In [1]:
import numpy as np
#from scipy.optimize import newton as nt
from scipy import optimize as op
import matplotlib.pyplot as plt
from george.kernels import ExpSquaredKernel #For Gaussian Processes
from george.kernels import ExpSine2Kernel #For Gaussian Processes
import george
%matplotlib inline

import emcee
import corner

In [36]:
#First data
#data = astro.io.ascii.read('Inputs/data/rvs_0001.txt', names=['time','vel','err'])
data = np.loadtxt('Inputs/data/rvs_0001.txt')
obser = [data[:,0],data[:,1],data[:,2]]

In [3]:
x = data[:,0]
y = data[:,1]
yerr = data[:,2]
# First illustrate basic pyplot interface, using defaults where possible.
plt.figure(figsize=(15,8))
#plt.xlabel('teste')
plt.xlabel('Time (s)', fontsize=20)
plt.ylabel('Star Radial velocity (m/s)', fontsize=20)
plt.errorbar(x, y, yerr=yerr,fmt='o')
plt.tick_params(labelsize=20)
plt.title("Data0001",fontsize=30)
#plt.plot(x,y,'o')


plt.show()



In [102]:
#From https://en.wikipedia.org/wiki/True_anomaly and 
#http://exoplanets.astro.yale.edu/workshop/EPRV/Bibliography_files/Radial_Velocity.pdf
#Returns the mean anomaly in the 2 pi interval
def mean_anomaly(M0,t,t0,tau):
    return (2 * np.pi * (t-t0) / tau + M0 ) % (2*np.pi)

#Returns the [cos(f),sin(f)], where f is the true anomaly.
def real_anomaly(M,e):
#    if M-e<0:
#        ec_anol = M+op.newton(lambda x: e * np.sqrt(1-(np.cos(M+x))**2)-x,e*np.sin(M),maxiter=100)
#    elif M+e>2*np.pi:
#        ec_anol = M+op.newton(lambda x: -e * np.sqrt(1-(np.cos(M+x))**2)-x,e*np.sin(M),maxiter=100)
#    else:
#        ec_anol = M+op.newton(lambda x: e * np.sin(M+x)-x,e*np.sin(M),lambda y: e * np.cos(M+y)-1)
    ec_anol = M+op.newton(lambda x: e * np.sin(M+x)-x,e*np.sin(M),lambda y: e * np.cos(M+y)-1,\
                          fprime2=lambda z: -e * np.sin(M+z))
    return [(np.cos(ec_anol)-e)/(1-e * np.cos(ec_anol)),(np.sqrt(1-e**2) * np.sin(ec_anol))/(1-e*np.cos(ec_anol))]

def RV(t, K, p, e, w, M0, t0=0):
    p = np.abs(p)
    K = np.abs(K)
    w = np.abs(w)%(2*np.pi)
    e=np.abs(e)
    if e>1: e=0.9
    M0 = np.abs(M0)%(2*np.pi)
    cosf, sinf = real_anomaly(mean_anomaly(M0,t,t0,p),e)
    return K * (np.cos(w)*cosf-np.sin(w)*sinf+e*np.cos(w))
#Radial velocity for one planet


#Model for velocity function.
#Input: Planets parameters: Last 2 ate C and J. Five extra parameters for each planet 
#Special thanks to Ben Nelson
def model(params, times, nPlanets):
    planets = [params[i*5:i*5+5] for i in range(nPlanets)]
    try:
        p, K, e, w, M = np.transpose(planets)
    except ValueError:
        p, K, e, w, M = 99999999., 0., 0., 0., 0.
    offset = params[5*nPlanets]
    jitter = params[-1]
    mod = np.zeros(len(times))
    for j in range(len(times)):
        mod[j] += sum([RV(times[j], K[i], p[i], e[i], w[i], M[i])\
                       for i in range(nPlanets)]) + offset
    return mod

#Gaussian Processes kernel
var, length_e, length_s, period = 3.0, 50., 0.5, 20.
gamma = 1/(2.*length_s*length_s)
kernel = var * ExpSquaredKernel(length_e*length_e) * ExpSine2Kernel(gamma=gamma, log_period=np.log(period))

### Define the likelihood function ###
#Thanks to Ben.
def lnlike(params, obs, nPlanets):
    times, rvs, sigs = obs
    jit = params[-1]
    sigs_plus_jitter = np.sqrt(sigs*sigs + jit*jit*np.ones(len(times)))
    gp = george.GP(kernel)
    gp.compute(times, sigs_plus_jitter)
    #    return gp.lnlikelihood(rvs - model_1(params, times, nPlanets))                                                                                                                                      
    return gp.lnlikelihood(rvs - model(params, times, nPlanets))

In [10]:
plt.plot(np.arange(100),model([1.2, 1, 0.1, 3., 4.,  1, 2],np.arange(100),1));
plt.title('Star velocity model (1 planet)')
plt.xlabel('Time')
plt.ylabel('Redshift velocity');



In [11]:
IC_0pl = [-0.72851, 2.08718] #Test parameters
lnlike(IC_0pl, [data[:,0],data[:,1],data[:,2]], 0) #Should be around -477


Out[11]:
-477.19968698126718

In [132]:
#Must define priors!
def log_prior( params, nPlanets):
    value=0
    planets = [params[i*5:i*5+5] for i in range(nPlanets)]
    try:
        p, K, e, w, M = np.transpose(planets)
    except ValueError:
        p, K, e, w, M = 99999999., 0., 0., 0., 0.
    offset = params[5*nPlanets]
    jitter = params[-1]
    if (offset<-1000) or (offset>1000) or (jitter<0) or (jitter>99):
        return -np.infty
    value+=-np.log(2000) #offset priors
    value+=-np.log(1+jitter)-np.log(np.log(100)) #Jitter prior
    if nPlanets>0:
        if ((K<=0) + (K>999) + (e<0) + (e>=1) + (w<0) + (w>2*np.pi) + (M<0) + (M>2*np.pi)).all():
            return -np.infty
        value+=-np.log(p)-np.log(np.log(10000/1.25)) #Period prior 
        value+=-np.log(1+K)-np.log(np.log(1000)) #K prior
        value+=-np.log(2*np.pi**2) #w, M priors
#        if (1-np.exp(-e**2/0.08)==0):
#            value+=np.log(e/0.04)-e**2/0.08-np.log((e**2/0.08)) #e prior
#        else:
        value+=np.log(e/0.04)-e**2/0.08-np.log(-np.expm1(-e**2/0.08)) #e prior
    return value.sum()

def log_posterior(params, obs, nPlanets):
    return log_prior(params, nPlanets) + lnlike(params, obs, nPlanets)

In [54]:
log_posterior([102,30,0.5,1.1,np.pi,-1,-2],obser,1)


Out[54]:
-inf

In [105]:
def mini(a,b,c):
    value = -log_posterior(a,b,c)
    if np.isfinite(value):
        return value
    else:
        return 10**10
sol0 = op.minimize(mini,IC_0pl,args=(obser,0))
print(sol0)


      fun: 487.454531660062
 hess_inv: array([[ 0.35446769, -0.0022139 ],
       [-0.0022139 ,  0.01958826]])
      jac: array([  0.00000000e+00,   3.81469727e-06])
  message: 'Optimization terminated successfully.'
     nfev: 28
      nit: 4
     njev: 7
   status: 0
  success: True
        x: array([-0.72023413,  2.08317069])

In [106]:
IC_1pl = [500, 4, 1e-20, 0, 0,0,1] #Test parameters
mini(IC_1pl,obser,1)


Out[106]:
528.70663220787628

In [107]:
sol1 = op.minimize(mini,IC_1pl,args=(obser,1),method='Powell')
print(sol1)


   direc: array([[  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          1.00000000e+00],
       [  0.00000000e+00,   1.00000000e+00,   0.00000000e+00,
          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00],
       [  0.00000000e+00,   0.00000000e+00,   1.00000000e+00,
          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00],
       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          1.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00],
       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00,   1.00000000e+00,   0.00000000e+00,
          0.00000000e+00],
       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00,   0.00000000e+00,   1.00000000e+00,
          0.00000000e+00],
       [  5.80322207e+00,   6.84341413e-03,   0.00000000e+00,
          2.84644162e-02,   3.90629533e-12,  -2.63665910e-02,
         -1.44862947e-03]])
     fun: 452.88576071295586
 message: 'Optimization terminated successfully.'
    nfev: 461
     nit: 3
  status: 0
 success: True
       x: array([  3.70915909e+02,   1.05666623e+00,   1.00000000e-20,
         3.15672189e-01,   1.57427744e-10,  -4.82983286e-01,
         2.07941042e+00])

In [133]:
IC_2pl = np.concatenate([[500, 4, 1e-20, 0, 0],sol1['x']]) #Test parameters
mini(IC_2pl,obser,2)


Out[133]:
442.80393234894291

In [134]:
sol2 = op.minimize(mini,IC_2pl,args=(obser,2),method='Powell')
print(sol2)


/home/arthur/anaconda2/envs/p36/lib/python3.6/site-packages/ipykernel_launcher.py:20: RuntimeWarning: invalid value encountered in log
/home/arthur/anaconda2/envs/p36/lib/python3.6/site-packages/ipykernel_launcher.py:25: RuntimeWarning: invalid value encountered in log
   direc: array([[  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          1.00000000e+00],
       [  0.00000000e+00,   1.00000000e+00,   0.00000000e+00,
          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00],
       [  0.00000000e+00,   0.00000000e+00,   1.00000000e+00,
          0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00],
       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          1.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00],
       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00,   1.00000000e+00,   0.00000000e+00,
          0.00000000e+00],
       [  0.00000000e+00,   0.00000000e+00,   0.00000000e+00,
          0.00000000e+00,   0.00000000e+00,   1.00000000e+00,
          0.00000000e+00],
       [  5.80322207e+00,   6.84341413e-03,   0.00000000e+00,
          2.84644162e-02,   3.90629533e-12,  -2.63665910e-02,
         -1.44862947e-03]])
     fun: 452.88576071295586
 message: 'Optimization terminated successfully.'
    nfev: 461
     nit: 3
  status: 0
 success: True
       x: array([  3.70915909e+02,   1.05666623e+00,   1.00000000e-20,
         3.15672189e-01,   1.57427744e-10,  -4.82983286e-01,
         2.07941042e+00])

In [138]:
IC_3pl = np.concatenate([[500, 4, 1e-20, 0, 0],sol2['x']]) #Test parameters
mini(IC_3pl,obser,3)


Out[138]:
388.59337657744152

In [139]:
sol3 = op.minimize(mini,IC_3pl,args=(obser,3),method='Powell')
print(sol3)


/home/arthur/anaconda2/envs/p36/lib/python3.6/site-packages/ipykernel_launcher.py:20: RuntimeWarning: invalid value encountered in log
/home/arthur/anaconda2/envs/p36/lib/python3.6/site-packages/ipykernel_launcher.py:25: RuntimeWarning: invalid value encountered in log
   direc: array([[ 1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,  0.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  1.,
         0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
         1.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
         0.,  1.,  0.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
         0.,  0.,  1.,  0.],
       [ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
         0.,  0.,  0.,  1.]])
     fun: 350.32224336493988
 message: 'Optimization terminated successfully.'
    nfev: 3003
     nit: 7
  status: 0
 success: True
       x: array([  5.16370020e+02,  -1.00000000e+00,   1.00000000e-20,
        -5.91639646e-12,  -6.74745985e-13,   3.48154671e+02,
        -1.00000000e+00,   1.00000000e-20,   1.83403791e-01,
         4.33820758e-04,   2.17200194e+02,   1.01240817e+00,
         1.00000000e-20,   2.96029162e-01,   1.21412629e-03,
        -8.47669348e-01,   2.05499848e+00])

In [140]:
x = data[:,0]
xm = np.arange(0,data[-1,0],data[-1,0]/1000)
y = data[:,1]
y0 = model(sol0['x'],xm,0)
y1 = model(sol1['x'],xm,1)
y2 = model(sol2['x'],xm,2)
y3 = model(sol3['x'],xm,3)
yerr = data[:,2]
# First illustrate basic pyplot interface, using defaults where possible.
plt.figure(figsize=(15,8))
#plt.xlabel('teste')
plt.xlabel('Time (s)', fontsize=20)
plt.ylabel('Star Radial velocity (m/s)', fontsize=20)
plt.errorbar(x, y, yerr=yerr,fmt='o')
plt.plot(xm,y0)
plt.plot(xm,y1)
plt.plot(xm,y2)
plt.plot(xm,y3)
plt.tick_params(labelsize=20)
plt.title("Data0001",fontsize=30)
#plt.plot(x,y,'o')


plt.show()


Emecee


In [161]:
ndim = 2  # number of parameters in the model
nwalkers = 50  # number of MCMC walkers
nburn = 1000  # "burn-in" period to let chains stabilize
nsteps = 2000  # number of MCMC steps to take

#starting guesses. Something around the IC_0pl
rand_offset = 3*(np.random.rand(nwalkers)-0.5)
rand_jitter = 2*(np.random.rand(nwalkers))
#rand_jitter = np.expm1(np.random.rand(nwalkers)*np.log(100))
starting_guesses = np.column_stack((rand_offset,rand_jitter))

In [162]:
sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=(obser,0))
sampler.run_mcmc(starting_guesses, nsteps);

#sample = sampler.chain  # shape = (nwalkers, nsteps, ndim)
#sample_join = [sampler.chain[:, nburn:, i].ravel() for i in range(ndim)]  # discard burn-in points


Out[162]:
(array([[-0.77531348,  2.18803002],
        [-0.08201122,  1.91908872],
        [-1.14226818,  2.08128887],
        [-1.6454635 ,  2.24530195],
        [-0.80543169,  2.12255858],
        [-0.11695722,  2.09194853],
        [ 0.57137351,  2.07763764],
        [-0.4671037 ,  2.14921612],
        [-1.30902158,  2.15285452],
        [-0.44833382,  1.92755456],
        [-0.30548696,  1.78575719],
        [ 0.3502451 ,  2.08997356],
        [-1.29737341,  2.13973026],
        [-0.5300814 ,  2.16429224],
        [-0.64333288,  2.02417777],
        [-1.44680233,  1.95169867],
        [-1.42211586,  2.27801838],
        [-0.18661804,  2.18758503],
        [-0.00473699,  2.19701521],
        [-0.70194903,  2.14291161],
        [-1.63122367,  1.81417557],
        [-0.44623351,  2.0553303 ],
        [-1.15030566,  1.99368526],
        [-1.02617781,  2.10369021],
        [-0.99431191,  2.01912374],
        [-1.52752739,  2.20575567],
        [-0.4699519 ,  1.97026166],
        [-0.33640844,  2.05562957],
        [-1.0654371 ,  2.36252715],
        [-0.07212359,  2.25329243],
        [-0.81584392,  1.95634673],
        [-1.84351301,  2.00577825],
        [-0.921945  ,  2.20979475],
        [-1.24106327,  2.25388127],
        [-1.12241813,  2.15622079],
        [-1.50201218,  2.17450463],
        [-1.69894972,  1.91790248],
        [-0.94331984,  2.42768494],
        [-0.96601551,  2.49272978],
        [-1.73267524,  2.13695131],
        [-1.76300274,  2.26886138],
        [-1.56053381,  2.14296524],
        [-0.45970583,  2.05872139],
        [ 0.22184959,  2.12406876],
        [ 0.15497733,  1.95828441],
        [-0.44158069,  1.96892848],
        [-0.83179267,  2.14365982],
        [-0.55232604,  2.23510514],
        [-0.37087942,  2.27065577],
        [-1.39379592,  2.19797348]]),
 array([-487.72193684, -488.76003305, -487.70634338, -489.20869721,
        -487.50241572, -487.97138628, -489.80930708, -487.6569288 ,
        -488.04635995, -488.22207774, -490.34589936, -489.07430198,
        -487.99051935, -487.67058935, -487.55329292, -488.71762616,
        -488.96464849, -488.13190347, -488.50402978, -487.54349265,
        -490.90205868, -487.57848082, -487.9458036 , -487.59497371,
        -487.67557699, -488.6895631 , -487.88169646, -487.67939438,
        -489.3034447 , -488.74340387, -487.91276321, -489.43920349,
        -487.88507923, -488.48057349, -487.80255509, -488.48842331,
        -489.65167257, -490.02208721, -490.95716685, -488.9470379 ,
        -489.69346564, -488.51690356, -487.5640265 , -488.75543532,
        -488.94249169, -487.91050392, -487.56018112, -488.04391897,
        -488.45367433, -488.37839451]),
 ('MT19937', array([ 163487975,  118367746, 2922928476, 1747047806, 1820228873,
         1336182972, 1470138777, 1671037103, 1683057534, 1489299645,
         2885279542, 2045630636, 3054050451, 4065387145, 1202432889,
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         3229670456, 3920809202,     383982, 4085111560, 1864397894,
         3249314255, 1655975033,  160353042, 3682798268, 2188361768,
         3590871327, 1297866287, 2982099691,  133342909, 2107225910,
         1566296429, 3746506404, 3791379370, 1135431283, 2327782416,
         3043944649, 3121988417, 3771882975, 2156607617, 2936713304,
          225044342, 3292663573, 3507387336, 1747318705, 2561327955,
         2462629977, 1575605921, 3889145124, 1659522285,   48057379,
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         3134270330, 1804965603, 2884860609,  201782100, 2813256247,
         3740357533, 3028475585, 2830046443,   39864350, 1266520951,
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In [164]:
labeles = ['C','J']
_ = corner.corner(sampler.flatchain,truths=sol0['x'],labels=labeles)


Looking for the parameters space

Based on Boris work

Zero planets


In [17]:
ndim = 2  # number of parameters in the model
nwalkers = 50  # number of MCMC walkers
nburn = 1000  # "burn-in" period to let chains stabilize
nsteps = 2000  # number of MCMC steps to take
nburn = 0 #test
nsteps = 20 #test

#starting guesses. Something around the IC_0pl
rand_offset = IC_0pl[0]+2*(np.random.rand(nwalkers)-0.5)
rand_jitter = IC_0pl[1]+4*(np.random.rand(nwalkers)-0.5)
starting_guesses = np.column_stack((rand_offset,rand_jitter))

In [18]:
sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[[data[:,0],data[:,1],data[:,2]],0])
sampler.run_mcmc(starting_guesses, nsteps)

sample = sampler.chain  # shape = (nwalkers, nsteps, ndim)
sample0 = sampler.chain[:, nburn:, 0].ravel()  # discard burn-in points
sample1 = sampler.chain[:, nburn:, 1].ravel()  # discard burn-in points

In [20]:
# plot a histogram of the sample
plt.hist(sample0, bins=50, histtype="stepfilled", alpha=0.3, normed=True)
plt.hist(sample1, bins=50, histtype="stepfilled", alpha=0.3, normed=True);



In [22]:
fig, ax = plt.subplots(2, sharex=True)
test = [sample0,sample1]
for i in range(2):
    ax[i].plot(test[i].T, '-k', alpha=0.2);



In [23]:
fig, axs = plt.subplots(1, 3, sharex=True, sharey=True)
for i in range(axs.size):
    axs[i].errorbar(sampler.chain[:, i, 0], sampler.chain[:, i, 1], fmt="-o", alpha=0.5, c='k');



In [24]:
from corner import hist2d
fig, axs = plt.subplots(1, 2, sharex=True, sharey=True)
axs[0].hist2d(sampler.flatchain[:, 0], sampler.flatchain[:, 1], 30, cmap="ocean_r");
hist2d(sampler.flatchain[:, 0], sampler.flatchain[:, 1], ax=axs[1])
axs[0].set_xlabel('C', fontsize=20); axs[0].set_ylabel('J', fontsize=20)
axs[1].set_xlabel('C', fontsize=20);
plt.ylim([0,5])
fig.tight_layout();



In [25]:
# SOLUTION
thechain = sampler.flatchain
print('Mean values:', np.mean(thechain, axis=0))
print('Standard deviation:', np.std(thechain, axis=0))


Mean values: [-0.65641624  1.72968661]
Standard deviation: [ 0.64206305  1.12894944]

In [26]:
plt.plot(data[:,0],model(np.mean(thechain, axis=0),data[:,0],0))
plt.errorbar(data[:,0], data[:,1], yerr=yerr,fmt='o');
plt.title('Star radial velocity',fontsize=25)
plt.xlabel('Time (days)',fontsize=20)
plt.ylabel('Velocity (m/s)',fontsize=20);


One planet


In [28]:
ndim = 7  # number of parameters in the model
nwalkers = 50  # number of MCMC walkers
nburn = 1000  # "burn-in" period to let chains stabilize
nsteps = 2000  # number of MCMC steps to take
nburn = 0 #test
nsteps = 20 #test

#starting guesses. Something around the IC_0pl
rand_offset = IC_0pl[0]+2*(np.random.rand(nwalkers)-0.5)
rand_jitter = IC_0pl[1]+4*(np.random.rand(nwalkers)-0.5)
rand_K = 30 + 10*(np.random.rand(nwalkers)-0.5)
rand_p = 1000 + 100*(np.random.rand(nwalkers)-0.5)
rand_M0 = np.pi+(np.random.rand(nwalkers)-0.5)
rand_w = np.pi+(np.random.rand(nwalkers)-0.5)
rand_e = 0.5+0.3*(np.random.rand(nwalkers)-0.5)
starting_guesses = np.column_stack((rand_p,rand_K,rand_e,rand_w,rand_M0,rand_offset,rand_jitter))

In [42]:
sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=[[data[:,0],data[:,1],data[:,2]],1])
sampler.run_mcmc(starting_guesses, nsteps)

sample = sampler.chain  # shape = (nwalkers, nsteps, ndim)


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