Post-doctorat en statistique

Summary description of the project :

In many applications where data is collected over time from several individuals, whether the data is continuous or counted, it may contain an excess of zeros, due to non-use of the device or malfunction of the data transmission. This is the case, for example, in genomics for clinical data on the use of medical devices, etc.

The aim of the project is to propose a method of clustering individuals according to their temporal behaviour. These excess zeros make statistical analysis difficult.

Our proposal is to use a model mixing a Hidden Markov Model approach and a mixture of distributions with a Dirac in zero to solve simultaneously the problem of taking into account the zeros and the clustering objective.

Missions/functions provided :

The objective will be to develop the estimation method for the Hidden Markov Model coupled to a mixture model between a continuous distribution and a Dirac in zero. For this, an EM algorithm will be developed, as well as its implementation in R or Python. Extensions to continuous or discrete distributions will be considered, as well as the introduction of random effects.

Main activities :

     Development of maximum likelihood estimation methods

Development of a package allowing the scaling up (programming in C++, parallelization)

Theoretical study of the estimator: identifiability, asymptotic properties