Non-linear regression help in Python

[Akand Islam]

On Feb 14, 4:28 pm, sturlamolden <sturlamol... at yahoo.no> wrote:
> On 14 Feb, 22:02, Akand Islam <sohel... at 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