anyHR 1.0.1

Library implementing hit-and-run methods for sampling open bounded sets.

anyHR

A collection of hit-and-run Markov Chain Monte Carlo algorithms for sampling of n-dimensional sets defined by arbitrary inequality constraints.

Introduction

This tool implements some variants of the hit and run or mixing algorithms.

Let S be an open bounded set in n dimensions defined by inequality constraints of the form

f(x₁,..., x_n) < g(x₁,..., x_n), where f and g are arbitrary functions.

Let all parameters also have parameter ranges defined as intervals, so S is a subset of a hyperrectangle.

(As an example, one could impose x + y < 1 in the two dimensional plane, with x in (0,1) and y in (0,1)).

Hit-and-run algorithms can be used to get a sample uniformly at random inside of this set S.

anyHR parses the parameters and their respective constraints and returns a number of samples that satisfy this spec,

while being distributed uniformly on the set of allowed values.

For more information on mixing algorithms see

Installation

It is necessary to have a working installation of Python 3,

pip and git for the following installation process.

Open the target installation directory in a terminal and type

pip install anyHR

Use

A minimal running example for the above specification can be sampled with the following code:

# Import modules

import numpy as np

import matplotlib.pyplot as plt

from anyHR.constraint.Constraint import Constraints

from anyHR.hit_and_run.hit_and_run import HitAndRun





# Define variables to use

var_names = ['x', 'y']



# Define the set of constraint

c = Constraints(var_names)

c.add_constraint('x+y < 1')



# Define the bounding hyperrectangle

x_bound = [0, 1]

y_bound = [0, 1]

bounds = [x_bound, y_bound]



# build hr object

hr = HitAndRun(constraint=c, bounding_box=bounds)



# generate samples

samples = []

total_rejections = 0

nb_samples = 100

mixing = 10

for i in range(nb_samples * mixing):

    sample, rejections = hr.next_sample()



    # do some mixing in between samples

    if i % mixing == 0:

        samples.append(sample)



xs = [sample[0] for sample in samples]

ys = [sample[1] for sample in samples]



plt.scatter(xs,ys)

plt.show()

References

For more information about mixing algorithms, see:

• Smith, R. L. (1984). Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions. Operations Research, 32(6), 1296-1308.

• Kiatsupaibul, S., Smith, R. L., & Zabinsky, Z. B. (2011). An analysis of a variation of hit-and-run for uniform sampling from general regions. ACM Transactions on Modeling and Computer Simulation (TOMACS), 21(3), 1-11.

• Neal, R. M. (2003). Slice sampling. The annals of statistics, 31(3), 705-767.

We also thank Abraham Lee for his implementation of the PSO algorithms which is used here.

See https://github.com/tisimst/pyswarm for more information.