Bayesian size-and-shape regression modelling
Gabriele Sega
Bayesian size-and-shape regression modelling.
Rel. Enrico Bibbona, Gianluca Mastrantonio. Politecnico di Torino, Corso di laurea magistrale in Ingegneria Matematica, 2024
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Abstract
Bayesian shape and size regression modellingStatistical shape analysis is a well-known branch of statistics that aims at inferring on objects' shape. The aim of this work is to implement already known methods, with some slight modifications when needed, and use them to make some simulations on synthetic and real datasets. This branch of statistics involves many other topics in mathematics, such as linear algebra, Markov Chains, MCMC algorithms and calculus. \par At first, some examples are presented: many practical applications of statistical shape analysis come from the biological framework and are useful to justify the need for such flexible methods that will be presented during the work.
Secondly, the problem of defining a correct mathematical framework for size-and-shape will be assessed, by reporting and reviewing the available literature, with particular care to Mardia’s work
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