Attribution

If you use this software for your research, please cite at least Cappellari et al. (2013) where the implementation was introduced. The BibTeX entry for the paper is:

@ARTICLE{Cappellari2013a,
    author = {{Cappellari}, M. and {Scott}, N. and {Alatalo}, K. and
        {Blitz}, L. and {Bois}, M. and {Bournaud}, F. and {Bureau}, M. and
        {Crocker}, A.~F. and {Davies}, R.~L. and {Davis}, T.~A. and {de Zeeuw},
        P.~T. and {Duc}, P.-A. and {Emsellem}, E. and {Khochfar}, S. and
        {Krajnovi{\'c}}, D. and {Kuntschner}, H. and {McDermid}, R.~M. and
        {Morganti}, R. and {Naab}, T. and {Oosterloo}, T. and {Sarzi}, M. and
        {Serra}, P. and {Weijmans}, A.-M. and {Young}, L.~M.},
    title = "{The ATLAS$^{3D}$ project - XV. Benchmark for early-type
        galaxies scaling relations from 260 dynamical models: mass-to-light
        ratio, dark matter, Fundamental Plane and Mass Plane}",
    journal = {MNRAS},
    eprint = {1208.3522},
    year = 2013,
    volume = 432,
    pages = {1709-1741},
    doi = {10.1093/mnras/stt562}
}

Installation

install with:

pip install adamet

Without writing access to the global site-packages directory, use:

pip install --user adamet

Documentation

The documentation is in the docstring of the file adamet.py or on PyPi.

AdaMet Purpose

This is the implementation by Cappellari et al. (2013) of the Adaptive Metropolis algorithm by Haario H., Saksman E., Tamminen J. (2001) for Bayesian analysis.

Usage Example

To learn how to use AdaMet run the example program in the adamet/examples directory, within the main package installation folder inside site-packages, and read the detailed documentation in the docstring of the file adamet.py or on PyPi.

Note: For dimensions = 1 to 6, the optimal acceptance rates are rate = [0.441, 0.352, 0.316, 0.279, 0.275, 0.266] and the asymptotic value for many parameters is 23%

Calling Sequence

pars, lnprob = adamet(lnprob_fun, pars, sigpars, bounds, nstep,
    fignum=None, inline=True, labels=None, labels_scaling=1,
    nprint=100, plot=True, quiet=False, seed=None, args=(), kwargs={}):

Parameters

lnprob_fun: callable

This function returns the natural logarithm of the conditional probability of the model, given the data. The probability does not need to be normalized as only relative probabilities matter. For this reason, inclusion of an arbitrary additive constant in lnprob_fun leaves the output of AdaMet unaffected:

P(model | data) ~ P(data | model)*P(model)

pars0: array_like, shape (n,)

vector with the mean of the multivariate Gaussian describing the proposal distribution from which samples are drawn. For maximum efficiency, this initial Gaussian should approximate the posterior distribution. This suggests adopting as pars0 an initial guess for the model best-fitting parameters.

sigpars0: array_like, shape (n,)

vector with the dispersion sigma of the multivariate Gaussian describing the proposal distribution. For maximum efficiency, this initial Gaussian should approximate the posterior distribution. This suggests adopting as sigpars an initial guess of the uncertainty in the model parameters pars.

bounds: 2-tuple of array_like

Lower and upper bounds on independent variables. Each array must match the size of pars. The model probability is set to zero outside the bounds. This keyword is also used to define the plotting ranges.

nsteps: integer

Number of attempted moves in the chain. Typical numbers are a few thousands nsteps.

Other Parameters

fignum: integer, optional

Specifies the figure number for the plot.

inline: boolean, optional

Specifies whether to show a plot of the results inline or in a window.

labels: array_like, shape (n,)

String labels for each parameter to be used in the corner_plot

labels_scaling: float

Relative scaling for the plotting labels.

nprint: integer

Specifies the frequency for the intermediate plots, in moves. A typical value could be nstep/10.

plot: boolean, optional

Specifies whether to show a plot of the results or not.

quiet: boolean, optional

Suppress the printing of the progress of the algorithm.

seed: integer

Seed for the random generator. Specify this value for a repeatable random sequence.

args, kwargs: tuple and dict, optional

Additional arguments passed to lnprob_fun. Both empty by default. The calling signature is lnprob_fun(x, *args, **kwargs).

Returns

pars: array_like, shape (nsteps, n)

Posterior distribution for the model parameters

lnprob: array_like, shape (nsteps, n)

Logarithm of the probbaility of the model, given the data, for each set of parameters in the posterior distribution pars.