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Abstract:
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A popular approach for flexible function estimation in nonparametric models is through spline smoothing using the general penalized likelihood method. In applying this method, one needs to specify a penalty functional which puts a soft constraint on the function to be estimated. A good choice of penalty functional is of key importance. In practice, specifying the penalty functional is mostly based on expert knowledge of the system. However, for many dynamic systems there naturally exist more than one sets of well-studied theory that explains the dynamics systems, i.e., there exist more than one sensible choices of penalties, raising the problem of ambiguous penalties. To tackle this problem, we propose an approach that takes into consideration of all candidate penalties. We take a fully Bayesian perspective, made use of the connection between penalized least squares and Bayesian estimation, and model the uncertainty of choosing penalty through introducing a mixture distribution as prior for parameters to be estimated. We also propose efficient sampling algorithm for making inference based on taking samples from posterior distribution.
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