A local approach for focussed Bayesian fusion

Abstract

Local Bayesian fusion approaches aim to reduce high storage and computational costs of Bayesian fusion which is separated from fixed modeling assumptions. Using the small world formalism, we argue why this proceeding is conform with Bayesian theory. Then, we concentrate on the realization of local Bayesian fusion by focussing the fusion process solely on local regions that are task relevant with a high probability. The resulting local models correspond then to restricted versions of the original one. In a previous publication, we used bounds for the probability of misleading evidence to show the validity of the pre-evaluation of task specific knowledge and prior information which we perform to build local models. In this paper, we prove the validity of this proceeding using information theoretic arguments. For additional efficiency, local Bayesian fusion can be realized in a distributed manner. Here, several local Bayesian fusion tasks are evaluated and unified after the actual fusion process. For the practical realization of distributed local Bayesian fusion, software agents are predestinated. There is a natural analogy between the resulting agent based architecture and criminal investigations in real life. We show how this analogy can be used to improve the efficiency of distributed local Bayesian fusion additionally. Using a landscape model, we present an experimental study of distributed local Bayesian fusion in the field of reconnaissance, which highlights its high potential

Global evaluation of focussed Bayesian fusion

“…Because of the theoretical similarity between the corresponding proceeding and the focussing mechanism of Bayesian fusion, 2 we termed local Bayesian fusion based on a restriction of the range of the PoIs focussed Bayesian fusion. 1 As demonstrated in previous publications, 1,3 the validity of a focussed Bayesian analysis is verifiable for example by a statistical error bound or by quality indicators based on information theory.…”

“…Focussing on the local context U mathematically corresponds to a conditioning on U . 1 The focussed posterior distribution p U (z|d) can be obtained via the application of the Bayesian theorem:…”

“…We continue an example which has been given in [1]. There, focussed Bayesian fusion has been used for the detection and classification of cars within a scene (landscape model, scale 1:160) on the basis of prior knowledge from a street map and IMINT information which is represented by a single gray-value image of the scene.…”

“…None of the common methods for complexity reduction is generally appropriate for the solution of real world fusion tasks without reducing thereby the theoretical power of the Bayesian methodology. 1 As alternative solution, we investigate local Bayesian fusion approaches by which high costs caused by Bayesian fusion are circumvented, see Sec. 2.3.…”

Bayesian fusion: Modeling and application

“…However, because of the way in that the probabilistic calculus shifts the global probability mass from Z \ U to U when "forgetting" Z \ U , solely on the basis of this local Bayesian model, it is not possible to decide if U has been appropriately chosen. To solve this issue, different criteria for the appropriateness of local Bayesian models have been developed [33], [34], [35], [36].…”