Issues with Parameter Extraction from Emcee

[AjlaTr]

My team and I were hoping to extract the inclination angle for an SB1 binary system using emcee. We ran it with 5 parameters: inclination, period, the semi-amplitude of radial velocity, period, eccentricity, periastron, and center-of-mass velocity. However, when we did so, we noticed that the value of inclination we received was too small compared to the actual value. Additionally, the corner plot has a large distribution of values.
When I attempted to increase the number of walkers, the value for inclination slightly improved, but this caused issues with the other 4 parameters. As I am new to emcee, I'm not certain how to proceed.

`def binary_model(params, t):
K, P, e, omega, i = params
M = 2 * np.pi * t / P
f = M + e * np.sin(M) # Kepler's equation approximation for eccentric anomaly
rv_pred = K * (np.cos(f + omega) + e * np.cos(omega)) * np.sin(np.radians(i))
return rv_pred

def log_likelihood(params, t, rv, rv_err):
rv_pred = binary_model(params, t)
sigma2 = rv_err**2
return -0.5 * np.sum((rv - rv_pred)**2 / sigma2 + np.log(sigma2))

def log_prior(params):
K, P, e, omega, i = params
if 0 < K < 100 and 0 < P < 100 and 0 <= e < 1 and 0 <= omega < 2*np.pi and 0 < i < 90:
return np.log(np.sin(np.radians(i))) # Prior proportional to sin(i)
return -np.inf

def log_posterior(params, t, rv, rv_err):
lp = log_prior(params)
if not np.isfinite(lp):
return -np.inf
return lp + log_likelihood(params, t, rv, rv_err)

nwalkers = 100
ndim = 5 # Number of parameters in the model
initial_params = [65.49682, 59.93311, 0.01499, 0.04211, 60] # Initial guesses for the parameters
p0 = [initial_params + 1e-4*np.random.randn(ndim) for i in range(nwalkers)]
sampler = emcee.EnsembleSampler(nwalkers, ndim, log_posterior, args=(t, rv_obs, rv_err))

sampler.run_mcmc(p0, 10000) # Increase the number of steps

samples = sampler.get_chain(discard=2000, thin=15, flat=True) # Discard a larger initial portion
incl_samples = samples[:, 3] # Extract inclination samples`