arXiv subjects

James Bentham

Publications and source records attributed to James Bentham.

2 recordsLinked to original sources

arXiv2021

Scaling priors in two dimensions for Intrinsic Gaussian MarkovRandom Fields

Intrinsic Gaussian Markov Random Fields (IGMRFs) can be used to induce conditional dependence in Bayesian hierarchical models. IGMRFs have both a precision matrix, which defines the neighbourhood structure of the model, and a precision, or scaling, parameter. Previous studies have shown the importance of selecting this scaling parameter appropriately for different types of IGMRF, as it can have a substantial impact on posterior results. Here, we focus on the two-dimensional case, where tuning of the parameter is achieved by mapping it to the marginal standard deviation of a two-dimensional IGMRF. We compare the effects of scaling various classes of IGMRF, including an application to blood pressure data using MCMC methods.

stat.CO↗

arXiv2021

A Two-Dimensional Intrinsic Gaussian Markov Random Field for Blood Pressure Data

Many real-world phenomena are naturally bivariate. This includes blood pressure, which comprises systolic and diastolic levels. Here, we develop a Bayesian hierarchical model that estimates these values and their interactions simultaneously, using sparse data that vary substantially between countries and over time. A key element of the model is a two-dimensional second-order Intrinsic Gaussian Markov Random Field, which captures non-linear trends in the variables and their interactions. The model is fitted using Markov chain Monte Carlo methods, with a block Metropolis-Hastings algorithm providing efficient updates. Performance is demonstrated using simulated and real data.

stat.ME↗