[ABE-L] Seminário de Probabilidade - IM-UFRJ - 24 de novembro - Rodrigo Barreto Alves

[Maria Eulalia Vares]

Dear colleagues,



Our next seminar will be held on Monday, November 24, from *3:30 p.m. to
4:30 p.m*. (Rio de Janeiro local time).  The meeting will take place at
room *C116- Bloco C - CT** – Instituto de Matemática – UFRJ. *There will be
no transmission online.



Speaker:   Rodrigo Barreto Alves (UERJ)

Title: *On the lumpability of tree-valued Markov chains*

Abstract:

Phylogenetic trees constitute an interesting class of objects for
stochastic processes due to the non-standard nature of the space they
inhabit.

In particular, many statistical applications require the construction of
Markov processes on the space of trees, whose cardinality grows
superexponentially with the number of leaves considered.

We investigate whether certain lower-dimensional projections of tree space
preserve the Markov property in tree-valued Markov processes.

We study exact lumpability of tree shapes and $\varepsilon$-lumpability of
clades, exploiting the combinatorial structure of the SPR graph to obtain
bounds on the lumping error under the random walk and Metropolis-Hastings
processes.

Finally, we show how to use these results in empirical investigation,
leveraging exact and $\varepsilon$-lumpability to improve Monte Carlo
estimation of tree-related quantities.



More complete information about the seminars can be found at

https://ppge.im.ufrj.br/seminarios-de-probabilidade/

Sincerely,

Organizers: Giulio Iacobelli and Maria Eulalia Vares


-- 
Maria Eulalia Vares
Professora Titular - Instituto de Matemática - UFRJ
Coordenadora do Programa de Pós-Graduação em Estatística
https://ppge.im.ufrj.br/
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