Bayesian methods for bivariate SUTSE model hyper-parameters estimation

Location: ABS Office, Preference Canberra ACT

Duration: 5 months

Proposed start date: April 2019

Project Background

The purpose of small area estimation is to borrow strength from time and auxiliary variables (administrative data without sampling error) to enhance small area estimates from the direct estimates of a repeated survey which subjects large survey sampling errors.

We proposed a bivariate seemly unrelated time series equation (SUTSE) model for the ABS LFS monthly unemployed person estimation at geographical statistical area 4 (SA4) level.   Bimodal distributions of the SUTSE model hyper-parameters were observed.  This phenomenon has been identified as a state space model (SSM) estimability problem referred in the SSM literature.  We have investigated and proposed a sensible scheme to select a suitable homogenous bivariate SUTSE model for small area estimation.

Such scheme heavily relies on the accuracy of SUTSE model hyper-parameters for the Australia total aggregated level and the homogeneity property between the SUTSE model at Australian total aggregates and SA4 levels. It is of concern that the variability of the estimated bivariate SUTSE model hyper parameters by the classical likelihood-based approach for the Australian total aggregates, and the lack of understanding their distribution properties.

This project is to explore the recent development of Bayesian multivariate structural time series model approach, Scott (2014), Rao, Qiu and Ning (2018).  These or similar Bayesian methods may provide better model hyper parameter estimation and their distribution property because the posterior distributions could be more unimodal and not as flat as the likelihood profiles produced by likelihood-based approach. However, Auger-Méthé, M. et al (2016) also warned that using Bayesian methods may not fix the estimation problems and in fact might have make them harder to detect based on their simulation study on an AR1 SSM model.

Research to be Conducted

The objective of the project is

  1. To investigate Bayesian multivariate structural time series model approach for the bivariate SUTSE model hyper-parameter estimation using two monthly series of Australian total unemployed person from ABS Labour Force Survey and the number social security benefit receivers who look for job from Department of Social Service data sets;
  2. To understand different/alternative Bayesian approaches and their performances, and recommend suitable one;
  3. To understand the hyper-parameter distribution properties and recommend mode or mean of the estimated hyper-parameters should be used for the homogenous bivariate SUTSE model at SA4 level.

The project will require a researcher with expertise in time series, state space modelling.

The ABS will provide the in-house computing environment, tools and synthetic data sets for the project.

Skills Required

It is expected that the intern will have high level programming experience in R (preferably).

Expected Outcomes

The expected outcomes of the project are:

  1. A project report addressing the key objectives,
  2. Understand the benefits of using the proposed Bayesian method,
  3. Analytical models and prototype software

It is expected that the results of this project will inform follow-on research and development work.

Additional Details

The intern will receive $3,000 per month of the internship, usually in the form of stipend payments.

It is expected that the intern will primarily undertake this research project during regular business hours, spending at least 80% of their time on-site with the industry partner.  The intern will be expected to maintain contact with their academic mentor throughout the internship either through face-to-face or phone meetings as appropriate.

The intern and their academic mentor will have the opportunity to negotiate the project’s scope, milestones and timeline during the project planning stage.

Applications Close

03 April 2019

Reference

APR – 0886