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Data Modelling and Calibration using a Two Level Hierarchical Bayesian Approach  
Maria Jose Marquez1,Luis Manuel Sarro2

Advanced Artificial Intelligence

UNED University

Madrid, Spain

2, UNED, Email :
Abstract .Calibration is nowadays one of the most important processes involved in the extraction of valuable data from measurements. The current availability of an optimum data cube measured from a heterogeneous set of instruments and surveys relies on a systematic and robust approach in the corresponding measurement analysis. In this sense, the inference of configurable instrument parameters, as part of data modelling, can considerably increase the quality of the data obtained. Any measurement devoted to scientific purposes contains an element of uncertainty. The level of noise, for example, determines the limit of usability of an image. Therefore, a mathematical model representing the reality of the measured data should also include at least the sources of noise which are the most relevant ones for the context of that measurement. This paper proposes a solution based on Bayesian inference for the estimation of the configurable parameters relevant to the signal-to-noise ratio. The information obtained by the resolution of this problem can be handled in a very useful way if it is considered as part of an adaptive loop for the overall measurement strategy, in such a way that the outcome of this parametric inference leads to an increase in the knowledge of a model comparison problem in the context of data modelling and measurement interpretation. The context of this problem is the multi-wavelength measurements coming from diverse cosmological surveys and obtained using various telescope instruments. As a first step, a thorough analysis of the typical noise contributions will be performed based on the current state-of-the-art of modern telescope instrumentation. A second step will then consist of identifying configurable parameters relevant to the noise model under consideration. Then, as a third step, a Bayesian inference for these parameters estimations will be applied, taking into account a proper identification of the nuisance parameters and the adequate selection of a prior probability. Finally, a corresponding set of conclusions will be derived.
Keywords : signal; noise; gain; quantum efficienty; count; read noise; dark current; nuisance parameters

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