Post date: 24-Jan-2014 18:17:40
* 15h, Didier Chauveau, Université d'Orléans
Simulation Based Nearest Neighbor Entropy Estimation for (Adaptive) MCMC Evaluation
(joint work with Pierre Vandekerkhove)
Many recent (including adaptive) MCMC methods are associated in practice to unknown rates of convergence. We propose a simulation-based methodology to estimate MCMC efficiency, grounded on a Kullback divergence criterion requiring an estimate of the entropy of the algorithm successive densities, computed from iid simulated chains. We recently proved in Chauveau and Vandekerkhove (2012) some consistency results in MCMC setup for an entropy estimate based on Monte-Carlo integration of a kernel density estimate based on Gyorfi et al. (1989).
Since this estimate requires some tuning parameters and deteriorates as dimension increases, we investigate here an alternative estimation technique based on Nearest Neighbor (NN) estimates. This approach has been initiated by Kozachenko et al. (1987) but used mostly in univariate situations until recently when entropy estimation has been considered in other fields like neuroscience. We show that in MCMC setup where moderate to large dimensions are common, this estimate seems appealing for both computational and operational considerations, and that the problem inherent to a non neglictible bias arising in high dimension can be overcome. All our algorithms for MCMC simulation and entropy estimation are implemented in an R package taking advantage of recent advances in high performance (parallel) computing.
* 16h15, Adeline Samson, Université Joseph Fourier, Grenoble
Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods
(joint work Susanne Ditlevsen, Copenhagen University)
Parameter estimation in multi-dimensional diffusion models with only one coordinate observed is highly relevant in many biological applications, but a statistically difficult problem. The coordinates are coupled, i.e. the unobserved coordinate is non-autonomous. Therefore the hidden Markov model framework is degenerate, and available methods break down. We propose a sequential Monte Carlo particle filter algorithm to impute the unobserved coordinate, and then estimate parameters maximizing a pseudo-likelihood through a stochastic version of the Expectation-Maximization algorithm.
An experimental data set of intracellular recordings of the membrane potential of a spinal motoneuron of a red-eared turtle is analyzed, and the performance is further evaluated in a simulation study.