Bayesian for curve fitting

Hi, I am trying to fit the data to a model: Signal = a*exp(-R1*t)+b*exp(-R2*t). The parameters to obtain are R1, R2, a and b. R1 and R2 are more important. There are 12 Signals at 12 time points. I would like to use Bayesian Probability Theory to obtain R1, R2, a and b. I have been reading this page about Bayesian Analysis for a Logistic Regression Model. But I haven't figured out how to form the prior distribution, the posterior distribution, or maximum likelihood for my question. This page on Curve Fitting and Distribution Fitting may also be related.

May someone teach me the essence of Bayesian Analysis for data fitting, or let me know how you implement Bayesian method in Matlab to estimate parameters? Many thanks!

Bayesian Spectrum Analysis and Parameter Estimation: http://bayes.wustl.edu/glb/book.pdf