ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

Analysing Data Streams of Doubtful Provenance

12 September 2017, 18:40 – 19:00


Submitted by
Kavya Jagan
Kavya Jagan (National Physical Laboratory), Alistair Forbes (National Physical Laboratory)
With the advent of the Internet of Things, sensors have become more ubiquitous. Each sensor creates a data stream and vast quantities of data can be collected every day from sensors networks, creating multiple data streams. The sensors may have been calibrated prior to installation but their performance in the field may be compromised. Hence, it may be prudent to regard the data from such a sensor as that of doubtful provenance; we may have an estimate of the uncertainty of the data (based on a prior calibration) but may not know how good that estimate is of the actual performance in the field.

This paper addresses the issue of how to make inferences about model parameters based on data from multiple streams, each of doubtful provenance. The data is modelled as a linear response subject to Gaussian noise and an estimate of the uncertainty, presented by a variance parameter for each stream, is known. In order to account for the unknown provenance of the data, Bayesian hierarchical models are used. Hyper parameters of a Gamma distribution are used to encode degree of belief in uncertainty statements. In this way, information on the variance can be updated based on the data. This method is a parallel to statistical transfer learning and using the degree of belief term as a hyper parameter is akin to using power priors.

The Bayesian posterior distribution for such hierarchical models cannot be expressed analytically in closed form and a Metropolis-Hastings algorithm is used to sample from the posterior distribution. This method is illustrated on coordinate metrology data and sensor collocation study data.
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