<div dir="ltr"><div class="gmail_quote gmail_quote_container"><br><br><div dir="ltr"><div><p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"><span lang="EN-US">Dear colleagues, </span></p>

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<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"><span lang="EN-US">Our next
seminar will be held on Monday, November 24,<b> </b>from <b>3:30 p.m. to 4:30 p.m</b>. (Rio de
Janeiro local time).  The meeting will
take place at room <b>C116- Bloco C - CT</b></span><b><span lang="DE"> – Instituto de Matemática – UFRJ. </span></b><span lang="DE">There will be no transmission online. </span><b><span lang="EN-US"></span></b></p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"><span lang="DE"> </span></p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"><span lang="EN-US">Speaker: <b>  </b>Rodrigo
Barreto Alves (UERJ)</span></p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"><span lang="EN-US">Title: </span><b>On
the lumpability of tree-valued Markov chains</b><b><span lang="EN-US"></span></b></p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"><span lang="EN-US">Abstract: </span></p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif">Phylogenetic trees
constitute an interesting class of objects for stochastic processes due to the
non-standard nature of the space they inhabit.</p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif">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.</p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif">We investigate
whether certain lower-dimensional projections of tree space preserve the Markov
property in tree-valued Markov processes.</p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif">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.</p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif">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.</p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"> </p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"><span lang="EN-US">More complete information about the seminars can be found at</span></p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"><span lang="EN-US"><a href="https://ppge.im.ufrj.br/seminarios-de-probabilidade/" target="_blank">https://ppge.im.ufrj.br/seminarios-de-probabilidade/</a></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"><span lang="EN-US">Sincerely, </span><span lang="EN-US"></span></p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"><span lang="EN-US">Organizers: Giulio Iacobelli and Maria Eulalia Vares</span></p>

<p class="MsoNormal" style="margin:0cm 0cm 8pt;line-height:107%;font-size:11pt;font-family:Aptos,sans-serif"><span lang="EN-US"> </span></p></div><span class="gmail_signature_prefix">-- </span><br><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr">Maria Eulalia Vares<div>Professora Titular - Instituto de Matemática - UFRJ</div><div>Coordenadora do Programa de Pós-Graduação em Estatística</div><div><a href="https://ppge.im.ufrj.br/" target="_blank">https://ppge.im.ufrj.br/</a></div><div><br></div></div></div></div>
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