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A graphical model is an approach which uses a graph to represent the conditional dependence between random variables.. In this project, we focus on undirected graphical models. The graph contains nodes which correspond to variables, and edges which connect some pairs of nodes. The absence of an edge between two nodes means that the corresponding variables are independent given the values of all remaining variables.
Graphical models have been applied in many fields, such as bioinformatics, image processing and statistical machine learning. However, there are few methods available for time-varying data. This project provides a method to analyse graphical models with continuous longitudinal data that we assume data come from a multivariate normal distribution and covariance matrices that change with time. One challenge is to estimate parameters by maximising the non-linear likelihood equations. We use method of moments estimators to initialise the parameters and Barzilai-Borwein iteration methods with constraints to maximise the likelihood.
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