class TestFisherInformation(DerandomizedTestCase):
# Test the implementation of numerical Fisher Information by comparing to
# numbers which were derived by doing analytic/numeric
# integrals of simple models (binomialm, poisson, and gaussian) in
# Mathematica. This test trusts that these calculations
# were done correctly.
ALPHA = 1
BETA = 3
PRIOR_BETA = BetaDistribution(alpha=ALPHA, beta=BETA)
N_PARTICLES = 10000
BIN_FI_MODELPARAMS = np.linspace(0.01, 0.99, 5)
NMEAS_EXPPARAMS = np.arange(1, 11, dtype=int)
def setUp(self):
super(TestFisherInformation, self).setUp()
# Set up relevant models.
self.coin_model = CoinModel()
self.binomial_model = DifferentiableBinomialModel(self.coin_model)
# Set up updaters for these models using particle approximations
# of conjugate priors
self.updater_binomial = SMCUpdater(self.binomial_model,
TestFisherInformation.N_PARTICLES,
TestFisherInformation.PRIOR_BETA)
def test_finite_outcomes_fi(self):
# The binomial model has a finite number of outcomes. Test the
# ig calculation in this case.
expparams = self.NMEAS_EXPPARAMS.astype(
self.binomial_model.expparams_dtype)
p = TestFisherInformation.BIN_FI_MODELPARAMS
# estimate the information gain
est_fi = self.binomial_model.fisher_information(
TestFisherInformation.BIN_FI_MODELPARAMS, expparams)[0, 0]
p = p[:, np.newaxis]
n = expparams.astype(np.float32)[np.newaxis, :]
exact_fi = n / ((1 - p) * p)
# see if they roughly match
assert_almost_equal(est_fi, exact_fi, decimal=3)
class TestInformationGain(DerandomizedTestCase):
# Test the implementation of numerical information gain by comparing to
# numbers which were derived by doing analytic/numeric
# integrals of simple models (binomialm, poisson, and gaussian) in
# Mathematica. This test trusts that these calculations
# were done correctly.
ALPHA = 1
BETA = 3
PRIOR_BETA = BetaDistribution(alpha=ALPHA, beta=BETA)
N_PARTICLES = 10000
# Calculated in Mathematica, IG for the binomial model and the given expparams
NMEAS_EXPPARAMS = np.arange(1, 11, dtype=int)
BINOM_IG = np.array([
0.104002, 0.189223, 0.261496, 0.324283, 0.379815, 0.429613, 0.474764,
0.516069, 0.554138, 0.589446
])
def setUp(self):
super(TestInformationGain, self).setUp()
# Set up relevant models.
self.coin_model = CoinModel()
self.binomial_model = BinomialModel(self.coin_model)
# Set up updaters for these models using particle approximations
# of conjugate priors
self.updater_binomial = SMCUpdater(self.binomial_model,
TestInformationGain.N_PARTICLES,
TestInformationGain.PRIOR_BETA)
def test_finite_outcomes_ig(self):
# The binomial model has a finite number of outcomes. Test the
# ig calculation in this case.
expparams = self.NMEAS_EXPPARAMS.astype(
self.binomial_model.expparams_dtype)
# estimate the information gain
est_ig = self.updater_binomial.expected_information_gain(expparams)
# see if they roughly match
assert_almost_equal(est_ig, TestInformationGain.BINOM_IG, decimal=2)
class TestBayesRisk(DerandomizedTestCase):
# Test the implementation of numerical Bayes Risk by comparing to
# numbers which were derived by doing analytic/numeric
# integrals of simple models in Mathematica. This test trusts that
# these calculations were done correctly.
ALPHA = 1.
BETA = 3.
PRIOR_BETA = BetaDistribution(alpha=ALPHA, beta=BETA)
N_PARTICLES = 10000
NMEAS_EXPPARAMS = np.arange(1, 11, dtype=int)
def setUp(self):
super(TestBayesRisk, self).setUp()
# Set up relevant models.
self.coin_model = CoinModel()
self.binomial_model = BinomialModel(self.coin_model)
# Set up updaters for these models using particle approximations
# of conjugate priors
self.updater_binomial = SMCUpdater(self.binomial_model,
TestBayesRisk.N_PARTICLES,
TestBayesRisk.PRIOR_BETA)
def test_finite_outcomes_risk(self):
# The binomial model has a finite number of outcomes. Test the
# risk calculation in this case.
expparams = self.NMEAS_EXPPARAMS.astype(
self.binomial_model.expparams_dtype)
# estimate the risk
est_risk = self.updater_binomial.bayes_risk(expparams)
# compute exact risk
a, b = TestBayesRisk.ALPHA, TestBayesRisk.BETA
exact_risk = a * b / ((a + b) * (a + b + 1) *
(a + b + expparams['n_meas']))
# see if they roughly match
assert_almost_equal(est_risk, exact_risk, decimal=3)
def instantiate_prior(self):
return BetaDistribution(mean=0.5, var=0.1)
def instantiate_prior(self):
return ProductDistribution(BetaDistribution(mean=0.5, var=0.1),
NormalDistribution(0, 0.05**2),
NormalDistribution(0, 0.05**2),
BetaDistribution(mean=0.5, var=0.1),
BetaDistribution(mean=0.5, var=0.1))