def testNormal(plot = False, perc = 1e-3):
N = int(1e6)
# effective number of simulations:
iterations = int(1e2)
y = nrm.likelihood.simul(3,100)
eps = ABC.findEpsilon(y = y, iterations = N, prior = nrm.prior,
likelihood = nrm.likelihood,
dist = misc.euclidean_dist, perc = perc,
sum_statistics = misc.meanVar)
thetas_all = []
t0 = time.clock()
thetas, zs = ABC.sampler(y = y, iterations = iterations,
prior = nrm.prior,
likelihood = nrm.likelihood,
dist = misc.euclidean_dist,
tolerance = eps,
sum_statistics = misc.meanVar)
thetas_all.append(thetas)
t1 = time.clock()
if plot:
misc.plotDensity(thetas_all, meanPrior = 0, sigmaPrior = 100,
empMean = np.mean(y), sigma = 4, n = 100)
print(np.mean(thetas))
return(t1-t0)
def test_Geom_Pois(trueGener = "Pois", naive = True, numBF = False):
if trueGener == "Pois":
theta = 4
gen = Pois.likelihood.simul
t0 = theta
elif trueGener == "Geom":
theta = 0.5
t0 = 1/theta
gen = Geom.likelihood.simul
else:
raise ValueError("Invalid value for the generator."
" Only Pois and Geom are allowed.")
# generate the data
y = gen(theta = theta, n = 50)
# total number of samples
N = int(1e6)
# percentage of accepted samples
perc = 1e-3
# expected number of accepted samples
iterations = int(N * perc)
if naive:
thetas, zs, ms = ABC.modelChoiceSampler(y = y, iterations = iterations,
paramPriors = [Pois.prior, Geom.prior],
likelihoods = [Pois.likelihood, Geom.likelihood],
modelPrior = misc.twoModelsPrior,
dist = misc.euclidean_dist,
tolerance = 0,
sum_statistics = np.sum)
ev0 = len([m for m in ms if m == 0])/len(ms)
else:
ms = ABCv.modelChoiceSampler(y = y, iterations = N,
paramPriors = [Pois.prior, Geom.prior],
likelihoods = [Pois.likelihood, Geom.likelihood],
modelPrior = misc.twoModelsPrior,
dist = misc.scalar_dist_multi,
tolerance = 0,
sum_statistics = misc.sumMulti)
ev0 = ms[0]/(ms[0]+ms[1])
if numBF:
poislogev, geomlogev = bf.GeomPoisLogBayesFactor(y)
misc.printModelChoice("Pois", "Geom", ev0, logBF = poislogev-geomlogev)
print("What I think it should be: ", 2 * np.log(t0 + 1) - np.log(t0) - t0)
return (np.log(ev0) - np.log(1-ev0), poislogev - geomlogev)
def test_RandField(trueGener = "trivial", theta = 4, naive = True, exactBF = False):
if trueGener == "trivial":
gen = rf1.likelihood.simul
else:
gen = rf2.likelihood.simul
y = gen(theta = theta, n = 50)
if (np.sum(y) == 50 or np.sum(y) == 0):
return (None,None)
N = int(1e6)
perc = 1e-3
iterations = int(N * perc)
if naive:
thetas, zs, ms = ABC.modelChoiceSampler(y = y, iterations = int(1e2),
paramPriors = [rf1.prior, rf2.prior],
likelihoods = [rf1.likelihood, rf2.likelihood],
modelPrior = misc.twoModelsPrior,
dist = misc.euclidean_dist,
tolerance = 0,
sum_statistics = misc.RFSumStats)
print(len([m for m in ms if m == 0]))
print(len(ms))
ev0 = len([m for m in ms if m == 0])/len(ms)
else:
ms = ABCv.modelChoiceSampler(y = y, iterations = N,
paramPriors = [rf1.prior, rf2.prior],
likelihoods = [rf1.likelihood, rf2.likelihood],
modelPrior = misc.twoModelsPrior,
dist = misc.euclidean_dist_multi,
tolerance = 0,
sum_statistics = misc.RFSumStats)
ev0v = ms[0]/(ms[0]+ms[1])
if exactBF:
ev0_true, ev1_true = bf.RFBayesFactor(y)
#misc.printModelChoice("trivial", "MarkovChain", ev0)
misc.printModelChoice("trivial", "MarkovChain", ev0, ev0_true)
return (ev0, ev0_true)
def test_MA2_samplers(which = "basic", noisy = False,
generator = "MA(2)", naive = True,
exactBF = False):
# simulate observation
if generator == "MA(2)":
y = MA2.likelihood.simul(theta = [0.6,0.2], n = 100+2)
elif generator == "MA(1)":
y = MA1.likelihood.simul(theta = 0.6, n = 100+1)
else:
raise ValueError("Invalid name of the generator, "
"only MA(1) and MA(2) are allowed.")
# total number of simulations
N = int(1e6)
# expected proportion of accepted simulations
perc = 1e-3
# effective number of simulations:
iterations = int(N * perc)
if which == "MCMC":
eps = 60
thetas, zs = ABC.MCMCsampler(y = y, iterations = iterations,
prior = MA2.prior,
likelihood = MA2.likelihood,
dist = misc.euclidean_dist,
tolerance = eps,
sum_statistics = misc.autocov,
transKernel = MA2.transKernel)
misc.plot_thetas(thetas)
elif which == "basic":
eps = ABC.findEpsilon(y = y, iterations = N, prior = MA2.prior,
likelihood = MA2.likelihood,
dist = misc.euclidean_dist, perc = perc,
sum_statistics = misc.autocov)
thetas, zs = ABC.sampler(y = y, iterations = iterations,
prior = MA2.prior,
likelihood = MA2.likelihood,
dist = misc.euclidean_dist,
tolerance = eps,
sum_statistics = misc.autocov)
misc.plot_thetas(thetas)
elif which == "importance":
thetas, zs, weights = ABC.importanceSampler(y = y,
iterations = int(1e5),
prior = MA2.prior,
likelihood = MA2.likelihood,
proposal = MA2.proposal,
densKernel = MA2.densKernel,
bandwidth = 10,
sum_statistics = misc.autocov,
noisy = noisy)
out = np.sum([t * w for t,w in
zip(thetas, weights)],axis = 0)/np.sum(weights)
print("Evaluation of E[theta] using importance sampler gives: ", out)
elif which == "KernelMCMC":
thetas, zs = ABC.kernelMCMCSampler(y = y, iterations = int(1e4),
prior = MA2.prior,
likelihood = MA2.likelihood,
densKernel = MA2.densKernel,
bandwidth = 10,
transKernel = MA2.transKernel,
sum_statistics = misc.autocov,
dist = misc.euclidean_dist,
tolerance = 10, noisy = noisy)
misc.plot_thetas(thetas)
elif which == "modelChoiceSampler":
eps = ABCv.findEpsilon(y = y, iterations = N, prior = MA2.prior,
likelihood = MA2.likelihood,
dist = misc.euclidean_dist_multi,
perc = np.array([0.01,0.001, 0.0001, 0.00001]),
sum_statistics = misc.autocov)
if naive:
evs = []
for e in eps:
thetas, zs, ms = ABC.modelChoiceSampler(y = y, iterations = iterations,
paramPriors = [MA1.prior, MA2.prior],
likelihoods = [MA1.likelihood, MA2.likelihood],
modelPrior = misc.twoModelsPrior,
dist = misc.euclidean_dist,
tolerance = 7,
sum_statistics = misc.autocov)
ev0 = len([m for m in ms if m == 0])/len(ms)
evs.append(ev0)
else:
evs = []
for e in eps:
ms = ABCv.modelChoiceSampler(y = y, iterations = N,
paramPriors = [MA1.prior, MA2.prior],
likelihoods = [MA1.likelihood, MA2.likelihood],
modelPrior = misc.twoModelsPrior,
dist = misc.euclidean_dist_multi,
tolerance = e,
sum_statistics = misc.autocov)
ev0 = ms[0]/(ms[0]+ms[1])
evs.append(ev0)
misc.plotMAModSel(evs)
if exactBF:
print("Finding actual Bayes Factor...\n")
ev0exact = bf.MALogBayesFactor(y, resolution=(100,200))
for e in evs:
misc.printModelChoice("MA(1)", "MA(2)", e, ev0exact)
else:
raise ValueError("Invalid name of tested model.")