Approximate Bayesian Procedures for Dynamic Linear Models in the Presence of Jumps

Abstract

The paper focuses on the computational difficulties in implementing a coherent Bayesian solution to dynamic linear models which are subject to jumps. Several approximate procedures are suggested and their relative merits are discussed.

The EM Algorithm, Variational Approximations and Expectation Propagation for Mixtures

“…j + w i+1,j , for j = 1, 2, and the probabilistic editor (Athans et al, 1977;Makov, 1983), in which a (i+1) 1 and a (i+1) 2 are calculated to ensure that the first two moments of the beta approximation match the 'correct' moments corresponding to the mixture. This moment-matching is possible beause there are two hyperparameters.…”

Modelling Expectations Formation With Parameter‐adaptive Filters: An Empirical Application to the Livingston Forecasts

“…It is, therefore, most important to draw distinctions between both the actual data generating process as seen by the econometrician and the data generating process as perceived by the agents, and between the econometrician's and agents' models of that process. If agents' information set is a subset of, or identical to, the econometricians' information set then agents' and econometrician's models should form a hierarchy of encompassing systems (for a discussion of 'encompassing' see Richard, 1982 and1983). Then, the econometrician's model should be able to 'mimic' agents' expectations (and decisions) by imposing appropriate restrictions on agents' information sets and models of the process.…”

Efficient Model Selection in Switching Linear Dynamic Systems by Graph Clustering

“…The computational burden of an SKF increases exponentially with the number of system modes, hence rendering its utility impractical if the number of dynamical modes and the state variable dimension are large [10]. Approximate filtering algorithms given the ground truth SLDS model are able to provide limited saving in computational complexity [10], [13]- [16], but implementing these filters remains computationally expensive if the state dimension and the number of modes are large. Similar to [10], [13]- [16], we also make the assumption that the ground truth SLDS model is given a priori or derived using online/batch system identification algorithms [17]- [22].…”

“…Approximate filtering algorithms given the ground truth SLDS model are able to provide limited saving in computational complexity [10], [13]- [16], but implementing these filters remains computationally expensive if the state dimension and the number of modes are large. Similar to [10], [13]- [16], we also make the assumption that the ground truth SLDS model is given a priori or derived using online/batch system identification algorithms [17]- [22]. Then, we reduce the number of system modes by combining those that minimize the ultimate impact on the estimation error based on a graph representation of the SLDS.…”