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Abstract:
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Kalman Filtering is a powerful filtering algorithm that reduces the computational burden of calculating estimators, predictors, and evaluation of likelihoods of stochastic processes that can be modeled using a state-space representation. However, the Kalman filter formulas, and its onerous notations, have intimidated the more applied statistician and restricted its influence. In this talk, we present examples of Kalman filtering implementation in the settings of ridge regression, randomized block designs, varying coefficient models, and regression with correlated errors. Our objective is to demystify the Kalman filter by explicitly writing the state-space model for each of these settings and show how to obtain estimators, predictors, and nuisance parameters by implementing an efficient, O(n), Kalman filter algorithm that also deals with diffuse initial conditions.
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