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Hierarchical Bayesian Modeling

Hierarchical Bayesian ModelingAngie Wolfgang NSF Postdoctoral Fellow, Penn Stateabout a populationMaking scientific inferencesbased on many individualsAstronomical PopulationsSchawinski et al. 2014 Lissauer, Dawson, & Tremaine, 2014 Once we discover an object, we look for more ..to characterize their properties and understand their planetsAstronomical PopulationsOr we use many (often noisy) observations of a single objectto gain insight into its physics. Hierarchical Modelingis a statistically rigorous way to make scientific inferences about a population (or specific object) based on many individuals (or observations).Frequentist multi-level Modeling techniques exist, but we will discuss the Bayesian approach : variability of sample(If __ is the true value, what fraction of many hypothetical datasets would be as or more discrepant from __ as the observed one?)

selection effects, upper limits, etc.!!!!! Going Hierarchical ... Shrinkage in action: Gray = data Red = posteriors. Practical Considerations 1) Pay attention to the structure of your model!! ... (HBM for linear regression, also applied to quasars) Loredo & Wasserman, 1998

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