https://github.com/theogf/BayesianQuadrature.jl

Is there anything we can't make Bayesian?
https://github.com/theogf/BayesianQuadrature.jl

bayesian bayesian-inference bayesian-quadrature gaussian integral julia quadrature

Last synced: about 2 months ago
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Is there anything we can't make Bayesian?

• Host: GitHub
• URL: https://github.com/theogf/BayesianQuadrature.jl
• Owner: theogf
• License: mit
• Created: 2021-02-08T13:26:33.000Z (over 3 years ago)
• Default Branch: main
• Last Pushed: 2022-03-08T13:25:10.000Z (over 2 years ago)
• Last Synced: 2024-07-10T02:18:09.799Z (2 months ago)
• Topics: bayesian, bayesian-inference, bayesian-quadrature, gaussian, integral, julia, quadrature
• Language: Julia
• Homepage:
• Size: 339 KB
• Stars: 13
• Watchers: 5
• Forks: 0
• Open Issues: 10
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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• awesome-sciml - theogf/BayesianQuadrature.jl: Is there anything we can't make Bayesian?

README

        
# BayesianQuadrature

[![Stable](https://img.shields.io/badge/docs-stable-blue.svg)](https://theogf.github.io/BayesianQuadrature.jl/stable)

[![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://theogf.github.io/BayesianQuadrature.jl/dev)

[![Build Status](https://github.com/theogf/BayesianQuadrature.jl/workflows/CI/badge.svg)](https://github.com/theogf/BayesianQuadrature.jl/actions)

[![Coverage Status](https://coveralls.io/repos/github/theogf/BayesianQuadrature.jl/badge.svg?branch=main)](https://coveralls.io/github/theogf/BayesianQuadrature.jl?branch=main)

[![Code Style: Blue](https://img.shields.io/badge/code%20style-blue-4495d1.svg)](https://github.com/invenia/BlueStyle)

[![DOI](https://zenodo.org/badge/337084342.svg)](https://zenodo.org/badge/latestdoi/337084342)

Package for implementing different methods of Bayesian quadrature.

Bayesian quadrature consists in estimating the integral `I = ∫ f(x) p(x) dx` by using Gaussian Processes where `p(x)` is assumed to be Gaussian.

More precisely we replace `f(x)` by a GP by estimating `f` for multiple samples `x_i`.

We then get a posterior distribution for the integral : `p(I|{x_i}) = N(m, S)`.

Given a Bayesian problem `p(x|y) = p(y|x) p_0(x) / p(y)` you can estimate `p(y)` by calling :

```julia

using BayesianQuadrature

using Distributions

using KernelFunctions

p_0 = MvNormal(ones(2)) # As for now the prior must be a MvNormal

log_f(x) = logpdf(MvNormal(0.5 * ones(2)), x) # The logarithm of the Integrand log_f, the log-likelihood function typically

model = BayesModel(p_0, log_f) # Combine both to create the model

bquad = BayesQuad(SEKernel(); l=0.1, σ=1.0) # Will simply approximate p(y|x) with a GP (only works with SEKernel for now

sampler = PriorSampling() # Will sample from the prior p_0

p_I, _ = bquad(model, sampler; nsamples=100) # Returns a Normal distribution

@show p_I # Normal{Float64}(μ=0.07063602778449946, σ=0.0028050929209120458)

```