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""" | ||
SMC and SMC-ABC common functions | ||
""" | ||
import numpy as np | ||
import pymc3 as pm | ||
from ..backends.ndarray import NDArray | ||
from ..backends.base import MultiTrace | ||
from ..theanof import floatX | ||
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def _initial_population(draws, model, variables): | ||
""" | ||
Create an initial population from the prior | ||
""" | ||
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population = [] | ||
var_info = {} | ||
start = model.test_point | ||
init_rnd = pm.sample_prior_predictive(draws, model=model) | ||
for v in variables: | ||
var_info[v.name] = (start[v.name].shape, start[v.name].size) | ||
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for i in range(draws): | ||
point = pm.Point({v.name: init_rnd[v.name][i] for v in variables}, model=model) | ||
population.append(model.dict_to_array(point)) | ||
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return np.array(floatX(population)), var_info | ||
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def _calc_covariance(posterior, weights): | ||
""" | ||
Calculate trace covariance matrix based on importance weights. | ||
""" | ||
cov = np.cov(posterior, aweights=weights.ravel(), bias=False, rowvar=0) | ||
if np.isnan(cov).any() or np.isinf(cov).any(): | ||
raise ValueError('Sample covariances not valid! Likely "draws" is too small!') | ||
return np.atleast_2d(cov) | ||
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def _tune(acc_rate, proposed, step): | ||
""" | ||
Tune scaling and/or n_steps based on the acceptance rate. | ||
Parameters | ||
---------- | ||
acc_rate: float | ||
Acceptance rate of the previous stage | ||
proposed: int | ||
Total number of proposed steps (draws * n_steps) | ||
step: SMC step method | ||
""" | ||
if step.tune_scaling: | ||
# a and b after Muto & Beck 2008. | ||
a = 1 / 9 | ||
b = 8 / 9 | ||
step.scaling = (a + b * acc_rate) ** 2 | ||
if step.tune_steps: | ||
acc_rate = max(1.0 / proposed, acc_rate) | ||
step.n_steps = min(step.max_steps, 1 + int(np.log(step.p_acc_rate) / np.log(1 - acc_rate))) | ||
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def _posterior_to_trace(posterior, variables, model, var_info): | ||
""" | ||
Save results into a PyMC3 trace | ||
""" | ||
lenght_pos = len(posterior) | ||
varnames = [v.name for v in variables] | ||
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with model: | ||
strace = NDArray(model) | ||
strace.setup(lenght_pos, 0) | ||
for i in range(lenght_pos): | ||
value = [] | ||
size = 0 | ||
for var in varnames: | ||
shape, new_size = var_info[var] | ||
value.append(posterior[i][size : size + new_size].reshape(shape)) | ||
size += new_size | ||
strace.record({k: v for k, v in zip(varnames, value)}) | ||
return MultiTrace([strace]) |