Update README.md

Author: maxbiostat

Undegraduate/README.md

@@ -42,6 +42,8 @@ Trabalho em conjunto com [Guido Moreira](https://github.com/GuidoAMoreira).
 
 Habilidades a serem desenvolvidas: programação científica em Python e C.
 
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 A3) **Análise conjunta de sensibilidade e especificidade de testes diagnósticos**
 
 Testes diagnósticos em geral são imperfeitos, isto é, detectam a condição de interesse com certas características de operação (sensibilidade e especificidade). Neste projeto vamos coletar e analisar dados de meta-análises sob diferentes modelos para a distribuição conjunta da sensibilidade e especificidade de testes diagnósticos para doenças. Vamos testar modelos beta bivariados e baseados em variáveis latentes gaussianas.
@@ -80,13 +82,16 @@ References: [Chira & Thomas (2016)](https://www.ncbi.nlm.nih.gov/pmc/articles/PM
 
 Skills to be developed: Statistical phylogenetics, Bayesian statistics, JAVA.
 
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 T3) **Studying phylogenetic distances for time-calibrated trees**
 Time-calibrated phylogenies are central objects in Molecular Epidemiology and Phylodynamics.
 Computing distances between trees is fundamental task in the analysis of samples of trees ([Smith, 2022](https://academic.oup.com/sysbio/article/71/5/1255/6486431)), but there is no canonical distance in the space of phylogenies.
 Faced with many choices of metric, what is the analyst to do? In this project the student will start by investigating an easily computable metric on phylogenies proposed by [Kendall & Coljin (2015)](https://arxiv.org/abs/1507.05211). The KC metric takes a convex combination `lambda*TD + (1-lambda)*BD`, where `TD` and `BD`are "topological" and "branch length" distances, respectively. The task is to figure out how to calibrate the free parameter `lambda` automatically such that distances capture important features.
 
 Skills to be developed: Computational statistics, Statistical phylogenetics.
 
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 A1) **Survival and reproductive analysis of _Rhodnius prolixus_, the Chagas disease vector**
 
@@ -99,18 +104,24 @@ References: [Carvalho, Struchiner & Bastos (2015)](https://github.com/maxbiostat
 
 Skills to be developed: Applied Statistics, Bayesian statistics, survival analysis, R.
 
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 A2) **PhyloPosteriorDB: a collection of curated phylogenetic data sets for method development**
 
 Having a set of curated, well-studied and realistic data sets is a great asset for the development of new analytical methods. In particular, Markov Chain Monte Carlo (MCMC) can be challenge to develop and test without a reliable benchmark. Inspired by the [**posteriordb**](https://github.com/stan-dev/posteriordb) project, the student will improve and expand [**this**](https://github.com/maxbiostat/MEP_data) collection of rich, real-world data sets in order to provide the [Phylogenetics community](https://www.phylobabble.org/) with easy-to-use data to check their new methods against. The student will also develop novel memmory-efficient ways of storing large posterior samples of trees that can be accessed and used for further processing. 
 
 Skills to be developed: [BEAST](https://github.com/beast-dev/beast-mcmc), Database programming, Statistical Phylogenetics.
 
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 A3) **Rao-Blackwellising Bayesian Stochastic Search Variable Selection**
 
 In statistical applications with limited data, it is important to enforce _regularisation_, that is to encode parsimony into the modelling process so that our models do not overfit the data and lose predictive power. Moreover, it is important to encode _sparsity_, that is the notion that big effects are few and far between, floating in a sea of irrelevance. In this project, we will return to basics and give the **Bayesian Stochastic Search Variable Selection (BSSVS)** model of [George & Mcculloch (1993)](https://people.eecs.berkeley.edu/~russell/classes/cs294/f05/papers/george+mcculloch-1993.pdf) a modern spin. In particular, we will marginalise over the discrete predictor assigments, effectively providing a Rao-Blackwellised version of the model. Implementation will be done in the [Stan](https://mc-stan.org/) probabilistic programming language. In particular, we will investigate how to exploit massive parallelisation in the form of the [`reduce_sum`](https://mc-stan.org/docs/2_23/stan-users-guide/reduce-sum.html) in order to speed things up.
 
 Skills to be developed: Stan and C++ programming, Bayesian statistics. 
 
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 A4) **Fitting generalised joint models in Stan** 
 
 In many applications one has more than one set of temporally-structured data on a set of subjects.
@@ -126,5 +137,3 @@ We will then apply these routines to problems in environmental epidemiology, mod
 
 Skills to be developed: Bayesian statistics, R, Stan, C++.
 Co-supervised with Professor [Claudio Struchiner](https://emap.fgv.br/professores/claudio-jose-struchiner).
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