Carson Chow

• 
  Using Bayesian and MCMC approaches for parameter estimation and model evaluation in physiology
  Carson Chow
  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 provide a self-consistent framework to do both tasks. In particular, Bayesian parameter estimation provides a natural measure of parameter sensitivity and Bayesian model comparison automatically evaluates models by rewarding fit to the data while penalizing the number of parameters.
• 
  Finite-size effects in neural networks
  Carson Chow
  The dynamics of neural networks have traditionally been analyzed for small systems or in the infinite size mean field limit. While both of these approaches have made great strides in understanding these systems, large but finite-sized networks have not been explored as much analytically. Here, I will show how the dynamical behavior of finite-sized systems can be inferred by expanding in the inverse system-size around the mean field solution. The approach can also be used to solve the inverse problem of inferring the effective dynamics of a single neuron embedded in a large network where only incomplete information is available. The formalism I will outline can be generalized to any high dimensional dynamical system.