Topic: Non-parametric bootstrapping of diffusion models with application to testing the Markov hypothesis
Speaker: Julie L. Forman, University of Copenhagen
Time: Monday, October 16, 14:00-15:00
Place: Room 217, Guanghua Building 2
Diffusion models are often used to describe the evolution of continuous time systems. However, a drift and diffusion term that describes the short-term evolution of a system may fail to predict the long-term evolution if the true data-generating process is not a Markov process.
Several tests of the Markov hypothesis have been proposed in the literature, for instance Ait-Sahalia, Fan & Jiang (2010) proposed a $chi^2$-type test for checking whether non-parametric estimates of the transitions densities agree with the Chapman-Kolmogorov equations. Unfortunately in finite samples the distribution of the test statistic may be far from the asymptotic $chi^2$-distribution. In this talk we propose a non-parametric bootstrap for stationary univariate diffusions which allows for unbiased inference from tests such as this. The key-idea is to sample from a discrete time Markov-chain on the set of observed data points and with transition matrix specified in accordance with non-paramtric estimates of the conditional cumulative distribution function for the observed transitions. We demonstrate in a simulation study that the non-parametric bootstrap match the distribution of the test statistic for the Markov hypothesis well in moderate size samples. Finally we apply the bootstrap to molecular dynamics data in which we show that attempts to infer the mean passage times between the modes of a bimodal system may lead to gross underestimation when based on a diffusion model.
Ait-Sahalia, Fan & Jiang: Nonparametric tests of the Markov hypothesis in continuous-time models, Ann. Stat, 38, 2010.
Forman & Sørensen: A transformation approach to modelling multi-modal diffusions, J.Stat. Planning & Inference, 346, 2014.
Dr. Julie Forman is an associate professor at the Section of Biostatistics, University of Copenhagen. Her research interests focus on stochastic dynamic models, longitudinal data analyses, mixed models, and applied statistics in biomedicine and medical science. Dr Forman has 10 years experience as a statistical consultant and teacher at the Medical school of the university of Copenhagen and has been engaged in numerous collaborative research projects in medicine, biomedicine and public health research. Together with Umberto Picchin, Centre of Mathematical Science, University of Lund she is currently the co-holder of a grant from the Swedish research council to investigate statistical modeling of protein folding. Julie Forman was awarded the Danish delegate for the European Young Statisticians meeting 2017 after completing her Ph.d. at the Department of Mathematical Sciences, University of Copenhagen.
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