Mathematics
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Department of Mathematics & Statistics
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Paula Bran Cardona

Studying for Doctor of Philosophy

Area of study:
Properties of gibbs samplers used for inference using genetics markers in capture-recapture models.

Supervisor: Richard Barker


Email: pbran@maths.otago.ac.nz  


Thesis

Title: Properties of Gibbs sampler used for inference using genetic markers in capture-recapture models.

Supervisors: Richard Barker and Matthew Schofield

Previous Degrees:

  • Bachelor in Mathematics (Universidad de Antioquia, Medellín, Colombia),
  • Master in Mathematics (Universidad de Antioquia, Medellín, Colombia).

I shifted to Bayesian statistics after beign studying some multivariate distributions. Now I am studying the convergence properties of the Markov chains generated by a Gibbs sampler implemented in order to estimate animal abundance using non-invasive DNA samples. Convergence is important because we need to ensure that a stationary distribution exists and that it coincides with the target (posterior) distribution. A necessary condition for convergence is irreducibility which is the freedom to move between any pair of states of the chain. The positivity condition is a sufficient condition for irreducibility of a Gibbs Markov chain, however it does not hold in this case. Thus, we are studying issues related with the efficiency of specific algorithms, including irreducibility and reversibility of the Markov chain for models in this class.