It is common that target variables distribute diversely and sparsely in geographical space. This results in noisy estimates, make it difficult to interpret results. In such situations, small area estimation techniques could help reduce the standard error to an acceptable rate, through borrowing strength over related areas, considering spatial effects, and smoothing parameter estimates. However, most small area estimation methods will give a point estimate or a range estimate with crude confidence intervals. Two approaches have been proposed which can provide distributions around the estimates produced by small area estimation. M-quantile provide robust technique of summarising the distribution of data in a classical likelihood-based (frequentist) framework. Alternatively, Bayesian small area estimation can help in the task of providing good quality small area estimates, and the model uncertainty is automatically captured by the posterior distribution. However, it is relatively rare to make estimation on more than one outcome, especially when estimating the joint distribution for two target variables. This could not only give a deeper understanding about the variables, but also provide an essential base for “what if” policy scenario analysis. 

In this light, this research aims to: (1) extend M-quantile method for a multivariate (two-way outcome) setting under spatial effect assumptions; (2) construct joint posterior of estimators using Bayesian hierarchical models with spatial-temporal effects; (3) illustrate both methods with innovative mapping of smoking prevalence rate and disadvantage level data; (4) make a comparison and discussion of how the different approaches improve the final estimates.

Mu Li is currently a PhD candidate in School of Demography at the Australian National University. He received a master’s degree in Research School of Finance, Actuarial Studies and Statistics from ANU in 2020.  

His main research interest focused on small area estimation on focusing on establishing model with spatial effects, like the childhood development level, the socio-economic status, and the smoking prevalence in Australia. It is his honor to join the SPARSE (Smoking Prevalence for Australia with Reliable Small Area Estimation) research team and School of Demography in ANU.