mle.rst

MLE

The .MLE class evaluates the maximum likelihood estimate θ̂ of the model parameters, i.e.

θ̂ = argmax_Θ p(𝒟|θ)

Note: for a Gaussian-error model of the form 𝒟 = h(θ) + ϵ, ϵ ∼ N(0, σ) with fixed σ and independent measurements 𝒟_i, maximizing the likelihood is mathematically equivalent to minimizing the sum of squared residuals ∑_i(𝒟_i−h(θ))².

A numerical optimization procedure is performed to compute the MLE. By default, the :pyminimize function of the :pyscipy.optimize module is used, however other optimizers can be leveraged via the optimizer input of the .MLE class.

MLE Class

The .MLE class is imported using the following command:

>>> from UQpy.inference.MLE import MLE

Methods

UQpy.inference.MLE

Attributes

UQpy.inference.MLE.mle

UQpy.inference.MLE.max_log_like

Examples

MLE Examples <../auto_examples/inference/mle/index>