Parameter Modes¶

sed_model.params is the single place that defines what a "stellar parameter" is, whether it is sampled or held fixed, and what its physical bounds are. Both the forward and inverse models speak this language, which is what makes the package genuinely bidirectional.

The five parameters¶

Every fit involves the same five physical quantities, each described by a ParamSpec:

Name	Quantity	Unit	Default in `fit_params_from_grid`
`teff`	effective temperature	K	free over the grid's Teff range
`logg`	log surface gravity	dex (log₁₀ g / cm s⁻²)	free over the grid's logg range
`meta`	metallicity [M/H]	dex	free over the grid's [M/H] range
`a_v`	V-band extinction	mag	fixed at 0.0
`d`	distance	cm	fixed at 1 pc

Modes¶

from sed_model import fixed, free, bounded

fixed(value)      # not sampled; passed unchanged to the forward model
free(lo, hi)      # sampled by MCMC, flat prior over [lo, hi]
bounded(lo, hi)   # alias for free — explicit about hard limits

Validation is enforced at construction: free specs require lo < hi; distance must be positive; Av must be non-negative.

Building a `FitParams`¶

From a grid, with overrides¶

from sed_model import fit_params_from_grid
from sed_model.params import PC_TO_CM

# Defaults: Teff/logg/[M/H] free over the grid, Av fixed 0, d fixed 1 pc
params = fit_params_from_grid(grid)

# Pass a float to fix a parameter, a (lo, hi) tuple to sample it:
params = fit_params_from_grid(
    grid,
    teff=(5200, 6400),
    logg=4.4,
    meta=0.0,
    a_v=(0.0, 1.5),
    d_cm=500 * PC_TO_CM,
)

Explicitly¶

from sed_model import FitParams, fixed, free
from sed_model.params import PC_TO_CM

params = FitParams(
    teff = free(4000, 8000),
    logg = free(3.0, 5.0),
    meta = free(-1.0, 0.5),
    a_v  = fixed(0.3),
    d    = fixed(500 * PC_TO_CM),
)

The theta vector¶

The MCMC samples only the free parameters, in the canonical order teff, logg, meta, a_v, d (skipping fixed ones). FitParams provides the conversion both ways:

params.free_names          # e.g. ['teff', 'meta', 'a_v']
params.n_free              # 3
params.fixed_names         # ['logg', 'd']

theta = params.pack(teff=5800, logg=4.4, meta=0.0, a_v=0.5)
full  = params.unpack(theta)   # {'teff': 5800, 'logg': 4.4, ...} with fixed filled in
params.in_prior(theta)         # True/False
print(params.summary())        # human-readable fixed/free table

initial_ball(n_walkers, centre=..., scatter=...) generates the starting walker positions used by run_inverse.

The Av–distance degeneracy¶

If Av and d are both free simultaneously the posterior will be correlated — the data genuinely cannot break the degeneracy without additional information, and the MCMC will show it honestly rather than hiding it. The Parameter Modes demo makes this visible by running the same observations through four sampling configurations, from everything-fixed-but-atmosphere up to everything-free.