and predictions opportunities, the number and diversity of sources over which this information is fragmented is growing at an even faster rate. As a consequence, there is real need for methods that aim at reconciling them inside an epistemically sound theoretical framework. In a statistical spatial prediction framework, classical methods are based on a multivariate approach of the problem, at the price of strong modeling hypotheses. Though new avenues have been recently opened by focusing on the integration of uncertain data sources, to the best of our knowledges there have been no systematic attemps to explicitly account for information redundancy through a data fusion procedure. Starting from the simple concept of measurement errors, this paper proposes an approach for integrating multiple information processing as a part of the prediction process itself through a Bayesian approach. A general formulation is first proposed for deriving the prediction distribution of a continuous variable of interest at unsampled locations using on more or less uncertain (soft) information at neighboring locations. The case of multiple information is then considered, with a Bayesian solution to the problem of fusing multiple information that are provided as separate conditional probability distributions. Well-known methods and results are derived as limit cases. The convenient hypothesis of conditional independence is discussed by the light of information theory and maximum entropy principle, and a methodology is suggested for the optimal selection of the most informative subset of information, if needed. Based on a synthetic case study, an application of the methodology is presented and discussed.

Updating Scarce High Resolution Images with Time Series of Coarser Images: a Bayesian Data Fusion Solution

“…In this chapter, a Bayesian data fusion (BDF; Bogaert & Fasbender, 2007) framework was applied for the update of scare high resolution images with time series of coarser images. This BDF framework aims at reconciling various secondary information sources into a unique prediction.…”

“…The main advantage of a Bayesian approach is to set the problem of data fusion into a clear probabilistic framework. The present chapter relies on a general Bayesian Data Fusion approach in the context of spatial data (Bogaert & Fasbender, 2007). Its specific implementation will focus here on the problem of updating high resolution images with time series of coarser images.…”

“…where i corresponds to the channel number and p i is the number of secondary information corresponding to the same Z i (see Bogaert & Fasbender, 2007 for more details). Using Bayes theorem again for It is worth noting that this BDF framework has interesting similarities with other multisensor data fusion methods (see Mitchell, 2007 for more details).…”

“…It is therefore relevant to focus our attention on data fusion methods that typically enable us to account for several information sources in order to produce a single but improved image. Recently, a new Bayesian Data Fusion (BDF) framework was proposed in a general space-time prediction context by (Bogaert & Fasbender, 2007), with the aim of merging various kind of information sources that are all different but relevant for a same target variable. Though initially developed with stochastic space-time random fields applications in mind, the method proved to be efficient for remotely sensed applications as well (e.g.…”

Integração de modelos espaciais e temporais para predições de níveis freáticos extremos

“…Quando há disponibilidade de informações auxiliares, é possível melhorar a acurácia das predições espaciais, estimar padrões espaciais mais plausíveis e atribuir sentido físico aos mapas resultantes com uso de produtos, como os modelos digitais de terreno (MDT) e as imagens de satélite classificadas (Odeha et al, 1994;Hengl et al, 2004;Bogaert & Fasbender 2007;Manzione et al, 2010;Peeters et al, 2010). A partir dessas estimativas, é possível elaborar cenários na forma de mapas.…”