Log(Likelihood)

orbitize.lnlike.chi2_lnlike(data, errors, corrs, model, jitter, seppa_indices)

Compute Log of the chi2 Likelihood

Parameters

• data (np.array) – Nobsx2 array of data, where data[:,0] = sep/RA/RV for every epoch, and data[:,1] = corresponding pa/DEC/np.nan.

• errors (np.array) – Nobsx2 array of errors for each data point. Same format as data.

• corrs (np.array) – Nobs array of Pearson correlation coeffs between the two quantities. If there is none, can be None.

• model (np.array) – Nobsx2xM array of model predictions, where M is the number of orbits being compared against the data. If M is 1, model can be 2 dimensional.

• jitter (np.array) – Nobsx2xM array of jitter values to add to errors. Elements of array should be 0 for for all data other than stellar rvs.

• seppa_indices (list) – list of epoch numbers whose observations are given in sep/PA. This list is located in System.seppa.

Returns

Nobsx2xM array of chi-squared values.

Return type

np.array

Note

Example: We have 8 epochs of data for a system. OFTI returns an array of 10,000 sets of orbital parameters. The model input for this function should be an array of dimension 8 x 2 x 10,000.

orbitize.lnlike.chi2_norm_term(errors, corrs)

Return only the normalization term of the Gaussian likelihood:

\[-log(\sqrt(2\pi*error^2))\]

or

\[-0.5 * (log(det(C)) + N * log(2\pi))\]

Parameters

• errors (np.array) – Nobsx2 array of errors for each data point. Same format as data.

• corrs (np.array) – Nobs array of Pearson correlation coeffs between the two quantities. If there is none, can be None.

Returns

sum of the normalization terms

Return type

float