Parameter Estimation with Redback

Overview

VegasAfterglow is a pure physics library focused on fast, accurate afterglow calculations. For parameter estimation, MCMC fitting, and comprehensive transient analysis, VegasAfterglow models are integrated into redback.

Redback provides:

• Unified interface for all transient types (afterglows, kilonovae, supernovae, TDEs, etc.)

• Multiple sampling algorithms (dynesty, emcee, ultranest, etc.)

• Data management and open-access catalogs

• Model comparison and selection

• Visualization tools and plotting utilities

• Prior specification with bilby integration

Quick Start

Loading Data and Basic Fitting

Redback provides multiple ways to load and work with GRB afterglow data. Here’s a complete example:

import redback

# Method 1: Load from Swift BAT+XRT catalogs (recommended for Swift GRBs)
GRB = '070809'

# Get flux/flux density data from Swift
redback.get_data.get_bat_xrt_afterglow_data_from_swift(
    grb=GRB,
    data_mode="flux"  # or "flux_density", "magnitude", "luminosity"
)
# This creates a GRBDir with all available Swift data

# Create transient object from Swift data
afterglow = redback.afterglow.SGRB.from_swift_grb(
    name=GRB,
    data_mode='flux'
)

# Method 2: Load from open access catalogs
afterglow = redback.afterglow.Afterglow.from_open_access_catalogue(
    GRB,
    data_mode='flux_density'
)

# Method 3: Load from your own data files
import pandas as pd
data = pd.read_csv('path/to/my_grb_data.csv')
afterglow = redback.transient.Afterglow(
    name=GRB,
    data_mode='flux_density',
    time=data['time'].values,
    flux_density=data['flux'].values,
    flux_density_err=data['flux_err'].values,
    frequency=data['frequency'].values
)

# Fit with VegasAfterglow tophat model
result = redback.fit_model(
    transient=afterglow,
    model='vegas_tophat',  # VegasAfterglow tophat jet model
    sampler='dynesty',
    nlive=1000
)

# Analyze results
result.plot_corner()
result.plot_lightcurve()
result.plot_residuals()

Data Modes and Formats:

Redback supports multiple data modes for afterglow analysis:

• flux_density - Flux density [erg/cm²/s/Hz] at specific frequencies

• flux - Integrated flux [erg/cm²/s] over energy bands

• magnitude - Optical/NIR magnitudes in various filters

• luminosity - Source-frame luminosity (requires known redshift)

Advanced Data Loading:

For comprehensive data management capabilities, including:

• Multi-wavelength data from different instruments

• Custom data formats and preprocessing

• Data filtering and quality cuts

• Combining multiple datasets

• Time-domain sampling strategies

See the complete redback data documentation.

Available VegasAfterglow Models

Redback includes multiple VegasAfterglow models for different jet structures and media:

Jet Models with ISM Medium

• vegas_tophat - Uniform tophat jet with sharp boundary

• vegas_gaussian - Gaussian energy profile

• vegas_powerlaw - Power-law energy and Lorentz factor structure

• vegas_powerlaw_wing - Power-law wings without discontinuity

• vegas_step_powerlaw - Pencil beam core with power-law wings

• vegas_two_component - Narrow core + wide component

Jet Models with Wind Medium

• vegas_tophat_wind - Tophat jet in stellar wind

• vegas_gaussian_wind - Gaussian jet in stellar wind

• vegas_powerlaw_wind - Power-law jet in stellar wind

Model Parameters

Each VegasAfterglow model requires specific parameters. Here are typical parameters for a tophat jet in ISM:

Common Parameters

• redshift - Source redshift

• thv - Viewing angle (radians)

• loge0 - log10 isotropic equivalent energy (ergs)

• thc - Jet core opening angle (radians)

• lognism - log10 ISM number density (cm^-3)

• p - Electron power-law index

• logepse - log10 electron energy fraction

• logepsb - log10 magnetic field energy fraction

• g0 - Initial Lorentz factor

Additional Parameters (via kwargs)

• spread - Enable jet spreading (default: False)

• reverse_shock - Enable reverse shock (default: False)

• reverse_logepse - Reverse shock electron fraction

• reverse_logepsb - Reverse shock magnetic fraction

• reverse_p - Reverse shock electron index

Example: Custom Priors

import bilby
import redback

# Load data
afterglow = redback.afterglow.Afterglow.from_open_access_catalogue(
    'GRB070809', data_mode='flux_density'
)

# Define custom priors
priors = bilby.prior.PriorDict()
priors['redshift'] = bilby.prior.Uniform(0.01, 3, 'redshift')
priors['thv'] = bilby.prior.Sine(maximum=np.pi/2, name='thv')
priors['loge0'] = bilby.prior.Uniform(48, 54, 'loge0')
priors['thc'] = bilby.prior.Uniform(0.01, 0.5, 'thc')
priors['lognism'] = bilby.prior.Uniform(-5, 2, 'lognism')
priors['p'] = bilby.prior.Uniform(2.0, 3.5, 'p')
priors['logepse'] = bilby.prior.Uniform(-4, 0, 'logepse')
priors['logepsb'] = bilby.prior.Uniform(-4, 0, 'logepsb')
priors['g0'] = bilby.prior.Uniform(50, 1000, 'g0')

# Run fit with custom priors
result = redback.fit_model(
    transient=afterglow,
    model='vegas_tophat',
    sampler='dynesty',
    priors=priors,
    nlive=1000
)

Example: Multi-band Fitting

import redback

# Load multi-band data
afterglow = redback.afterglow.Afterglow.from_open_access_catalogue(
    'GRB070809', data_mode='flux_density'
)

# Fit with VegasAfterglow model
result = redback.fit_model(
    transient=afterglow,
    model='vegas_gaussian',  # Gaussian jet structure
    sampler='dynesty',
    nlive=2000,  # More live points for complex posteriors
    dlogz=0.1    # Tighter evidence tolerance
)

# Generate posterior predictions at new frequencies
result.plot_multiband(frequencies=[1e9, 5e14, 1e18])

Example: Model Comparison

import redback

afterglow = redback.afterglow.Afterglow.from_open_access_catalogue(
    'GRB070809', data_mode='flux_density'
)

# Fit multiple models
models = ['vegas_tophat', 'vegas_gaussian', 'vegas_powerlaw']
results = {}

for model in models:
    results[model] = redback.fit_model(
        transient=afterglow,
        model=model,
        sampler='dynesty',
        nlive=1000
    )

# Compare evidences
for model, result in results.items():
    print(f"{model}: log(Z) = {result.log_evidence:.2f}")

# Plot comparison
redback.plot_model_comparison(results)

Advanced Features

Reverse Shock Modeling

import redback

# Enable reverse shock with different microphysics
kwargs = {
    'reverse_shock': True,
    'reverse_logepse': -1.5,  # Different from forward shock
    'reverse_logepsb': -2.5,
    'reverse_p': 2.2
}

result = redback.fit_model(
    transient=afterglow,
    model='vegas_tophat',
    model_kwargs=kwargs,
    sampler='dynesty',
    nlive=1000
)

Jet Spreading

# Enable jet spreading dynamics
kwargs = {'spread': True}

result = redback.fit_model(
    transient=afterglow,
    model='vegas_tophat',
    model_kwargs=kwargs,
    sampler='dynesty',
    nlive=1000
)

Best Practices

Start Simple

Always begin with the simplest physically motivated model:

1. Start with vegas_tophat + ISM + forward shock only

2. Examine residuals and fit quality

3. Add complexity (reverse shock, different jet structure) only if justified

Choose Appropriate Priors

• Use physical constraints to set prior ranges

• For viewing angle, use Sine prior (uniform in solid angle)

• For energies/densities, use Uniform in log space

• Check prior predictive distributions before fitting

Sampler Selection

• dynesty: Best for evidence calculation and multimodal posteriors

• emcee: Faster for unimodal posteriors, good for quick checks

• ultranest: Most robust for complex, multimodal posteriors

Computational Considerations

• VegasAfterglow is extremely fast (~1ms per light curve)

• Can fit 1000s of MCMC samples in minutes on laptop

• Use nlive=1000 for quick runs, nlive=2000+ for publication

• Parallel chains with npool parameter for faster sampling

Redback’s Full Capabilities

Redback is a comprehensive transient analysis framework that provides everything you need for parameter estimation with VegasAfterglow models. Through the redback interface, you can:

Data Management:

• Load data from multiple sources: Swift, Fermi, BATSE, open catalogs, private data

• Support for all data types: flux density, flux, magnitude, luminosity

• Multi-wavelength data from radio to X-ray

• Automatic unit conversions and data preprocessing

• Filter and quality-cut data

• Combine datasets from multiple instruments

• Handle upper limits and non-detections

Model Fitting:

• Access all VegasAfterglow models (tophat, gaussian, power-law jets, etc.)

• Multiple sampling backends: dynesty, emcee, ultranest, nessai

• Custom prior specification with bilby

• Parallel sampling for faster computation

• Model comparison via Bayesian evidence

• Fit multiple transient types beyond afterglows

Analysis & Visualization:

• Corner plots for posterior distributions

• Light curve plots with model predictions

• Residual analysis

• Multi-band visualization

• Posterior predictive checks

• Evidence comparison tables

• Publication-ready figures

Advanced Features:

• Joint analysis of multiple transients

• Population inference

• Model selection and comparison

• Custom likelihood functions

• Systematic uncertainty modeling

• Time-dependent viewing angle effects

• Energy injection modeling

Example: Complete Workflow

import redback

# 1. Get data (multiple methods available)
GRB = 'GRB070809'

# From Swift
redback.get_data.get_bat_xrt_afterglow_data_from_swift(grb=GRB, data_mode="flux")
afterglow = redback.afterglow.SGRB.from_swift_grb(name=GRB, data_mode='flux')

# Or from your own data
# import pandas as pd
# data = pd.read_csv('my_grb_data.csv')
# afterglow = redback.transient.Afterglow(
#     name=GRB, data_mode='flux_density',
#     time=data['time'].values, flux_density=data['flux'].values,
#     flux_density_err=data['flux_err'].values, frequency=data['frequency'].values
# )

# 2. Fit model
result = redback.fit_model(
    transient=afterglow,
    model='vegas_tophat',
    sampler='dynesty',
    nlive=2000
)

# 3. Analyze
result.plot_corner()
result.plot_lightcurve(save=True)
result.print_summary()

# 4. Make predictions
result.plot_multiband(frequencies=[1e9, 1e14, 1e18])

For complete documentation on all these capabilities and more, see the comprehensive redback documentation.

Quick Links:

• Redback Installation

• Data Loading Guide

• Fitting Tutorial

• Model Library

• API Reference

For VegasAfterglow physics details, see:

• GRB Afterglow Physics - Detailed physics description

• Parameter Reference - Complete parameter reference

• Examples - VegasAfterglow usage examples