Statistical inference for periodic and partially observable poisson processes

Jovan, Ferdian (2019). Statistical inference for periodic and partially observable poisson processes. University of Birmingham. Ph.D.

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Abstract

This thesis develops practical Bayesian estimators and exploration methods for count data collected by autonomous robots with unreliable sensors for long periods of time. It addresses the problems of drawing inferences from temporally incomplete and unreliable count data.
This thesis contributes statistical models with spectral analysis which are able to capture the periodic structure of count data on extended temporal scales from temporally sparse observations. It is shown how to use these patterns to i) predict the human activity level at particular times and places and ii) categorize locations based on their periodic patterns.
The second main contribution is a set of inference methods for a Poisson process which takes into account the unreliability of the detection algorithms used to count events. Two tractable approximations to the posterior of such Poisson processes are presented to cope with the absence of a conjugate density. Variations of these processes are presented, in which (i) sensors are uncorrelated, (ii) sensors are correlated, (iii) the unreliability of the observation model, when built from data, is accounted for. A simulation study shows that these partially observable Poisson process (POPP) filters correct the over- and under-counts produced by sensors.
The third main contribution is a set of exploration methods which brings together the spectral models and the POPP filters to drive exploration by a mobile robot for a series of nine-week deployments. This leads to (i) a labelled data set and (ii) solving an exploration exploitation trade-off: the robot must explore to find out where activities congregate, so as to then exploit that by observing as many activities.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):