def log_likelihood(theta, x, y, yerr, fixed):
_, model = transit_spectra_model(x, theta, fixed)
# print('model.size', model.size)
# print('y.size', y.size)
sigma = yerr**2
return -0.5 * np.sum((y - model)**2 / sigma + np.log(sigma))
def log_likelihood(theta):
# retrieve the global variables
global pixel_bins
global transit_data
global photon_noise
global fixed_parameters
# only 'y' changes on the fly
fixed = fixed_parameters
x = pixel_bins
y = transit_data
yerr = photon_noise
_, model = transit_spectra_model(x, theta, fixed)
sigma = yerr**2
return -0.5 * np.sum((y - model)**2 / sigma + np.log(sigma))
# test the model generation function
# this produces the 'true' transit spectrum
fixed_parameters = (fine_wavelengths,
water_cross_sections,
co_cross_sections,
hcn_cross_sections,
h2_cross_sections,
g_planet,
rad_star,
R)
theta = (rad_planet,
T,
log_f_h2o,
log_fco,
log_fhcn)
pixel_wavelengths, pixel_transit_depth = transit_spectra_model(pixel_bins, theta, fixed_parameters)
# generate photon noise from a signal value
# signal = 1.22e9
# noise = (np.random.poisson(lam=signal, size=pixel_transit_depth.size) - signal)/signal
# generate noise instances
num_noise_inst = 10
photon_noise = 75 * 1e-6 # set noise to 75ppm
noise_inst = []
while len(noise_inst) < num_noise_inst:
noise_inst.append( np.random.normal(scale=photon_noise, size=pixel_transit_depth.size) )
# add noise to the transit spectrum
noisey_transit_depth = pixel_transit_depth + noise_inst
# Choose the Nyquest sampling rate at the blue end
samplerate_per_pixel = resolution / 2
number_pixels = int((flipped_wl[-1] - flipped_wl[0]) / samplerate_per_pixel)
# make pixel bins
pixel_bins = np.linspace(flipped_wl[0], flipped_wl[-1], num=number_pixels + 1)
# pixel_wavelengths = np.linspace(flipped_wl[0], flipped_wl[-1], num=number_pixels)
# pixel_bins = pixel_wavelengths
# test the model generation function
# this produces the 'true' transit spectrum
fixed_parameters = (fine_wavelengths, water_cross_sections, co_cross_sections,
hcn_cross_sections, h2_cross_sections, g_planet, rad_star,
R)
variables = (rad_planet, T, log_f_h2o, log_fco, log_fhcn)
pixel_wavelengths, pixel_transit_depth = transit_spectra_model(
pixel_bins, variables, fixed_parameters)
# generate photon noise from a signal value
# signal = 1.22e9
# noise = (np.random.poisson(lam=signal, size=pixel_transit_depth.size) - signal)/signal
photon_noise = 75 * 1e-6 # set noise to 75ppm
noise = np.random.normal(scale=photon_noise, size=pixel_transit_depth.size)
# add noise to the transit spectrum
noisey_transit_depth = pixel_transit_depth + noise
# mean spectral resolution
# spec_res = resolution
plt.figure('transit depth R%.2f' % R, figsize=(8, 8))