lartillot-gaussian 0.0.2

A simple multi-dimensional Gaussian model from Lartillot et al '06, useful for testing Bayesian applications.

Lartillot Gaussian model

The multidimensional Gaussian model from Lartillot et al '06 is useful for testing Bayesian applications.

The model is parameterised by a vector $\theta = (\theta_1, \theta_2, \ldots, \theta_d)$ of dimension $d$. The prior on $\theta$ is a product of independent normals with a null mean and unit variance. The likelihood function is given by $$\mathcal{L}(\theta, v) = {(2\pi v)^{-d/2}} \prod_{i = 1}^d \text{exp}\bigg[\frac{-\theta_i^2}{2v}\bigg],$$ where $v$ is the common variance for all $d$ dimensions.

The joint posterior is given by $d$ products of $\mathcal{N}(0, v/(1+v))$. Finally, the evidence is given by $$ \mathcal{Z} = (2\pi v)^{-d/2} \left(\frac{v}{1 + v} \right)^{d/2}=\left(2\pi(1+v)\right)^{-d/2}\ . $$

This codebase provides a simple implementation of the Lartillot Gaussian model in Python.

pip install lartillot_gaussian

from lartillot_gaussian import LartillotGaussianModel
import numpy as np

model = LartillotGaussianModel(d=10, v=1.0)
theta = np.array([[0]])
print(model.lnz)