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| Typically, coupling two models (say, climate and oceans) requires that both be recalibrated, often with parameter values that are not internally reasonable. I'd like to find another option.
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| My approach is to consider {X_i} to be an underlying "true" process, which is passed through a parallel collection of noisy channels, which are the models. The goal is uncover an estimate of each X_i. X_i may not be encoded before being passed through the channel.
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| If the X_i and Z_i errors are independent, the solution might just be an average or a maximum likelihood. But what if the Z_i's are correlated? Suppose that the {X_i} come from a Gauss-Markov process with unknown coefficients-- can the coefficients be simultaneously estimated? Suppose that something is known about the power spectrum of X-- how can that be used? The entropy rate is a function of the spectrum, and determines the error bounds on the estimates of X_i, but what is that best estimate?
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| [[Media:Couplingdiag.png]]
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