Statistics
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Department of Mathematics & Statistics
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Yue Wang

Studying for Master of Science

Area of study:
Modeling functional data with baysian workflow

Supervisor: Matthew Parry


Email: wanyu368@student.otago.ac.nz  


Thesis

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.