Department of Economics and Business Economics

A transformation approach to modelling multi-modal diffusions

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  • Julie Lyng Forman, Department of Biostatistics, The University of Copenhagen, Denmark
  • Michael Sørensen, Department of Mathematical Sciences, University of Copenhagen, Denmark

This paper demonstrates that flexible and statistically tractable multi-modal diffusion models can be attained by transformation of simple well-known diffusion models such as the Ornstein-Uhlenbeck model, or more generally a Pearson diffusion. The transformed diffusion inherits many properties of the underlying simple diffusion including its mixing rates and distributions of first passage times. Likelihood inference and martingale estimating functions are considered in the case of a discretely observed bimodal diffusion. It is further demonstrated that model parameters can be identified and estimated when the diffusion is observed with additional measurement error. The new approach is applied to molecular dynamics data in the form of a reaction coordinate of the small Trp-zipper protein, from which the folding and unfolding rates of the protein are estimated. Because the diffusion coefficient is state-dependent, the new models provide a better fit to this type of protein folding data than the previous models with a constant diffusion coefficient, particularly when the effect of errors with a short time-scale is taken into account.

Original languageEnglish
JournalJournal of Statistical Planning and Inference
Volume146
Pages (from-to)56-69
Number of pages14
ISSN0378-3758
DOIs
Publication statusPublished - 1 Jan 2014

    Research areas

  • Diffusion, Martingale estimating function, Measurement error, Multi-modality, Protein folding, Stochastic differential equation

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