On Feb 14, 4:28 pm, sturlamolden <sturlamol...@yahoo.no> wrote: > On 14 Feb, 22:02, Akand Islam <sohel...@gmail.com> wrote: > > > Hello all, > > I want to do non-linear regression by fitting the model (let say, y = > > a1*x+b1*x**2+c1*x**3/exp(d1*x**4)) where the parameter (say "c1") must > > be in between (0 to 1), and others can be of any values. How can I > > perform my job in python? > > First, install NumPy and SciPy! > > scipy.optimize.leastsq implements Levenberg-Marquardt, which is close > to the 'gold standard' for non-linear least squares. The algorithm > will be a bit faster and more accurate if you provide the Jacobian of > the residuals, i.e. the partial derivative of > > r = y - a1*x+b1*x**2+c1*x**3/exp(d1*x**4) > > with respect to a1, b1, c1, and d1 (stored in a 4 by n matrix). > > If you have prior information about c1, you have a Bayesian regression > problem. You can constrain c1 between 1 and 0 by assuming a beta prior > distribution on c1, e.g. > > c1 ~ Be(z,z) with 1 < z < 2 > > Then proceed as you would with Bayesian regession -- i.e. EM, Gibbs' > sampler, or Metropolis-Hastings. Use scipy.stats.beta to evaluate and > numpy.random.beta to sample the beta distribution. The problem is not > programming it in Python, but getting the correct equations on paper. > Also beware that running the Markov chain Monte Carlo might take a > while. > > Sturla
Dear Sturlamolden, Thanks for reply. I will follow-up if I need further assistance. -- Akand -- http://mail.python.org/mailman/listinfo/python-list
