Pioran

Pioran is a Julia package for the inference of bending power-law power spectra from arbitrarily sampled time series using scalable Gaussian processes.

This method was designed to aid the estimation of bending frequencies and slopes in the power spectra of irregularly sampled light curves of active galaxies but it can be applied to any time series data. The method is formally introduced in Lefkir et al. (2025) and uses the fast celerite algorithm of Foreman-Mackey et al. (2017).

Installation

The package can be installed add follows:

import Pkg; Pkg.add("Pioran")

Content

• Getting started
• • Installation
  • Usage
• Spectral analysis in Pioran
• • Gaussian process regression
  • Gaussian processes in Pioran
• Modelling
• • Modelling the power spectral density
  • Approximating the power spectral density
  • Building the Gaussian process
• Simulations
• • Sampling from the Gaussian process
  • Conditioning the Gaussian process
• Time series and priors
• • Log-normal distributed time series
  • Defining the priors
• Diagnostics post-inference
• • In the Fourier domain
  • In the time domain
• About the basis functions
• • Approximation
  • Integral of the basis functions
• Using custom mean function
• • Implementation
  • Sampling from the GP
  • Inference
• Modelling features in the power spectrum
• • Defining the model and simulating form the model
• API Reference
• • Power spectral densities
  • Covariance functions
  • Gaussian processes
  • Solvers
  • Plotting
  • Utilities
  • CARMA