https://github.com/mlefkir/pioran.jl

Power spectrum inference of irregularly sampled time series using Gaussian Processes in Julia

Science Score: 44.0%

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Low similarity (12.1%) to scientific vocabulary

Keywords

fourier-analysis gaussian-processes julia power-spectrum-estimation time-series time-series-analysis

Last synced: 11 months ago · JSON representation ·

Repository

Power spectrum inference of irregularly sampled time series using Gaussian Processes in Julia

Basic Info

Host: GitHub
Owner: mlefkir
License: mit
Language: Julia
Default Branch: main
Homepage: https://mlefkir.github.io/Pioran.jl/
Size: 114 MB

Statistics

Stars: 13
Watchers: 1
Forks: 0
Open Issues: 2
Releases: 9

Topics

fourier-analysis gaussian-processes julia power-spectrum-estimation time-series time-series-analysis

Created over 2 years ago · Last pushed 11 months ago

Metadata Files

Readme License Citation

Pioran is a Julia package to estimate bending power-law power spectrum of time series. This method uses Gaussian process regression with the fast algorithm of Foreman-Mackey, et al. 2017. The bending power-law model is approximated using basis functions as shown in the Figure below:

The method is described in Lefkir et. al 2025, where it is used to model the random flux variability observed in active galaxies.

Installation

julia using Pkg; Pkg.add("Pioran")

Documentation

Read the documentation here: https://mlefkir.github.io/Pioran.jl/stable/.

Examples

Example scripts are provided in the examples directory. To infer the parameters of the power spectrum, I use either Turing.jl for Hamiltonian Monte Carlo or the Python library ultranest for nested sampling.

Ultranest

Here a very quick example on how to use it with ultranest. I assume you have installed PyCall and ultranest following the guide in the documentation here.

Assuming you have a Gaussian time series y at times t with errorbars σ. The GP can be built using a function as follows:

```julia using Pioran, Distributions

function GPmodel(t, y, σ, params, ncomponents = 20, basis_function = "DRWCelerite") T = (t[end] - t[1]) # duration of the time series Δt = minimum(diff(t)) # min time separation

f_min, f_max = 1 / T, 1 / Δt / 2

# Get the parameters
α₁, f₁, α₂, variance, ν, μ = params

# Rescale the measurement variance
σ² = ν .* σ .^ 2

# Define the power spectral density function
𝓟 = SingleBendingPowerLaw(α₁, f₁, α₂)

# Approximate the PSD to form a covariance function
𝓡 = approx(𝓟, f_min, f_max, n_components, variance, basis_function = basis_function)

# Build the GP
GP = ScalableGP(μ, 𝓡)

# return the conditioned GP on the times and errors and the transformed values
return GP(t, σ²)

end ```

The log-likelihood can be obtained using the logpdf function from Distributions.jl:

julia function loglikelihood(t, y, σ, params) GP = GP_model(t, y, σ, params) return logpdf(GP, y) end logl(pars) = loglikelihood(t, y, yerr, pars) We use distributions from Distributions.jl to define the priors for nested sampling. For this example, we can have:

julia function prior_transform(cube) α₁ = quantile(Uniform(0.0, 1.5), cube[1]) f₁ = quantile(LogUniform(1e-3, 1e3), cube[2]) α₂ = quantile(Uniform(α₁, 4.0), cube[3]) variance = quantile(LogNormal(0, 1), cube[4]) ν = quantile(Gamma(2, 0.5), cube[5]) μ = quantile(Normal(x̄, 5 * sqrt(va)), cube[6]) return [α₁, f₁, α₂, variance, ν, μ] end paramnames = ["α₁", "f₁", "α₂", "variance", "ν", "μ"]

We can load ultranest using PyCall: julia using PyCall ultranest = pyimport("ultranest")

and start sampling the posterior:

julia sampler = ultranest.ReactiveNestedSampler(paramnames, logl, resume = true, transform = prior_transform, log_dir = "path/to/dir", vectorized = false) results = sampler.run() sampler.print_results() sampler.plot()

Citing the method

If this method or code was useful to you, you can cite Lefkir et. al 2025 for method and Foreman-Mackey, et al. 2017 for the celerite algorithm.

If you have used ultranest or Turing.jl to sample the posterior, have a look at their documentation on how to cite them properly.

Owner

Name: Mehdy Lefkir
Login: mlefkir
Kind: user
Location: Toulouse

Repositories: 2
Profile: https://github.com/mlefkir

Citation (CITATION.cff)

cff-version: 1.2.0
message: "If you use this software, please cite it as below."
authors:
  - family-names: Lefkir
    given-names: Mehdy
    orcid: https://orcid.org/0000-0002-6972-2429
title: "Pioran.jl"
version: 1.0.0
identifiers:
  - type: doi
    value: 10.1093/mnras/staf532
date-released: 2025-07-08
url: "https://github.com/mlefkir/Pioran.jl"

GitHub Events

Total

Create event: 14
Commit comment event: 5
Release event: 3
Issues event: 7
Watch event: 9
Delete event: 15
Issue comment event: 27
Push event: 71
Pull request event: 17

Last Year

Create event: 14
Commit comment event: 5
Release event: 3
Issues event: 7
Watch event: 9
Delete event: 15
Issue comment event: 27
Push event: 71
Pull request event: 17

Issues and Pull Requests

Last synced: 11 months ago

All Time

Total issues: 7
Total pull requests: 38
Average time to close issues: 3 months
Average time to close pull requests: 8 days
Total issue authors: 1
Total pull request authors: 3
Average comments per issue: 2.43
Average comments per pull request: 0.34
Merged pull requests: 33
Bot issues: 0
Bot pull requests: 20

Past Year

Issues: 4
Pull requests: 17
Average time to close issues: 10 days
Average time to close pull requests: 20 days
Issue authors: 1
Pull request authors: 3
Average comments per issue: 0.5
Average comments per pull request: 0.76
Merged pull requests: 12
Bot issues: 0
Bot pull requests: 7

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Top Authors

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mlefkir (7)

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github-actions[bot] (30)
mlefkir (26)
pre-commit-ci[bot] (2)

Top Labels

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enhancement (1) performance (1)

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Packages

Total packages: 1
Total downloads:
- julia 2 total

Total dependent packages: 0
Total dependent repositories: 0
Total versions: 7

juliahub.com: Pioran

Power spectrum inference of irregularly sampled time series using Gaussian Processes in Julia

Homepage: https://mlefkir.github.io/Pioran.jl/
Documentation: https://docs.juliahub.com/General/Pioran/stable/
License: MIT
Latest release: 1.0.0
published about 1 year ago

Versions: 7
Dependent Packages: 0
Dependent Repositories: 0
Downloads: 2 Total

Rankings

Dependent repos count: 9.7%

Average: 24.4%

Dependent packages count: 39.1%

Last synced: 11 months ago

Dependencies

.github/workflows/testbuild.yml actions

actions/checkout v2 composite
julia-actions/julia-buildpkg v1 composite
julia-actions/julia-runtest v1 composite
julia-actions/setup-julia v1 composite

.github/workflows/documentation.yml actions

actions/checkout v4 composite
julia-actions/setup-julia v1 composite

.github/workflows/CompatHelper.yml actions

julia-actions/setup-julia v1 composite

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Open Source Science

https://github.com/mlefkir/pioran.jl

Science Score: 44.0%

Keywords

Repository

Basic Info

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Metadata Files

README.md

Installation

Documentation

Examples

Ultranest

Citing the method

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Citation (CITATION.cff)

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juliahub.com: Pioran

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