Overview

What bayesn-td does

bayesn-td extends the BayeSN optical-NIR SED model to strongly-lensed Type Ia supernovae. It jointly fits the light curves of all images of a lensed SN Ia, sharing the intrinsic SN parameters across images and inferring per-image time of maximum, magnification, and microlensing. bayesn-td provides a joint posterior over time delays and magnifications between images along with SN parameters.

Relationship to BayeSN

bayesn-td uses the same pre-trained SED surfaces, Hsiao template, dust law, and filter infrastructure as BayeSN. The main extension is handling \(N\) lensed images of the same SN in a single fit: intrinsic parameters are shared while per-image \(t_{\max}^{(i)}\), magnification, and (optionally) a microlensing Gaussian process are fit independently.

Any pre-trained BayeSN model can be used; see Built-in models.

In addition to fitting, bayesn-td includes a simple simulator for multi-image lensed SN Ia light curves with configurable time delays and magnifications. It is intended for quick end-to-end tests of the fitting pipeline rather than realistic survey simulations. See Simulating lensed light curves.

The probabilistic model

The intrinsic SN parameters — light-curve shape \(\theta\), host-galaxy dust extinction \(A_V\), residual colour variation \(\epsilon\), and dust law slope \(R_V\) — are shared across all images. Each image has its own time of peak brightness \(t_{\max}^{(i)}\) and effective distance modulus \(D_s^{(i)}\), which absorbs the absolute magnification from lensing. When enabled, each image also has its own microlensing GP hyperparameters. See Grayling et al. (2026) for full details.

Inference is performed using the No-U-Turn Sampler (NUTS) via numpyro.

Time conventions

Observation times (time_col) should be provided in observer-frame MJD, along with an estimated peak MJD (peak_mjds) for each image. These estimates don’t need to be precise — the model fits for a rest-frame correction tmax around each initial estimate, with a uniform prior over \(\pm 10\) rest-frame days.

The observer-frame peak MJD for each image is then computed as \(\mathrm{peak\_mjd}^{(i)} = \mathrm{peak\_mjds}^{(i)} + t_{\max}^{(i)} \times (1 + z)\), and the time delays delta_t are defined as \(\Delta t_{0i} = \mathrm{peak\_mjd}^{(0)} - \mathrm{peak\_mjd}^{(i)}\) in observer-frame days. Negative values mean image \(i\) arrives later than image 0 (i.e. has a larger peak MJD). Alternatively, if your times are already in rest-frame phase, you can set time_format='phase'.

GPU acceleration

bayesn-td is built on numpyro and JAX, so all model evaluations and MCMC sampling can run on GPU. See Installation for details on setting up JAX with GPU support.