Reliable Uncertain Evidence Modeling in Bayesian Networks by Credal Networks

A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard updating in an augmented credal network, equivalent to a set of consistent Bayesian networks. A characterization of the computational complexity for this task is derived together with an efficient exact procedure for a subclass of instances. In the case of multiple uncertain evidences over the same variable, the proposed procedure can provide a set-valued version of the geometric approach to opinion pooling.Comment: 19 page

A Naive Bayes Source Classifier for X-ray Sources

The Chandra Carina Complex Project (CCCP) provides a sensitive X-ray survey of a nearby starburst region over >1 square degree in extent. Thousands of faint X-ray sources are found, many concentrated into rich young stellar clusters. However, significant contamination from unrelated Galactic and extragalactic sources is present in the X-ray catalog. We describe the use of a naive Bayes classifier to assign membership probabilities to individual sources, based on source location, X-ray properties, and visual/infrared properties. For the particular membership decision rule adopted, 75% of CCCP sources are classified as members, 11% are classified as contaminants, and 14% remain unclassified. The resulting sample of stars likely to be Carina members is used in several other studies, which appear in a Special Issue of the ApJS devoted to the CCCP.Comment: Accepted for the ApJS Special Issue on the Chandra Carina Complex Project (CCCP), scheduled for publication in May 2011. All 16 CCCP Special Issue papers are available at http://cochise.astro.psu.edu/Carina_public/special_issue.html through 2011 at least. 19 pages, 7 figure

Risk, Unexpected Uncertainty, and Estimation Uncertainty: Bayesian Learning in Unstable Settings

Recently, evidence has emerged that humans approach learning using Bayesian updating rather than (model-free) reinforcement algorithms in a six-arm restless bandit problem. Here, we investigate what this implies for human appreciation of uncertainty. In our task, a Bayesian learner distinguishes three equally salient levels of uncertainty. First, the Bayesian perceives irreducible uncertainty or risk: even knowing the payoff probabilities of a given arm, the outcome remains uncertain. Second, there is (parameter) estimation uncertainty or ambiguity: payoff probabilities are unknown and need to be estimated. Third, the outcome probabilities of the arms change: the sudden jumps are referred to as unexpected uncertainty. We document how the three levels of uncertainty evolved during the course of our experiment and how it affected the learning rate. We then zoom in on estimation uncertainty, which has been suggested to be a driving force in exploration, in spite of evidence of widespread aversion to ambiguity. Our data corroborate the latter. We discuss neural evidence that foreshadowed the ability of humans to distinguish between the three levels of uncertainty. Finally, we investigate the boundaries of human capacity to implement Bayesian learning. We repeat the experiment with different instructions, reflecting varying levels of structural uncertainty. Under this fourth notion of uncertainty, choices were no better explained by Bayesian updating than by (model-free) reinforcement learning. Exit questionnaires revealed that participants remained unaware of the presence of unexpected uncertainty and failed to acquire the right model with which to implement Bayesian updating

Galaxy Zoo: Disentangling the Environmental Dependence of Morphology and Colour

We analyze the environmental dependence of galaxy morphology and colour with two-point clustering statistics, using data from the Galaxy Zoo, the largest sample of visually classified morphologies yet compiled, extracted from the Sloan Digital Sky Survey. We present two-point correlation functions of spiral and early-type galaxies, and we quantify the correlation between morphology and environment with marked correlation functions. These yield clear and precise environmental trends across a wide range of scales, analogous to similar measurements with galaxy colours, indicating that the Galaxy Zoo classifications themselves are very precise. We measure morphology marked correlation functions at fixed colour and find that they are relatively weak, with the only residual correlation being that of red galaxies at small scales, indicating a morphology gradient within haloes for red galaxies. At fixed morphology, we find that the environmental dependence of colour remains strong, and these correlations remain for fixed morphology \textit{and} luminosity. An implication of this is that much of the morphology--density relation is due to the relation between colour and density. Our results also have implications for galaxy evolution: the morphological transformation of galaxies is usually accompanied by a colour transformation, but not necessarily vice versa. A spiral galaxy may move onto the red sequence of the colour-magnitude diagram without quickly becoming an early-type. We analyze the significant population of red spiral galaxies, and present evidence that they tend to be located in moderately dense environments and are often satellite galaxies in the outskirts of haloes. Finally, we combine our results to argue that central and satellite galaxies tend to follow different evolutionary paths.Comment: 19 pages, 18 figures. Accepted for publication in MNRA