The insufficient informativeness of measurements in Bayesian detection problems

Overview

Shiryaev's Bayesian Quickest Change Detection (QCD) problem is to detect a change in the statistical problems of an observed process. This is an important signal processing problem with application in a diverse range of areas, including:

• automatic control
• quality control
• statistics
• target detection.

Recently a critical deficiency in Shiryaev's QCD problem has been identified to occur due to the insufficient informativeness of measurement in low signal-to-noise (SNR) to overcome geometric prior assumption on the change event.

These deficiencies are due to the non-ergodic nature of the model underlying Shiryaev’s problem with results in the measurement being ignored.

The issues arising from non-ergodic signal problems are not limited to the Shiryaev's Bayesian QCD problem and have already been shown to occur in detection and isolation problems. We believe these issues are occurring in applications with the left-to-right models such as (historically) those used in natural language processing and in industry equipment condition monitoring.

To avoid this feature of QCD, an alternative intermittent signal detection (ISD) problem has been proposed which considers an (ergodic) detection problem that allows repeating change events. Moreover, these ISD approaches have been shown to be extremely effective detecting low SNR change events (in vision based detection problems).

Research activities

This PhD project will identify, characterise and create new solutions to a number of signal processing problems where the non-ergodic signal model is used.

This includes looking at:

• the mathematics of statistical processing, such as Markov chain
• probability and mathematical expectation operations
• dynamic programming/recursion equations.

Some algorithm development and data analysis will take place during this project. Likely MATLAB will be enough for what we're looking to achieve.

View an example of the types of mathematics that will be used

View an example of the types of applications that will be used

Outcomes

We expect the research project to produce:

• new algorithms to better solve a range of change-detection problems
• new mathematics that characterise the deficiencies of a range of detection problems and the properties of newly proposed approaches.

Skills and experience

For this student topic we expect you to have the following skills:

• mathematics, or the willingness to learn
• MATLAB programming
• data analysis.

Scholarships

You may be eligible to apply for a research scholarship.

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Contact

Contact the supervisor for more information.