4,420 research outputs found
Estimating model evidence using data assimilation
We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the discrimination between a factual modelāwhich corresponds, to the best of the modeller's knowledge, to the situation in the actual world in which a sequence of events has occurredāand a counterfactual model, in which a particular forcing or process might be absent or just quantitatively different from the actual world. Three different ensembleāDA methods are reviewed for this purpose: the ensemble Kalman filter (EnKF), the ensemble fourādimensional variational smoother (Enā4DāVar), and the iterative ensemble Kalman smoother (IEnKS). An original contextual formulation of model evidence (CME) is introduced. It is shown how to apply these three methods to compute CME, using the approximated timeādependent probability distribution functions (pdfs) each of them provide in the process of state estimation. The theoretical formulae so derived are applied to two simplified nonlinear and chaotic models: (i) the Lorenz threeāvariable convection model (L63), and (ii) the Lorenz 40āvariable midlatitude atmospheric dynamics model (L95). The numerical results of these three DAābased methods and those of an integration based on importance sampling are compared. It is found that better CME estimates are obtained by using DA, and the IEnKS method appears to be best among the DA methods. Differences among the performance of the three DAābased methods are discussed as a function of model properties. Finally, the methodology is implemented for parameter estimation and for event attribution
A Tutorial on Fisher Information
In many statistical applications that concern mathematical psychologists, the
concept of Fisher information plays an important role. In this tutorial we
clarify the concept of Fisher information as it manifests itself across three
different statistical paradigms. First, in the frequentist paradigm, Fisher
information is used to construct hypothesis tests and confidence intervals
using maximum likelihood estimators; second, in the Bayesian paradigm, Fisher
information is used to define a default prior; lastly, in the minimum
description length paradigm, Fisher information is used to measure model
complexity
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