def test_mvt_pdf(self):
cov3 = self.cov3
mu3 = self.mu3
mvt = MVT((0, 0), 1, 5)
assert_almost_equal(mvt.logpdf(np.array([0., 0.])),
-1.837877066409345,
decimal=15)
assert_almost_equal(mvt.pdf(np.array([0., 0.])),
0.1591549430918953,
decimal=15)
mvt.logpdf(np.array([1., 1.])) - (-3.01552989458359)
mvt1 = MVT((0, 0), 1, 1)
mvt1.logpdf(np.array([1., 1.])) - (-3.48579549941151) #decimal=16
rvs = mvt.rvs(100000)
assert_almost_equal(np.cov(rvs, rowvar=0), mvt.cov, decimal=1)
mvt31 = MVT(mu3, cov3, 1)
assert_almost_equal(mvt31.pdf(cov3), [
0.0007276818698165781, 0.0009980625182293658, 0.0027661422056214652
],
decimal=17)
mvt = MVT(mu3, cov3, 3)
assert_almost_equal(
mvt.pdf(cov3),
[0.000863777424247410, 0.001277510788307594, 0.004156314279452241],
decimal=17)
def __init__(self, mean, cov, df=None, random_state=1):
self.mean = mean
self.cov = cov
self.sd = sd = np.sqrt(np.diag(cov))
if df is None:
self.dist = stats.multivariate_normal(mean=mean, cov=cov)
self.udist = stats.norm(loc=mean, scale=sd)
self.std_udist = stats.norm(loc=0., scale=1.)
else:
sigma = cov * (df - 2) / df
self.dist = MVT(mean=mean, sigma=sigma, df=df)
self.udist = stats.t(loc=mean, scale=sd, df=df)
self.std_udist = stats.t(loc=0., scale=1., df=df)
self.dist.random_state = random_state
self.udist.random_state = random_state
self.std_udist.random_state = random_state
self._chol = cholesky(self.cov)
self._pchol = pivoted_cholesky(self.cov)
e, v = np.linalg.eigh(self.cov)
# To match Bastos and O'Hagan definition
# i.e., eigenvalues ordered from largest to smallest
e, v = e[::-1], v[:, ::-1]
ee = np.diag(np.sqrt(e))
self._eig = (v @ ee)
def train_analytic(self):
""" Calculating the analytic distribution posteriors given on page 15 of Lori's
Optimal Classification eq 34. """
self.nustar = self.nu + self.n
samplemean = self.data.mean(axis=0)
samplecov = np.cov(self.data.T)
self.mustar = (self.nu * self.priormu + self.n * samplemean) \
/ (self.nu + self.n)
self.kappastar = self.kappa + self.n
self.Sstar = self.S + (self.n-1)*samplecov + self.nu*self.n/(self.nu+self.n)\
* np.outer((samplemean - self.priormu), (samplemean - self.priormu))
# Now calculate effective class conditional densities from eq 55 page 21
self.fx = MVT(
self.mustar,
(self.nustar+1)/(self.kappastar-self.D+1)/self.nustar * self.Sstar,
self.kappastar - self.D + 1)
def __init__(self):
np.random.seed(1234)
self.n = 4 # Data points
self.true_mu = 0.0
self.true_sigma = 1 #di.invgamma.rvs(3)
# For G function calculation and averaging
self.grid_n = 100
low, high = -4, 4
self.gextent = (low, high)
self.grid = np.linspace(low, high, self.grid_n)
self.gavg = np.zeros(self.grid_n)
self.numgavg = 0
#self.data = di.norm.rvs(size=self.n)
self.data = np.array([0.0, -0.0, 0.5, -0.5])
assert self.data.size == self.n
######## Starting point of MCMC Run #######
self.mu = 0.0
self.sigma = 2.0
###### Bookeeping ######
self.oldmu = None
self.oldsigma = None
##### Prior Values and Confidences ######
self.priorsigma = 2
self.kappa = 1
self.priormu = 0
self.nu = 8.0
#### Calculating the Analytic solution given on page 15 of Lori's
#### Optimal Classification eq 34.
self.nustar = self.nu + self.n
samplemean = self.data.mean()
samplevar = np.cov(self.data)
self.mustar = (self.nu*self.priormu + self.n * samplemean) \
/ (self.nu + self.n)
self.kappastar = self.kappa + self.n
self.Sstar = self.priorsigma + (self.n-1)*samplevar + self.nu*self.n/(self.nu+self.nu)\
* (samplemean - self.priormu)**2
#### Now calculate effective class conditional densities from eq 55
#### page 21
#self.fx = MVT(
#self.mu0star,
#(self.nu0star+1)/(self.kappa0star-self.D+1)/self.nu0star * self.S0star,
#self.kappa0star - self.D + 1)
# So I'm pretty sure this is incorrect below, off by some scaling
# parameters
self.fx = MVT([self.mustar],
[(self.nustar + 1) /
(self.kappastar) / self.nustar * self.Sstar / 2],
self.kappastar / 2)
self.analyticfx = self.fx.logpdf(self.grid.reshape(-1, 1))