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#!/usr/bin/env python
"""
Multimodal demonstration using gaussian mixture model.
The model is a mixture model representing the probability density from a
product of gaussians.
This example show performance of the algorithm on multimodal densities,
with adjustable number of densities and degree of separation.
The peaks are distributed about the x-y plane so that the marginal densities
in x and y are spaced every 2 units using latin hypercube sampling. For small
peak widths, this means that the densities will not overlap, and the marginal
maximum likelihood for a given x or y value should match the estimated density.
With overlap, the marginal density will over estimate the marginal maximum
likelihood.
Adjust the width of the peaks, *S*, to see the effect of relative diameter of
the modes on sampling. Adjust the height of the peaks, *I*, to see the
effects of the relative height of the modes. Adjust the count *n* to see
the effects of the number of modes.
Note that dream.diffev.de_step adds jitter to the parameters at the 1e-6 level,
so *S* < 1e-4 cannot be modeled reliably.
*draws* is set to 1000 samples per mode. *burn* is set to 100 samples per mode.
Population size *h* is set to 20 per mode. A good choice for number of
sequences *k* is not yet determined.
"""
from pylab import *
from bumps.dream import *
if 1: # Fixed layout of 5 minima
n = 5
S = [0.1]*5
x = [-4, -2, 0, 2, 4]
y = [2, -2, -4, 0, 4]
z = [-2, -1, 0, 1, 3]
I = [5, 2.5, 1, 4, 1]
else: # Semirandom layout of n minima
d = 3
n = 40
S = [0.1]*n
x = linspace(-n+1,n-1,n)
y = permutation(x)
z = permutation(x)
I = 2*linspace(-1,1,n)**2 + 1
args = [] # Sequence of density, weight, density, weight, ...
for xi,yi,zi,Si,Ii in zip(x,y,z,S,I):
args.extend( (MVNormal([xi,yi,zi],Si*eye(3)), Ii) )
#args.extend( (MVNormal([xi,yi],Si*eye(2)), Ii) )
model = Mixture(*args)
k = 20*n
h = int(20*n/k)
sampler = Dream(model=model,
population=randn(h,k,2),
#use_delayed_rejection=False,
DE_snooker_rate=0.5,
outlier_test='none',
draws=4000*n,burn=500*k,
thinning=1)
mc = sampler.sample()
mc.show()
show()
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