Parameter tracking with partial forgetting method

Abstract

This paper concerns the Bayesian tracking of slowly varying parameters of a linear stochastic regression model. The modelled and predicted system output is assumed to possess time-varying mean value, whereas its dynamics are relatively stable. The proposed estimation method models the system output mean value by time-varying offset. It formulates three extreme hypotheses on model parameters' variability: (i) no parameter varies; (ii) all parameters vary; and (iii) the offset varies. The Bayesian paradigm then provides a mixture as posterior distribution, which is appropriately projected to a feasible class. Exponential forgetting at 'second' hypotheses level allows tracking of slow variations of respective hypotheses.The developed technique is an example of a general procedure called partial forgetting. Focus on a simple example allows to demonstrate essence of the approach. Moreover, it is important per se as it corresponds with a varying load of otherwise (almost) time-invariant dynamic system.

Bayesian model mixing for cold rolling mills: Test results

“…If the parameters vary slowly, they can be estimated using various techniques, e.g. the exponential forgetting [2], directional forgetting [4] or partial forgetting [5]. Another possibility is finite data window approach, however, at the cost of higher computational burden.…”

Dynamic Diffusion Estimation in Exponential Family Models

“…For , the point estimators of and are easily reachable after partitioning the matrix into blocks [10] Then (10) The diffusion estimator is as follows: The adapt step prescribed by Proposition 2 has the form (11) The combine step is a direct application of the prescribed rules, too. The first case, the whole adapt-posterior pdfs combination using (7) and (11) reads The point estimates combination puts (10) into (8).…”

“…Since the proposed distributed estimation method is rooted in this realm, it is directly possible to use most of the elaborated Bayesian tracking methods, for instance forgetting, e.g. [10], [11] and the references therein.…”

Determining Time-Varying Drivers of Spot Oil Price in a Dynamic Model Averaging Framework

“…For example, Baur et al [16] have noticed that for their a data lower value of a forgetting factor (i.e., allowance for more abrupt coefficients' changes) resulted in smaller forecast errors. On the other hand, lower values of a forgetting factor might lead DMA model to "catch the noise", which is not a desired property [55,56].…”