#first optimise the function and get parameter errors from the conditionals
guess_pars, err_pars = Infer.ConditionalErrors(LogLikelihood_iid_mf,
guess_pars,
err_pars,
(Transit_aRs, time, flux),
plot=0,
opt=True)
Infer.MCMC(LogLikelihood_iid_mf,
guess_pars, (Transit_aRs, time, flux),
chain_len,
err_pars,
n_chains=no_ch,
adapt_limits=adapt_lims,
glob_limits=glob_lims,
thin=thin)
par, par_err = Infer.AnalyseChains(conv / thin, n_chains=no_ch)
#plot the chains and correlations
#pylab.figure(2)
#Infer.PlotChains(conv/thin,n_chains=no_ch,p=[0,2,3,4],labels=lab)
pylab.figure(3)
Infer.PlotCorrelations(conv / thin,
n_chains=no_ch,
p=np.where(np.array(par_err) > 0.)[0])
#importance sampling to get the evidence and re-estimate the mean/std of each parameter
pylab.figure(4)
m, K = Infer.NormalFromMCMC(conv / thin, n_chains=no_ch,
plot=1) #get covariance matrix of MCMC chains
Infer.ImportanceSamp(LogLikelihood_iid_mf, (Transit_aRs, time, flux), m, 2 * K,
10000) #importance sample
#create example with some noise/systematics
tpar = [0,3.0,10,0.1,0.2,0.2,0.2,1.0,0.0]
time = np.linspace(-0.1,0.1,300)
flux = MF.Transit_aRs(tpar,time) + 0.001*np.sin(2*np.pi*40*time) + np.random.normal(0.,0.0005,time.size)
#construct the GP
gp = GeePea.GP(time,flux,p=tpar+[0.1,0.01,0.001],mf=MF.Transit_aRs)
gp.opt() #optimise
#run quick MCMC to test predictions:
ch_len = 10000
lims = (0,5000,10)
epar = [0,0,0,0.001,0,0,0,0,0,] + [0.001,0.01,0.001]
Infer.MCMC_N(gp.logPosterior,gp.p,(),ch_len,epar,adapt_limits=lims,glob_limits=lims,chain_filenames=['test_chain'])
p,perr = Infer.AnalyseChains(lims[1],chain_filenames=['test_chain'])
X = Infer.GetSamples(5000,100,chain_filenames=['test_chain']) #get samples from the chains
os.remove('test_chain.npy')
#standard plot
pylab.figure()
gp.plot()
#pylab.savefig('test.pdf')
#density plot for single parameter set
pylab.figure()
f,ferr = gp.predict()
GeePea.PlotDensity(time,f,ferr)
pylab.plot(time,flux,'ro',ms=3)
#density plot for sample of params
#get residuals
resid = f - MF.Transit_aRs(p, t)
#compare with MCMC fit - use LM values as inputs
lims = (0, 4000, 4)
MCMC_p = list(p) + [
wn,
]
MCMC_pe = list(pe) + [
epar[-1],
]
Infer.MCMC_N(MF.LogLikelihood_iid_mf,
MCMC_p, (MF.Transit_aRs, t, f),
10000,
MCMC_pe,
adapt_limits=lims,
glob_limits=lims,
N=2)
MCMC_p, MCMC_pe = Infer.AnalyseChains(lims[1], n_chains=2, N_obs=t.size)
os.remove('MCMC_chain_1.npy')
os.remove('MCMC_chain_2.npy')
#plot the data
pylab.plot(t, f, 'k.')
pylab.plot(t, MF.Transit_aRs(gpar[:-1], t), 'g-')
pylab.plot(t, MF.Transit_aRs(p, t), 'r-')
pylab.plot(t, resid + 1.0 - 1.5 * np.ptp(MF.Transit_aRs(p, t)), 'k.')
pylab.axhline(1.0 - 1.5 * np.ptp(MF.Transit_aRs(p, t)), color='r')
pylab.plot(t, MF.Transit_aRs(MCMC_p[:-1], t), 'b-')
raw_input()
chain_len = 40000
conv = 10000
thin = 10
no_ch = 2
lims = (1000, conv, 5)
err_pars = np.array([0.001, 0.001, 0.0001] +
[0.00001, 0, 0.2, 0.0003, 0.02, 0.0, 0.0, 0.001, 0.0001])
Infer.MCMC(MyGP.logPosterior,
MyGP._pars, (),
chain_len,
err_pars,
n_chains=no_ch,
adapt_limits=lims,
glob_limits=lims,
thin=thin)
MyGP.pars, par_err = Infer.AnalyseChains(conv / thin, n_chains=no_ch)
pylab.figure(2)
Infer.PlotCorrelations(conv / thin, n_chains=no_ch)
#do an Affine Invariant MCMC
n = 100
err_pars = 0.01 * np.array(
[0.001, 0.001, 0.0001] +
[0.00001, 0, 0.2, 0.0003, 0.02, 0.0, 0.0, 0.001, 0.0001])
Infer.AffInvMCMC(MyGP.logPosterior,
MyGP._pars, (),
n,
chain_len / n,
err_pars,
n_chains=no_ch)
MyGP.pars, par_err = Infer.AnalyseChains(conv, n_chains=no_ch)
gp.plot()
#can also run an MCMC by using GP.logPosterior()
ch = 10000
conv = 0.4 * ch
lims = (0, conv, 10)
Infer.MCMC_N(gp.logPosterior,
gp.p, (),
ch,
gp.ep,
N=2,
adapt_limits=lims,
glob_limits=lims)
#Infer.AffInvMCMC(gp.logPosterior,gp.p,(),500,ch/500,gp.ep*0.01,n_chains=2)
pylab.figure(2)
Infer.PlotCorrelations(conv, n_chains=2, p=np.where(np.array(gp.ep) > 0)[0])
#pylab.savefig('Correlations.png')
#get the parameters and uncertainties from the MCMC
gp.p, gp.ep = Infer.AnalyseChains(conv, n_chains=2)
#and plot
pylab.figure(1)
gp.plot()
#delete the MCMC chains
# if os.path.exists('MCMC_chain_1.npy'): os.remove('MCMC_chain_1.npy')
# if os.path.exists('MCMC_chain_2.npy'): os.remove('MCMC_chain_2.npy')
#raw_input()
par_guess, (time, ),
f,
fixed=~(np.array(epar[:-1]) > 0))
#fit with simple MCMC
lims = [1000, 20000, 5]
Infer.MCMC_N(MF.LogLikelihood_iid_mf,
np.concatenate([par_guess, [
wn,
]]), (mf, time, f),
30000,
epar,
adapt_limits=lims,
glob_limits=lims,
N=2)
MCMC_par, MCMC_epar = Infer.AnalyseChains(20000, n_chains=2)
os.system('rm MCMC_chain_?.npy')
#fit with nelder mead
NM_par = Infer.Optimise(MF.LogLikelihood_iid_mf,
np.concatenate([par_guess, [
wn,
]]), (mf, time, f),
fixed=fp)
#fit with brute force/Infer
BR_par = Infer.Brute(MF.LogLikelihood_iid_mf,
np.concatenate([par_guess, [
wn,
]]), (mf, time, f),
epar,
if _e == 0.: bounds_mf[i] = None
gp.opt_global(bounds=bounds_mf + bounds_hp) #and optimise
#finally make a plot
plt.figure(1)
gp.plot()
#can also run an MCMC by using GP.logPosterior()
lims = (0, 10000, 4)
Infer.MCMC_N(gp.logPosterior,
gp.p, (),
20000,
gp.ep,
N=2,
adapt_limits=lims,
glob_limits=lims)
#get the parameters and uncertainties from the MCMC
gp.p, gp.ep = Infer.AnalyseChains(10000, n_chains=2)
#and plot the correlations
plt.figure(2)
Infer.PlotCorrelations(10000, n_chains=2, p=np.where(np.array(gp.ep) > 0)[0])
#pylab.savefig('Correlations.png')
#delete the MCMC chains
if os.path.exists('MCMC_chain_1.npy'): os.remove('MCMC_chain_1.npy')
if os.path.exists('MCMC_chain_2.npy'): os.remove('MCMC_chain_2.npy')
raw_input()