Tutorial: Generating Synthetic Light Curves

This notebook demonstrates how to use the pgmuvi.synthetic module to:

  1. Draw synthetic light curves from a GP with known hyperparameters

  2. Verify that pgmuvi can recover those hyperparameters

  3. Simulate multiband observations with different cadences

Why synthetic data?

Synthetic experiments (sometimes called simulation-based calibration or parameter recovery tests) are essential for:

  • Validating that the fitting pipeline is correctly implemented

  • Understanding parameter degeneracies

  • Setting realistic expectations about what the data can constrain

  • Survey planning (e.g., what cadence is needed to detect a given period?)

Prerequisites: the pgmuvi_tutorial notebook.

1. Setup

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import numpy as np
import matplotlib.pyplot as plt
import pgmuvi
import pgmuvi.synthetic

2. Generating a Synthetic Single-Band Light Curve

We specify a set of hyperparameters — one mixture component with a period of 100 days and a modest bandwidth — and draw a realisation from the corresponding GP.

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# TODO: Expand with pgmuvi.synthetic API calls once this tutorial is developed
# The pgmuvi.synthetic module contains tools for drawing GP samples.

# Placeholder: define observation grid
rng = np.random.default_rng(0)
times = np.sort(rng.uniform(0, 500, 200))
print(f"Synthetic observation grid: {len(times)} points over {times[-1]:.0f} days")

3. Fitting the Synthetic Data

We fit a GP model to the synthetic data and check that the inferred period matches the input period.

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# TODO: Expand with GP MAP fitting via fit(model="1D") and compare inferred
# parameters against the true synthetic values. Optionally call fit_LS() first
# to inspect candidate periods / diagnostics.

4. Parameter Recovery: Varying Cadence

Here we repeat the synthetic experiment with different observation cadences to understand the minimum sampling required to detect the 100-day period.

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# TODO: Loop over cadences and summarise recovery fraction

5. Multiband Synthetic Data

We demonstrate generating a synthetic two-band light curve where the variability amplitude changes with wavelength.

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# TODO: Expand with 2D synthetic example using pgmuvi.synthetic

Next Steps

  • See the pgmuvi.synthetic API reference in the documentation for the full list of available functions.

  • For MCMC-based parameter uncertainty: MCMC support (mcmc()) is planned for a future release and is not yet available.

  • For sampling quality assessment, see the Preprocessing tutorial.