BayesianGLS.jl

Bayesian Generalized Lomb-Scargle periodogram for Julia, implementing the methods of Mortier et al. (2015) and the stacked variant from Mortier & Collier Cameron (2017).

Features

• BGLS: Bayesian periodogram that analytically marginalizes over amplitude, phase, and offset
• Stacked BGLS (sBGLS): 2D map of signal evolution as observations accumulate — real signals grow monotonically, aliases and activity signals appear/disappear
• Zero non-stdlib dependencies (only LinearAlgebra)
• Accepts any AbstractVector{<:Real} inputs

Installation

using Pkg
Pkg.add("BayesianGLS")

Quick Start

using BayesianGLS

# Synthetic RV data
t = sort(rand(100) .* 200.0)
y = 20.0 .* sin.(2π .* 0.1 .* t) .+ randn(100) .* 2.0
err = fill(2.0, 100)

# BGLS periodogram
result = bgls_auto(t, y, err)
println("Best period: ", best_period(result), " days")

# Stacked BGLS
sresult = sbgls_auto(t, y, err; n_min=15)
# sresult.matrix is a 2D array: rows = accumulating observations, cols = frequencies

API

BGLS

Function	Description
bgls(t, y, err, freqs)	Compute BGLS for a given frequency grid
bgls_auto(t, y, err; min_freq, max_freq, samples_per_peak)	BGLS with automatic frequency grid

Stacked BGLS

Function	Description
sbgls(t, y, err, freqs; n_min)	Compute stacked BGLS for a given frequency grid
sbgls_auto(t, y, err; min_freq, max_freq, samples_per_peak, n_min, max_frequencies)	Stacked BGLS with automatic frequency grid

Utilities

Function	Description
autofrequencies(t; min_freq, max_freq, samples_per_peak)	Build a frequency grid from time baseline
best_frequency(result)	Frequency of highest log-probability
best_period(result)	Period of highest log-probability
frequencies(result)	Frequency grid
periods(result)	Period grid (1 ./ frequencies)
power(result)	Log-probability spectrum (or matrix for sBGLS)

All result types support tuple destructuring:

freqs, logp = bgls(t, y, err, freqs)
freqs, obs_times, matrix = sbgls(t, y, err, freqs)

Citation

If you use this package, please cite:

Mortier, A., Faria, J. P., Correia, C. M., Santerne, A., & Santos, N. C. (2015). BGLS: A Bayesian formalism for the generalised Lomb-Scargle periodogram. Astronomy & Astrophysics, 573, A101.

Mortier, A. & Collier Cameron, A. (2017). The stacked Bayesian general Lomb-Scargle periodogram. Astronomy & Astrophysics, 601, A110.

@article{Mortier2015,
  author  = {Mortier, A. and Faria, J. P. and Correia, C. M. and Santerne, A. and Santos, N. C.},
  title   = {{BGLS}: A {B}ayesian formalism for the generalised {L}omb-{S}cargle periodogram},
  journal = {Astronomy \& Astrophysics},
  volume  = {573},
  pages   = {A101},
  year    = {2015},
  doi     = {10.1051/0004-6361/201424908}
}

@article{Mortier2017,
  author  = {Mortier, A. and Collier Cameron, A.},
  title   = {The stacked {B}ayesian general {L}omb-{S}cargle periodogram},
  journal = {Astronomy \& Astrophysics},
  volume  = {601},
  pages   = {A110},
  year    = {2017},
  doi     = {10.1051/0004-6361/201630092}
}

See Also

• LombScargle.jl -- Classical Lomb-Scargle periodogram
• L1Periodograms.jl -- LASSO-based sparse periodogram (Hara et al. 2017)

License

MIT