Particle filters + system idenfitication.
A placeholder.
State augmentation
The classic; just include the parameter vector in the state vector and give it a “small” magnitude random evolution. (But how small?)
Via MCMC
a.k.a. particle MCMC. See Frei and Künsch (2012). Kantas et al. (2015) and Fearnhead and Künsch (2018) introduce more.
References
Evensen, Geir. 2009. Data Assimilation - The Ensemble Kalman Filter. Berlin; Heidelberg: Springer.
Fearnhead, Paul, and Hans R. Künsch. 2018. “Particle Filters and Data Assimilation.” Annual Review of Statistics and Its Application 5 (1): 421–49.
Frei, Marco, and Hans R. Künsch. 2012. “Sequential State and Observation Noise Covariance Estimation Using Combined Ensemble Kalman and Particle Filters.” Monthly Weather Review 140 (5): 1476–95.
Kantas, Nikolas, Arnaud Doucet, Sumeetpal S. Singh, Jan Maciejowski, and Nicolas Chopin. 2015. “On Particle Methods for Parameter Estimation in State-Space Models.” Statistical Science 30 (3): 328–51.
Künsch, Hans R. 2013. “Particle Filters.” Bernoulli 19 (4): 1391–1403.
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