def metropolis(initial_theta,proposal_params,lnpdf,pdf_params,symmetric=False,
sample_proposal=sample_gaussian_proposal,
eval_ln_proposal=eval_ln_gaussian_proposal,
nsamples=1,randomize_directions=True,callback=None):
"""
NAME:
metropolis
PURPOSE:
metropolis mcmc
INPUT:
initial_theta - initial sample
proposal_params - parameters for the proposal function
(e.g., typical steps)
(single for all dimensions or list of
functions)
lnpdf - function evaluating the log of the pdf to be sampled
pdf_params - parameters to pass to the pdf (tuple)
sample_proposal - given x and proposal_params, sample a proposal
using this function DEFAULT: GAUSSIAN
(single function for all dimensions or list of
functions)
eval_ln_proposal - given x and proposal_params, evaluate the log of
the proposal density DEFAULT: GAUSSIAN
(single function for all dimensions or list of
functions)
symmetric - (bool) if True, the proposal distribution is symmetric and will not be evaluated (bool or list of bools
randomize_directions - (bool) pick a random coordinate to update
nsamples - number of samples desired
callback - function of current parameters to call after each new sample
OUTPUT:
tuple consisting of
list of samples, number if nsamples=1
acceptance ratio, 1 or 0 if nsamples=1
REVISION HISTORY:
2011-07-27 - Written - Bovy (NYU)
"""
try:
ndim = len(initial_theta)
except TypeError:
ndim= 1
if ndim == 1: #1D
return bovy_mcmc_oned.metropolis(initial_theta,
sample_proposal,
eval_ln_proposal,
proposal_params,lnpdf,
pdf_params,symmetric=symmetric,
nsamples=nsamples,callback=callback)
else: #multi-D
return bovy_mcmc_multid.metropolis(initial_theta,
sample_proposal,
eval_ln_proposal,
proposal_params,lnpdf,
pdf_params,symmetric=symmetric,
nsamples=nsamples,
randomize_directions=\
randomize_directions,
callback=callback)
def metropolis(initial_theta,
proposal_params,
lnpdf,
pdf_params,
symmetric=False,
sample_proposal=sample_gaussian_proposal,
eval_ln_proposal=eval_ln_gaussian_proposal,
nsamples=1,
randomize_directions=True,
callback=None):
"""
NAME:
metropolis
PURPOSE:
metropolis mcmc
INPUT:
initial_theta - initial sample
proposal_params - parameters for the proposal function
(e.g., typical steps)
(single for all dimensions or list of
functions)
lnpdf - function evaluating the log of the pdf to be sampled
pdf_params - parameters to pass to the pdf (tuple)
sample_proposal - given x and proposal_params, sample a proposal
using this function DEFAULT: GAUSSIAN
(single function for all dimensions or list of
functions)
eval_ln_proposal - given x and proposal_params, evaluate the log of
the proposal density DEFAULT: GAUSSIAN
(single function for all dimensions or list of
functions)
symmetric - (bool) if True, the proposal distribution is symmetric and will not be evaluated (bool or list of bools
randomize_directions - (bool) pick a random coordinate to update
nsamples - number of samples desired
callback - function of current parameters to call after each new sample
OUTPUT:
tuple consisting of
list of samples, number if nsamples=1
acceptance ratio, 1 or 0 if nsamples=1
REVISION HISTORY:
2011-07-27 - Written - Bovy (NYU)
"""
try:
ndim = len(initial_theta)
except TypeError:
ndim = 1
if ndim == 1: #1D
return bovy_mcmc_oned.metropolis(initial_theta,
sample_proposal,
eval_ln_proposal,
proposal_params,
lnpdf,
pdf_params,
symmetric=symmetric,
nsamples=nsamples,
callback=callback)
else: #multi-D
return bovy_mcmc_multid.metropolis(initial_theta,
sample_proposal,
eval_ln_proposal,
proposal_params,lnpdf,
pdf_params,symmetric=symmetric,
nsamples=nsamples,
randomize_directions=\
randomize_directions,
callback=callback)
def metropolis(initial_theta,sample_proposal,eval_ln_proposal,
proposal_params,lnpdf,pdf_params,symmetric=False,
nsamples=1,randomize_directions=True,callback=None):
"""
NAME:
metropolis
PURPOSE:
metropolis mcmc
INPUT:
initial_theta - initial sample
sample_proposal - given x and proposal_params, sample a proposal
using this function
(single function for all dimensions or list of
functions)
eval_ln_proposal - given x and proposal_params, evaluate the log of
the proposal density
(single function for all dimensions or list of
functions)
proposal_params - parameters for the proposal function
(e.g., typical steps)
(single for all dimensions or list of
functions)
lnpdf - function evaluating the log of the pdf to be sampled
pdf_params - parameters to pass to the pdf (tuple)
symmetric - (bool) if True, the proposal distribution is symmetric and will not be evaluated (bool or list of bools
randomize_directions - (bool) pick a random coordinate to update
nsamples - number of samples desired
OUTPUT:
tuple consisting of
list of samples, number if nsamples=1
acceptance ratio, 1 or 0 if nsamples=1
REVISION HISTORY:
2011-07-27 - Written - Bovy (NYU)
DOCTEST:
>>> import numpy as nu
>>> nu.random.seed(1)
>>> import scipy as sc
>>> from scipy import linalg
>>> from scipy import stats
>>> def lngaussian(x,params):
... return -sc.log(2.*sc.pi)+.5*sc.log(linalg.det(params[1]))-0.5*sc.dot(x-params[0],sc.dot(params[1],x-params[0]))
>>> def sample_gaussian_proposal(mean,stddev):
... return stats.norm.rvs()*stddev+mean
>>> def eval_ln_gaussian_proposal(new,old,stddev):
... return -0.5*sc.log(2.*sc.pi*stddev**2.)-0.5*(old-new)**2./stddev**2.
>>> lnpdf= lngaussian
>>> pdf_params= ([sc.array([0.,1.]),sc.array([[1.,0.],[0.,4.]])],)
>>> sample_proposal= sample_gaussian_proposal
>>> eval_ln_proposal= eval_ln_gaussian_proposal
>>> proposal_params= (2.,)
>>> symmetric=False
>>> initial_theta= nu.array([5.,-3])
>>> nsamples= 40000
>>> samples,faccept= metropolis(initial_theta,sample_proposal,eval_ln_proposal,proposal_params,lnpdf,pdf_params,symmetric=symmetric,nsamples=nsamples)
>>> print "%4.1f%% of the samples were accepted" % (100.*nu.mean(faccept))
39.6% of the samples were accepted
>>> samples= samples[nsamples/2:-1] #discard burn-in
>>> xs= [s[0] for s in samples]
>>> ys= [s[1] for s in samples]
>>> logprecision= -2.
>>> assert (nu.mean(xs)-0.)**2. < 10.**(logprecision*2.)
>>> assert (nu.mean(ys)-1.)**2. < 10.**(logprecision*2.)
>>> assert (nu.std(xs)-1.)**2. < 10.**(logprecision*2.)
>>> assert (nu.std(ys)-.5)**2. < 10.**(logprecision*2.)
>>> proposal_params= [(2.,),(4.,)]
>>> initial_theta= nu.array([5.,-3])
>>> nsamples= 80000
>>> samples,faccept= metropolis(initial_theta,sample_proposal,eval_ln_proposal,proposal_params,lnpdf,pdf_params,symmetric=symmetric,nsamples=nsamples)
>>> print "%4.1f%% of the samples were accepted" % (100.*nu.mean(faccept))
32.6% of the samples were accepted
>>> samples= samples[nsamples/2:-1] #discard burn-in
>>> xs= [s[0] for s in samples]
>>> ys= [s[1] for s in samples]
>>> logprecision= -2.
>>> assert (nu.mean(xs)-0.)**2. < 10.**(logprecision*2.)
>>> assert (nu.mean(ys)-1.)**2. < 10.**(logprecision*2.)
>>> assert (nu.std(xs)-1.)**2. < 10.**(logprecision*2.)
>>> assert (nu.std(ys)-.5)**2. < 10.**(logprecision*2.)
"""
out= []
d= len(initial_theta) #dimensionality
if isinstance(proposal_params,tuple):
proposal_params= [proposal_params for ii in range(d)]
elif isinstance(proposal_params,list) \
and isinstance(proposal_params[0],(int,float)):
proposal_params= [(proposal_params[ii],) for ii in range(d)]
elif isinstance(proposal_params,(int,float)):
proposal_params= [(proposal_params,) for ii in range(d)]
if not isinstance(sample_proposal,list):
sample_proposal= [sample_proposal for ii in range(d)]
if not isinstance(eval_ln_proposal,list):
eval_ln_proposal= [eval_ln_proposal for ii in range(d)]
if isinstance(symmetric,bool):
symmetric= [symmetric for ii in range(d)]
current_sample= initial_theta.copy()
params= []
params.append(lnpdf)
params.append(pdf_params)
naccept= sc.zeros(d)
for ii in range(nsamples):
if randomize_directions:
permuterange= sc.random.permutation(d)
else:
permuterange= range(d)
for dd in permuterange:
thisparams= copy.copy(params)
thisparams.append(dd)
thisparams.append([current_sample[jj] for jj in range(d) if jj != dd])#list comprehensions are supposedly faster than numpy slicing
new_up_sample,accepted= oned_mcmc.metropolis(current_sample[dd],
sample_proposal[dd],
eval_ln_proposal[dd],
proposal_params[dd],
oned_lnpdf,(thisparams,),
symmetric=symmetric[dd],
nsamples=1)
current_sample= current_sample.copy()
current_sample[dd]= new_up_sample
naccept[dd]+= accepted
if not callback is None: callback(current_sample)
out.append(current_sample)
if nsamples == 1:
return (out[0],naccept)
else:
return (out,naccept/float(nsamples))
def metropolis(initial_theta,
sample_proposal,
eval_ln_proposal,
proposal_params,
lnpdf,
pdf_params,
symmetric=False,
nsamples=1,
randomize_directions=True,
callback=None):
"""
NAME:
metropolis
PURPOSE:
metropolis mcmc
INPUT:
initial_theta - initial sample
sample_proposal - given x and proposal_params, sample a proposal
using this function
(single function for all dimensions or list of
functions)
eval_ln_proposal - given x and proposal_params, evaluate the log of
the proposal density
(single function for all dimensions or list of
functions)
proposal_params - parameters for the proposal function
(e.g., typical steps)
(single for all dimensions or list of
functions)
lnpdf - function evaluating the log of the pdf to be sampled
pdf_params - parameters to pass to the pdf (tuple)
symmetric - (bool) if True, the proposal distribution is symmetric and will not be evaluated (bool or list of bools
randomize_directions - (bool) pick a random coordinate to update
nsamples - number of samples desired
OUTPUT:
tuple consisting of
list of samples, number if nsamples=1
acceptance ratio, 1 or 0 if nsamples=1
REVISION HISTORY:
2011-07-27 - Written - Bovy (NYU)
DOCTEST:
>>> import numpy as nu
>>> nu.random.seed(1)
>>> import scipy as sc
>>> from scipy import linalg
>>> from scipy import stats
>>> def lngaussian(x,params):
... return -sc.log(2.*sc.pi)+.5*sc.log(linalg.det(params[1]))-0.5*sc.dot(x-params[0],sc.dot(params[1],x-params[0]))
>>> def sample_gaussian_proposal(mean,stddev):
... return stats.norm.rvs()*stddev+mean
>>> def eval_ln_gaussian_proposal(new,old,stddev):
... return -0.5*sc.log(2.*sc.pi*stddev**2.)-0.5*(old-new)**2./stddev**2.
>>> lnpdf= lngaussian
>>> pdf_params= ([sc.array([0.,1.]),sc.array([[1.,0.],[0.,4.]])],)
>>> sample_proposal= sample_gaussian_proposal
>>> eval_ln_proposal= eval_ln_gaussian_proposal
>>> proposal_params= (2.,)
>>> symmetric=False
>>> initial_theta= nu.array([5.,-3])
>>> nsamples= 40000
>>> samples,faccept= metropolis(initial_theta,sample_proposal,eval_ln_proposal,proposal_params,lnpdf,pdf_params,symmetric=symmetric,nsamples=nsamples)
>>> print "%4.1f%% of the samples were accepted" % (100.*nu.mean(faccept))
39.6% of the samples were accepted
>>> samples= samples[nsamples/2:-1] #discard burn-in
>>> xs= [s[0] for s in samples]
>>> ys= [s[1] for s in samples]
>>> logprecision= -2.
>>> assert (nu.mean(xs)-0.)**2. < 10.**(logprecision*2.)
>>> assert (nu.mean(ys)-1.)**2. < 10.**(logprecision*2.)
>>> assert (nu.std(xs)-1.)**2. < 10.**(logprecision*2.)
>>> assert (nu.std(ys)-.5)**2. < 10.**(logprecision*2.)
>>> proposal_params= [(2.,),(4.,)]
>>> initial_theta= nu.array([5.,-3])
>>> nsamples= 80000
>>> samples,faccept= metropolis(initial_theta,sample_proposal,eval_ln_proposal,proposal_params,lnpdf,pdf_params,symmetric=symmetric,nsamples=nsamples)
>>> print "%4.1f%% of the samples were accepted" % (100.*nu.mean(faccept))
32.6% of the samples were accepted
>>> samples= samples[nsamples/2:-1] #discard burn-in
>>> xs= [s[0] for s in samples]
>>> ys= [s[1] for s in samples]
>>> logprecision= -2.
>>> assert (nu.mean(xs)-0.)**2. < 10.**(logprecision*2.)
>>> assert (nu.mean(ys)-1.)**2. < 10.**(logprecision*2.)
>>> assert (nu.std(xs)-1.)**2. < 10.**(logprecision*2.)
>>> assert (nu.std(ys)-.5)**2. < 10.**(logprecision*2.)
"""
out = []
d = len(initial_theta) #dimensionality
if isinstance(proposal_params, tuple):
proposal_params = [proposal_params for ii in range(d)]
elif isinstance(proposal_params,list) \
and isinstance(proposal_params[0],(int,float)):
proposal_params = [(proposal_params[ii], ) for ii in range(d)]
elif isinstance(proposal_params, (int, float)):
proposal_params = [(proposal_params, ) for ii in range(d)]
if not isinstance(sample_proposal, list):
sample_proposal = [sample_proposal for ii in range(d)]
if not isinstance(eval_ln_proposal, list):
eval_ln_proposal = [eval_ln_proposal for ii in range(d)]
if isinstance(symmetric, bool):
symmetric = [symmetric for ii in range(d)]
current_sample = initial_theta.copy()
params = []
params.append(lnpdf)
params.append(pdf_params)
naccept = sc.zeros(d)
for ii in range(nsamples):
if randomize_directions:
permuterange = sc.random.permutation(d)
else:
permuterange = range(d)
for dd in permuterange:
thisparams = copy.copy(params)
thisparams.append(dd)
thisparams.append([
current_sample[jj] for jj in range(d) if jj != dd
]) #list comprehensions are supposedly faster than numpy slicing
new_up_sample, accepted = oned_mcmc.metropolis(
current_sample[dd],
sample_proposal[dd],
eval_ln_proposal[dd],
proposal_params[dd],
oned_lnpdf, (thisparams, ),
symmetric=symmetric[dd],
nsamples=1)
current_sample = current_sample.copy()
current_sample[dd] = new_up_sample
naccept[dd] += accepted
if not callback is None: callback(current_sample)
out.append(current_sample)
if nsamples == 1:
return (out[0], naccept)
else:
return (out, naccept / float(nsamples))
