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In this survey, we present and compare different approaches to estimate Mutual Information (MI) from data to analyse general dependencies between variables of interest in a system. We demonstrate the performance difference of MI versus correlation analysis, which is only optimal in case of linear dependencies. First, we use a piece-wise constant Bayesian methodology using a general Dirichlet prior. In this estimation method, we use a two-stage approach where we approximate the probability distribution first and then calculate the marginal and joint entropies. Here, we demonstrate the performance of this Bayesian approach versus the others for computing the dependency between different variables. We also compare these with linear correlation analysis. Finally, we apply MI and correlation analysis to the identification of the bias in the determination of the aerosol optical depth (AOD) by the satellite based Moderate Resolution Imaging Spectroradiometer (MODIS) and the ground based AErosol RObotic NETwork (AERONET). Here, we observe that the AOD measurements by these two instruments might be different for the same location. The reason of this bias is explored by quantifying the dependencies between the bias and 15 other variables including cloud cover, surface reflectivity and others. [ABSTRACT FROM AUTHOR]

Optical spectroscopy is investigated with respect to its capabilities to yield temperature information from line intensities of low temperature plasmas. The method is non-invasive and easy to perform experimentally. The data analysis model consists of a population model describing the intensities of light emission. Geometry effects and measurement errors are encountered. The quantity of interest is the electron energy distribution function. A Bayesian framework was chosen to incorporate systematic uncertainties and to incorporate physics information coherently. As an example, results from in-situ wavelength calibrations are discussed. Sensitivity studies of modeled spectra are outlined. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]

I describe a work in progress that uses Bayes’ theorem, model selection, and marginalization in the analysis of photon count data frames from a stellar optical interferometer (the Navy Prototype Optical Interferometer). These data frames in general have between 1–6 stellar fringes (baselines) present. I show how Bayes factors provide a direct way of determining the number of fringes that are present in each data frame. I describe briefly the traditional Fourier-based technique for computing optical interferometry data products. A Bayesian approach, in addition to providing model selection directly from the data frames, also provides a way of combining the computed data products from each data frame in a manner that intrinsically handles the varying SNRs between the data frames. I use simulated data to show comparisons between my Bayesian approach and the traditional Fourier-based technique for the analysis of such data. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

General theoretical principles that enable the derivation of prior probabilities are of interest both in practical data analysis and, more broadly, in the foundations of probability theory. In this paper, it is shown that the general rule for the assignment of priors proposed by Jeffreys can be obtained from, and is logically equivalent to, an intuitively reasonable information-theoretical invariance principle Some of the implications for the priors proposed by Hartigan, Jaynes, and Skilling, are also discussed. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

We deal with the problem of constructing priors for data analysis in order to asses brain activity in functional Magnetic Resonance Imaging (fMRI). Our method is an example of how a prior distribution can incorporate what could be termed as conventional prior information as well as other information such as that steming from knowledge of what constitues a reasonable likelihood. Brain activity during a cognitive, sensorial or motor task presents a certain level of localization and spatial correlations with different scales involved in the problem. These suggests a multiscale iterative procedure to construct the prior. Grids of different scales are constructed over the image. Spatially coarse grain data variables are defined for each scale, until a single voxel time series is obtained. The process consists in iterating back to finer scales, determining for each coarse scale a set of posterior probabilities. The posterior on a coarse scale is used as the prior for activity at the next finer scale. We have applied our method both to real as well as synthetic data of block experiments. A linear model and a standard hemodynamic response function are used to construct the likelihood. ROC curves are used to compare the results with other Bayesian and orthodox methods. By systematically deleting images in each period or by corrupting the signal with noise, we can study the robustness of the method under information loss. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]