Intuitive syntax for complex statistical model fitting and parameter sensitivity analysis.
Project description
About
Pykelihood is a Python package for statistical analysis designed to give more flexibility to likelihood-based inference than is possible with scipy.stats. Distributions are designed from an Object Oriented Programming (OOP) point of view.
Main features include:
use any scipy.stats distribution, or make your own,
fit distributions of arbitrary complexity to your data,
add trends of different forms in the parameters of any distribution,
condition the likelihood with any form of penalty,
profile parameters with a penalised likelihood,
fit joint distributions and point processes with self exciting or time dependent intensity,
more to come…
Installation
Using pip (soon)
pip install pykelihoodFrom sources
git clone https://www.github.com/OpheliaMiralles/pykelihoodor
gh repo clone OpheliaMiralles/pykelihoodUsage
Basics
The most basic thing you can use pykelihood for is creating and manipulating distributions as objects.
>>> from pykelihood.distributions import Normal >>> n = Normal(1, 2) >>> n Normal(loc=1.0, scale=2.0)
n is an object of type Normal. It has 2 parameters, loc and scale. They can be accessed like standard Python attributes:
>>> n.loc 1.0
Using the Normal object, you can calculate standard values using the same semantics as scipy.stats:
>>> n.pdf([0, 1, 2]) array([0.17603266, 0.19947114, 0.17603266]) >>> n.cdf([0, 1, 2]) array([0.30853754, 0.5 , 0.69146246])
Or you can also generate random values according to this distribution:
>>> n.rvs(10)
array([ 3.31370986, 5.02699468, -0.3573229 , 1.00460378, -3.26044871,
1.86362711, -0.84192901, 0.81132182, -2.03266978, 1.48079944])
Fitting
Let’s generate a larger sample from our previous object:
>>> data = n.rvs(1000) >>> data.mean() 1.025039359276458 >>> data.std() 1.9376460645596842
We can fit a Normal distribution to this data, which will return another Normal object:
>>> n.fit(data) Normal(loc=1.0250822420920338, scale=1.9376400770300832)
As you can see, the values are slightly different from the moments in the data. This is due to the fact that the fit method returns the Maximum Likelihood Estimator (MLE) for the data, and is thus the result of an optimisation (using scipy.optimize).
We can also fix the value for some parameters if we know them:
>>> n.fit(data, loc=1) Normal(loc=1.0, scale=1.9377929687500024)
Trend fitting
One of the most powerful features of pykelihood is the ability to fit arbitrary distributions. For instance, say our data has a linear trend with a very little gaussian noise we would like to capture:
>>> import numpy as np
>>> data = np.linspace(-1, 1, 365) + np.random.normal(0, 0.001, 365)
>>> data[:10]
array([-0.99802364, -0.99503679, -0.98900434, -0.98277981, -0.979487 ,
-0.97393519, -0.96853445, -0.96149152, -0.95564004, -0.95054887])
If we try to fit this without a trend, the resulting distribution will miss out on most of the information:
>>> n.fit(data) Normal(loc=-3.6462053656578005e-05, scale=0.5789668679237372)
Let’s fit a Normal distribution with a trend in the loc parameter:
>>> from pykelihood import kernels >>> n.fit(data, loc=kernels.linear(np.arange(365))) Normal(loc=linear(a=-1.0000458359290572, b=0.005494714384381866), scale=0.0010055323717468906)
kernels.linear(X) builds a linear model in the form a + bX where a and b are parameters to be optimised for, and X is some covariate used to fit the data. If we assume the data were daily observations, then we find all the values we expected: -1 was the value on the first day, 0.05 was the daily increment (2 / 365 = 0.05), and there was a noise with std deviation 0.001.
Why do I have to create an instance to be able to fit my data?
In the above example, we didn’t specify any value or trend for the scale parameter. The reason it still worked is that pykelihood assumed scale would have the same form as n’s scale, which in this case is a simple float parameter. Hence using an instance to fit the data avoids having to give a value for all parameters.
In some cases, it can become tedious to write everything out in one statement:
>>> from pykelihood.distributions import Beta >>> X = np.arange(365) >>> b = Beta(loc=kernels.linear(X), scale=kernels.linear(X), alpha=kernels.linear(X), beta=kernels.linear(X))
To avoid having so many parameters to optimise, you could decide to fix some parameters:
>>> b.fit(data, loc=0) ... >>> b.fit(data, loc=1) ...
This syntax allows you to keep scale, beta and alpha as linear trends while varying the value for the loc parameter.
Contributing
Poetry is used to manage pykelihood’s dependencies and build system. To install Poetry, you can refer to the installation instructions, but it boils down to running:
curl -sSL https://raw.githubusercontent.com/python-poetry/poetry/master/get-poetry.py | pythonTo configure your environment to work on pykelihood, run:
git clone https://www.github.com/OpheliaMiralles/pykelihood # or any other clone method
cd pykelihood
poetry install -DThis will create a virtual environment for the project and install the required dependencies. To activate the virtual
environment, be sure to run poetry shell prior to executing any code.
Some parts of the code base use the matplotlib and hawkeslib package, but are for now not required to run most of the code, including the tests.
Tests
Tests are run using pytest. To run all tests, navigate to the root folder or the
tests folder and type pytest.
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Source Distribution
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