Forecasting

The forecast module provides classes for Fisher matrix forecasting using power spectrum and bispectrum data.

FullForecast

class forecast.FullForecast(cosmo_funcs, kmax_func=None, s_k=2, nonlin=False, N_bins=None, bkmax_func=None, WS_cut=True, n_mu=8, n_phi=8)

Main class for full survey forecasts over redshift bins.

Parameters:

cosmo_funcs: ClassWAP instance
kmax_func: Maximum k (float or callable kmax_func(z))
s_k: k-bins per decade (default: 2)
nonlin: Use HALOFIT power spectra (default: False)
N_bins: Number of redshift bins (default: auto)
bkmax_func: Separate kmax for bispectrum (default: same as kmax_func)
WS_cut: Apply wide-separation validity cuts (default: True)
n_mu, n_phi: Angular integration points for covariances

Attributes:

z_bins: Redshift bin edges, shape (N_bins, 2)
z_mid: Bin centre redshifts
k_max_list: Maximum k per bin
N_bins: Number of bins

Methods:

get_fish(param_list, terms='NPP', cov_terms=None, pkln=None, bkln=None, verbose=True, sigma=None, bias_list=None)

Compute Fisher matrix.

Parameters:

param_list (list) – Parameters (e.g., ['A_s', 'n_s', 'h', 'Omega_m'])
terms (str) – Contribution terms (see Available Terms)
pkln (list) – Pk multipoles (e.g., [0, 2])
bkln (list) – Bk multipoles (e.g., [0])
verbose (bool) – Show progress
sigma (float) – FoG damping
bias_list – Terms for best-fit bias calculation

Returns:

FisherMat object

pk_SNR(term, pkln, verbose=True, sigma=None): Compute power spectrum SNR per redshift bin.

bk_SNR(term, bkln, verbose=True, sigma=None): Compute bispectrum SNR per redshift bin.

combined_SNR(term, pkln, bkln, verbose=True, sigma=None): Compute combined Pk + Bk SNR.

best_fit_bias(param, bias_term, terms='NPP', pkln=None, bkln=None, verbose=True, sigma=None)

Compute parameter bias from neglecting a contribution.

Returns:: Tuple of (bias_dict, fisher_diagonal)

get_pk_bin(i=0): Get PkForecast for redshift bin i.

get_bk_bin(i=0): Get BkForecast for redshift bin i.

sampler(param_list, terms=None, pkln=None, bkln=None, R_stop=0.005, max_tries=100, name=None, planck_prior=False, verbose=True, sigma=None): Create Sampler instance for MCMC.

Usage

import cosmo_wap as cw
from cosmo_wap.lib import utils
from cosmo_wap.forecast import FullForecast

cosmo = utils.get_cosmo(h=0.67, Omega_m=0.31)
survey = cw.SurveyParams.Euclid(cosmo)
cosmo_funcs = cw.ClassWAP(cosmo, survey)

forecast = FullForecast(cosmo_funcs, kmax_func=0.15, N_bins=4)

# Fisher from Pk monopole + quadrupole
fisher = forecast.get_fish(
    ["fNL_loc", "A_b_1", "A_Q", "A_be"],
    terms=["NPP", "Loc", "GR2", "IntNPP"],
    pkln=[0, 2],
    bkln=None
)

# Combined Pk + Bk
fisher_combined = forecast.get_fish(
    ["fNL_loc", "A_b_1", "A_Q", "A_be"],
    terms=["NPP", "Loc", "GR2", "IntNPP"],
    pkln=[0, 2],
    bkln=[0]
)

Available Parameters

We can forecast over the core cosmological parameter as well as our bias parameters or simply some specific contribution

Cosmological parameters:

A_s, n_s, h, Omega_m, Omega_cdm, Omega_b, sigma8

PNG amplitudes:

fNL (local), fNL_eq (equilateral), fNL_orth (orthogonal)

Survey/nuisance parameters:

A_b_1, A_b_2, A_be, A_Q, A_loc_b_01, A_loc_b_01 (bias amplitude parameters)

We can also refer to bias amplitude linked to one survey: e.g. - X_b_1, Y_b_1

Available Terms

Terms can be passed as a single string (e.g. terms='NPP') or a list (e.g. terms=['NPP', 'Loc']). The full list of available terms is:

Base:

'NPP' – Newtonian plane-parallel (Kaiser RSD)

Wide-separation (WS):

'WS' – Combined wide-separation (WA + RR)
'WA1' – Wide-angle first order
'WA2' – Wide-angle second order
'RR1' – Radial redshift first order
'RR2' – Radial redshift second order

Relativistic (GR):

'GR' – All relativistic corrections
'GR1' – First order relativistic
'GR2' – Second order relativistic
'GRX' – Cross relativistic terms

Combined WS + GR:

'WAGR' – Wide-angle + GR
'WARR' – Wide-angle + Radial redshift
'RRGR' – Radial redshift + GR
'WSGR' – Wide-separation + GR
'Full' – All terms

Primordial non-Gaussianity (PNG):

'Loc' – Local PNG
'Eq' – Equilateral PNG
'Orth' – Orthogonal PNG

Integrated effects (Pk only):

'IntNPP' – Integrated x NPP
'IntInt' – Integrated x Integrated
'GRI' – GR + Integrated
'GRL' – GR + Lensing

Individual integrated components:

'LxNPP' – Lensing x NPP
'ISWxNPP' – ISW x NPP
'TDxNPP' – Time-delay x NPP
'LxL' – Lensing x Lensing
'LxTD' – Lensing x Time-delay
'LxISW' – Lensing x ISW
'ISWxISW' – ISW x ISW
'ISWxTD' – ISW x Time-delay
'TDxTD' – Time-delay x Time-delay

Multi-Tracer Forecasting

# Bright-faint split for multi-tracer
survey = cw.SurveyParams.Euclid(cosmo)
bright, faint = survey.BF_split(5e-16)
cosmo_funcs_mt = cw.ClassWAP(cosmo, [bright, faint])

forecast_mt = FullForecast(cosmo_funcs_mt, kmax_func=0.15, N_bins=4)

# Multi-tracer Fisher (accounts for cross-correlations)
fisher_mt = forecast_mt.get_fish(
    ["fNL_loc", "A_b_1", "A_Q", "A_be"],
    terms=["NPP", "Loc", "GR2", "IntNPP"],
    pkln=[0, 2]
)

PNG Forecasting

# Include local PNG contribution
fisher_png = forecast.get_fish(
    ["fNL_loc", "A_b_1", "A_Q", "A_be"],
    terms=["NPP", "Loc", "GR2", "IntNPP"],
    pkln=[0, 2],
    bkln=[0]
)

print(f"sigma(fNL_loc) = {fisher_png.get_error('fNL_loc'):.2f}")

MCMC Sampling

Note

For sampling over cosmology we recommend using the CosmoPower extension. See Installation Guide for setup instructions.

# Create sampler (requires CosmoPower)
sampler = forecast.sampler(
    ["A_s", "n_s", "h"],
    terms="NPP",
    pkln=[0, 2],
    R_stop=0.01  # Convergence criterion
)

# Run MCMC
sampler.run()

# Plot posteriors
sampler.plot()

FisherMat

class forecast.FisherMat

Stores Fisher matrix results.

Attributes:

fisher_matrix: Fisher information matrix (numpy array)
covariance: Inverse Fisher (parameter covariance)
errors: 1-sigma marginalised errors
correlation: Correlation matrix
param_list: Parameter names
bias: Best-fit bias values (if computed)

Methods:

get_error(param): Get 1-sigma error for parameter.

get_correlation(param1, param2): Get correlation coefficient.

summary(): Print formatted summary.

add_chain(c=None, bias_values=None, name=None): Add as chain to ChainConsumer for plotting.

plot_errors(relative=False, figsize=(8, 6)): Plot parameter errors as bar chart.

plot_1D(param, ci=0.68, ax=None, shade=True, color='royalblue'): Plot 1D Gaussian posterior.

save(filename): Save to .npz file.

classmethod load(filename): Load from file.

Usage

fisher = forecast.get_fish(
    ["fNL_loc", "A_b_1", "A_Q", "A_be"],
    terms=["NPP", "Loc", "GR2", "IntNPP"],
    pkln=[0, 2]
)

fisher.summary()
print(fisher.get_error("fNL_loc"))
print(fisher.get_correlation("fNL_loc", "A_b_1"))

# Plot with ChainConsumer
c = fisher.add_chain(name="Pk only")
c.plotter.plot()

FisherList

class forecast.FisherList

Container for multiple Fisher matrices (e.g., varying flux cuts/splits).

Created via FullForecast.get_fish_list().

PkForecast / BkForecast

class forecast.PkForecast

class forecast.BkForecast

Single-bin forecast classes. Usually accessed via FullForecast.get_pk_bin() / get_bk_bin().

Methods:

get_data_vector(terms, ln, param=None): Get data vector (or derivative w.r.t. param).

get_cov_mat(ln, sigma=None): Get covariance matrix.

SNR(term, ln, param=None): Compute SNR.

Sampler

class forecast.Sampler

MCMC sampler using cobaya. Created via FullForecast.sampler(). Requires CosmoPower for efficient cosmology evaluation.

Methods:

run(): Run MCMC chains.

plot(extents=None, truth=True): Plot posteriors with ChainConsumer.

save(filename): Save chains to file.

Usage

# Create sampler
sampler = forecast.sampler(
    ["A_s", "n_s"],
    terms="NPP",
    pkln=[0, 2],
    R_stop=0.005,      # Gelman-Rubin convergence
    planck_prior=True  # Add Planck prior
)

# Run chains
sampler.run()

# Plot with fiducial values marked
sampler.plot(truth=True)