Likelihood Functions¶
likelihood.py - Example Likelihood Functions¶
This file contains routines for simple test, likelihood, prior, and sampling functions for cases like the Wang & Li (2017) Rosenbrock function example.
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approxposterior.likelihood.rosenbrockLnlike(theta)[source]¶ Rosenbrock function as a loglikelihood following Wang & Li (2017)
- Parameters
theta (array) –
- Returns
l – likelihood
- Return type
float
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approxposterior.likelihood.rosenbrockLnprior(theta)[source]¶ Uniform log prior for the 2D Rosenbrock likelihood following Wang & Li (2017) where the prior pi(x) is a uniform distribution over [-5, 5] x [-5, 5] x … for however many dimensions (dim = x.shape[-1])
- Parameters
theta (array) –
- Returns
l – log prior
- Return type
float
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approxposterior.likelihood.rosenbrockSample(n=1, dim=2)[source]¶ Sample N points from the prior pi(x) is a uniform distribution over [-5, 5] x [-5, 5]
- Parameters
n (int, optional) – Number of samples. Defaults to 1.
dim (int, optional) – Dimensionality. Defaults to 2.
- Returns
sample – n x 2 array of floats samples from the prior
- Return type
floats
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approxposterior.likelihood.rosenbrockLnprob(theta)[source]¶ Compute the log probability (log posterior) as likelihood * prior
- Parameters
theta (array) –
- Returns
l – log probability
- Return type
float
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approxposterior.likelihood.testBOFn(theta)[source]¶ Simple 1D test Bayesian optimization function adapted from https://krasserm.github.io/2018/03/21/bayesian-optimization/
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approxposterior.likelihood.testBOFnSample(n=1)[source]¶ Sample N points from the prior pi(x) is a uniform distribution over [-2, 1]
- Parameters
n (int, optional) – Number of samples. Defaults to 1.
- Returns
sample – n x 1 array of floats samples from the prior
- Return type
floats
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approxposterior.likelihood.testBOFnLnPrior(theta)[source]¶ Log prior distribution for the test Bayesian Optimization function. This prior is a simple uniform function over [-2, 1]
- Parameters
theta (float/array) –
- Returns
l – log prior
- Return type
float
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approxposterior.likelihood.sphereLnlike(theta)[source]¶ Sphere test 2D optimization function. Note: This is actually the negative of the sphere function and it’s just a 0 mean, unit std Gaussian. Taken from: https://en.wikipedia.org/wiki/Test_functions_for_optimization
- Parameters
theta (array) –
- Returns
val – Function value at theta
- Return type
float