Studying for Master of Science
Area of study:
Modeling functional data with baysian workflow
Supervisor: Matthew Parry
Title: Modeling functional data with baysian workflow
Supervisor M Parry
In many cases of statistical interest, observations can be viewed as measurements taken at
different times of an underlying unknown function. In health-related fields, such measurements
may be crucial to the health and well-being of patients. For example, measurements
over time of mean arterial blood pressure in pregnant women may help doctors gauge the
risks of pre-eclampsia or low birth weight. In this case, the goal is the construction of an
individual profile so that any changes in the response can be noted quickly. In a sense, the
individual acts as their own referee.
For each individual, the response variable is viewed as a vector of measurements in
a fixed time interval. The underlying function is modelled in terms of a set of basis
functions, with a sparse latent factor regression model introduced for the coefficients of
the basis functions.
Bayesian methods are used to quantify uncertainty in observations, model parameters
and model structure. More precisely, a full Bayesian workflow is implemented
that includes inference but also progressive model building, model checking, validation
and troubleshooting problems in computation, understanding the model, and model comparison.
As Bayesian models are complex in nature, it is imperative their performance
can be practically evaluated. Pareto smoothed importance sampling leave one out crossvalidation
is used because it does not require refitting the model multiple times with different
subsets of the data. This is applied to the problem of model selection, especially
the determination of the number of latent factors in the model.