Improving grid-based Bayesian methods using Low Discrepancy Sequences

Paul Tamataatoi Brown (Waikato, Ngaati Hikairo), University of Waikato

I am currently at the final stages of writing up the thesis. The submission deadline for the thesis is 31st May 2018, which we are currently on target for. We plan to disseminate our research through two separate journal papers. The first paper is titled “Improving grid-based Bayesian methods using Low Discrepancy Sequences”, which will be submitted to the international journal “Bayesian Analysis”. 

The second paper will be titled “The incorporation of physical barriers in a spatio temporal model of crime”, with the current aim of submitting this to the journal “Australian and New Zealand Journal of Statistics”. b. the innovations and significance of the work Statistical analyses of data using a Bayesian approach allows a researcher to combine prior knowledge about the phenomena being measured with the current data. Bayesian inference holds many advantages of more classical approaches to inference, but it has computational drawbacks. 

Our research deals with the computational issues surrounding the construction and analysis of complex models under the Bayesian paradigm. Several methods have been proposed using so called grid-based methods, which have had some success in speeding up the computational process. We show that you can do better using a type of deterministic pointset known as low discrepancy sequences. We have constructed the methodology and the necessary algorithms to perform Bayesian inference using low discrepancy sequences. 

Along with a methodology known as the Integrated-Nested Laplace Approximations (INLA), we use our new method on an original example of modelling crime in Hamilton which incorporates space and time factors, and also takes into account physical barriers such as Lake Rotoroa and the Waikato river. 

The aim is to use this model to predict future hot-spots of crime, and perhaps more importantly, to test the predictive capabilities of such a model. Testing the predictive capabilities properly informs us if the model is a suitable tool for policing use. c. how the objectives will be achieved (specific targets) 

The objective is to complete the final draft of the thesis by 1st May, and have it ready for submission by the 31st May. This gives some time to start writing up both papers which we hope to have submitted before the 30th June. The writing of the first paper is already in progress and we aim to have that complete before the submission of the thesis. The second paper is based off the final chapter of the thesis, so we plan to submit this before the end of June. d. the nature and extent of collaboration We have collaborated with Professor Havard Rue from Trondheim University, Norway (now a Professor at the King Abdullah University of Science and Technology, Saudi Arabia). 

Professor Rue is the main person behind the development of the INLA methodology, a very successful grid based method for Bayesian inference which is widely used throughout the world. We were invited to Saudi Arabia to work alongside him in the development of our own methodology, and he will be a contributing author in our first paper. We have also collabor