4.5.2019 New computational method allows for exact calculation and statistical estimation of multi-dimensional random processes observed in nature

Computer-age statistical inference is redefining the limits of what is possible to estimate or predict in the universe in the big data era. Hash tags include machine learning and Bayesian statistics. In his doctoral thesis at the Ģֱ, M.Sc. Jordan Franks has worked on computationally efficient methods to understand the relationship of unknown variables from known data.
Published
4.5.2019

Consider the nonlinear random motion of a fish submerged in a lake, and observed from the surface with distortion and noise every hour.  Where does the fish spend most of its time in a year, and at what depth?  Using the method developed in Jordan Franks’ thesis, the answer for such continuous-time models with discrete-time observations can be calculated with vanishing error on a computer.  The method is based on random number generation, movement approximations, and probabilistic correction methods, and is an example of a so-called Markov chain Monte Carlo importance sampler. 

Previous state-of-the-art methods could only be used for some 1-dimensional problems, while the approach introduced in the thesis allows for exact calculation for such problems regardless of dimension.  This has relevance to our example of fish in lakes, since lakes are 3-dimensional.

Jordan Franks completed his master degree in mathematics at the University of Bonn, Germany, in 2016.  He started doctoral studies in the Department of Mathematics and Statistics at the Ģֱ in April 2016.  He has worked with his adviser, Academy Research Fellow and Associate Professor Matti Vihola, in the Academy of Finland research project ‘Exact approximate Monte Carlo methods for complex Bayesian inference.’

Master in Mathematics Jordan Franks will defend his doctoral dissertation in computational Statistics with the title “Markov chain Monte Carlo importance samplers for Bayesian models with intractable likelihoods” on Saturday 4th of May at Seminaarinmäki (H320) at 12 o’clock.  The opponent is Professor Nicolas Chopin (ENSAE, France) and the custos is Matti Vihola.  The language of the event is English.

The dissertation is published in JYU Dissertations series, Ģֱ, N:o. 79. ISBN: 978-951-39-7738-2

Link to publication: 

More information:

Doctoral Student Jordan Franks, jordan.j.franks@jyu.fi

Communications Officer Tanja Heikkinen, tanja.s.heikkinen@jyu.fi, tel. +358 50 581 8351

Faculty of Mathematics and Science