Efficient MCMC for Continuous Time Discrete State Systems A variety of phenomena are best described using dynamical models whichoperate on a discrete state space and in continuous time. Examplesinclude Markov jump processes, continuous time Bayesian networks,renewal processes and other point processes, with applications rangingfrom systems biology, neuroscience, genetics, computing networks andhuman-computer interactions. Posterior computations typically…

Towards Uncertainty Quantification and Inference in the stochastic SIR Epidemic Model We introduce a novel method to conduct inference with models defined through a continuous-time Markov process, and we apply these results to a classical stochastic SIR model as a case study. We obtain approximations for first and second moments for the state variables. These…

Symmetries of probability distributions, their geometric meaning and financial applications The talk starts with the known put-call symmetry property and its application to semi-static hedging of barrier options. Then it is explained how to interpret this property geometrically and extend it in various ways, most importantly for the multivariate (multiasset) case that would correspond to…

A Bayesian analysis of reversible time series with an uncertain length of memory We propose a Bayesian analysis of reversible time series using a Probabilistic Suffix Automaton (PSA) model. We show that PSAs have a representation as higher-order Markov chains, and that the class of reversible PSAs generalize reversible variable-order Markov chains. The analysis uses…

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