In this talk I will analyse the effects of various treatments on cotton aphids Aphis gossypii. The standard analysis of count data on cotton aphids determines parameter values by assuming a deterministic growth model and combines these with the corresponding stochastic model to make predictions on population sizes, depending on treatment. Here, we use an integrated stochas...
Parameter inference of ordinary differential equations from noisy data can be seen as a nonlinear regression problem, within a parametric setting. The use of a classical statistical method such as Nonlinear Least Squares (NLS) gives rise to difficult and heavy optimization problems due to the corresponding badly posed inverse problem. Gradient Matching algorithms use a smo...
Presentation: http://mbi.osu.edu/2011/rasmaterials/mbibayes20121_chow.pdf
Differential equations are often used to model biological and physiological systems. An important and difficult problem is how to estimate parameters and decide which model among possible models is the best. I will show in several examples how Bayesian and Markov Chain Monte Carlo approaches p...
Ed Ionides, Statistics, University of Michigan
Presentation: http://mbi.osu.edu/2011/rasmaterials/mbi12_ionides.pdf
Characteristic features of biological dynamic systems include stochasticity, nonlinearity, measurement error, unobserved variables, unknown system parameters, and even unknown system mechanisms. I will consider the resulting inferential ...
Douglas Bates, Department of Statistics, University of Wisconsin - Madison
Presentation (slides version): http://mbi.osu.edu/2011/rasmaterials/ProfilingD.pdf
Presentation (notes version): http://mbi.osu.edu/2011/rasmaterials/ProfilingN.pdf
The use of Markov-chain Monte Carlo methods for Bayesian inference has increased awareness of the need to ...
Most ecological models are constructed to understand the relationship between environmental variables and an ecological response, be it site occupancy or population abundance or changes to them. The usual regression models take into account the environmental variation in the response but in many cases, the measurement of the environmental variables themselves are made with...
Andrew Golightly, School of Mathematics & Statistics, Newcastle University
Presentation: http://mbi.osu.edu/2011/rasmaterials/AGmbi12.pdf
We consider the problem of performing Bayesian inference for the rate constants governing stochastic kinetic models. As well as considering inference for the resulting Markov jump process (MJP) we consider worki...
Dennis Prangle, Mathematics & Statistics, Lancaster University
Presentation: http://mbi.osu.edu/2011/rasmaterials/MBI_DennisPrangle.pdf
ABC is a powerful method for inference of statistical models with intractable likelihoods. Recently there has been much interest in using ABC for model choice and concerns have been raised that the results are not...
A central challenge in computational modeling of dynamic biological systems is parameter inference from experimental time course measurements. Here we present an overview of the modeling approaches based on stochastic population dynamic models and their approximations. For an application on the mesoscopic scale, we present a two dimensional continuous-time Bayesian hierarc...
Dynamic models of biochemical networks contain unknown parameters like the reaction rates and the initial concentrations of the compounds. The large number of parameters as well as their nonlinear impact on the model responses hampers the determination of confidence regions for parameter estimates. At the same time, classical approaches translating the uncertainty of the p...
Bursting is a ubiquitous phenomenon in neuroscience which involves multiple time scales (fast spikes vs. long quiescent intervals). Parameter estimation for bursting models is difficult due to these multiple scales. I will describe an approach to parameter estimation for these models which utilizes the geometry underlying bursting. This is joint work with John Guckenheimer...