[Forum SIS] Statistics and Probability Seminars @University of Nottingham: Karthik Bharath (3pm Italian time)

[Fabrizio Leisen]

Con preghiera di diffusione.

*Italian time: 15:00*

Cordiali Saluti,
Fabrizio

Dear All,

the Statistics and Probability group at the University of Nottingham
organize a series of internal seminars which will be available to anyone
interested, even outside the University of Nottingham.

Our next speaker is Karthik Bharath. Seminar date and time: *4**th* * of
March at 2pm. *

Below you can find the Abstract and Title. Furthermore, you can find the
Teams link to join the seminar.

Best Wishes,

Fabrizio Leisen
Professor of Statistics
University of Nottingham
School of Mathematical Sciences
University Park, Nottingham, NG7 2RD, UK

http://sites.google.com/site/fabrizioleisen/

You are cordially invited to the following seminar:


Karthik Bharath
<https://www.nottingham.ac.uk/mathematics/people/karthik.bharath> (Internal
Seminar) ----> 4th of March *at 2pm*


Title: Shape space and models for functional data


Abstract: Statements such as “death rate curve needs to remain single
peaked”; “we expect the second peak of infected cases to be smaller
compared to the first”, are, unfortunately, all too familiar nowadays. They
represent instances of informal descriptions of shapes of functions we can
relate to readily, wherein the notion of shape relates exclusively to ‘y
direction’ variation. To formalise this, in this talk, I will consider a
group-theoretic description of the shape of a function as that which is
left behind once ‘x direction’ variability is ignored: only the number and
values of local extrema are relevant to describe its shape and not their
timings. Accordingly, the shape of a function is shown to be uniquely
encoded by a polynomial, and this connection allows us to study structural
aspects of the shape space of functions.



For statistical analysis of functional data (e.g., densely sampled multiple
time series data) the upside to this perspective is that (i) a natural
dimension reduction mechanism based on local extrema becomes available when
analysing amplitudes that avoids the task of registering (or aligning) the
data; and (ii) simple finite-dimensional generative shape models can be
defined. On the other hand, geometry of the shape space is complicated, and
this makes it difficult to compute descriptive statistics (e.g., average
shape) and study models induced on the shape space from the original
(simpler) function space.



This is joint work with Ian Jermyn (Durham).
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-- 
Fabrizio Leisen
Professor of Statistics
University of Nottingham
School of Mathematical Sciences
University Park, Nottingham, NG7 2RD, UK

http://sites.google.com/site/fabrizioleisen/
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