def lincombo_hierregress_taubybeta(yy, stderrs, XX, maxtau=None, guess_range=False, draws=100):
yy, stdvars, XX = helpers.check_arguments(yy, stderrs, XX)
nummus = XX.shape[1]
print "Sampling tau..."
if maxtau is None:
maxtau = pooling.estimated_maxlintau(yy, stderrs, XX)
print "Using maximum tau =", maxtau
if maxtau[0] > 0:
probability_prior_tau = uniform(0, maxtau)
# Prepare to sample from from p(tau | yy)
# Create pdf for p(tau | yy)
def pdf(tau):
# Requires mus, but is invarient to them
return probability_tau([np.mean(yy)] * nummus, tau, yy, stdvars, XX, probability_prior_tau)
dist = ContinuousSampled(pdf, 2)
if guess_range:
mini, maxi = dist.guess_ranges([0, 0], maxtau, draws * 10)
else:
mini, maxi = 0, maxtau
dist.prepare_draws(mini, maxi, count=draws)
else:
# maxtau == 0
dist = MultivariateDelta(np.zeros(2))
print "Sampling mus..."
return sample_posterior(yy, stderrs, XX, dist, draws)
def lincombo_pooled(betas, stderrs, portions):
betas, stdvars, portions = helpers.check_arguments(betas, stderrs, portions)
numalphas = portions.shape[1]
## Fill in the inverse sigma matrix
overvars = 1.0 / stdvars
invsigma = np.zeros((numalphas, numalphas))
for jj in range(numalphas):
print "Row", jj
for kk in range(numalphas):
if helpers.issparse(portions):
invsigma[jj, kk] = sum_multiply2(portions, jj, kk, overvars)
else:
invsigma[jj, kk] = sum(portions[:, jj] * portions[:, kk] * overvars)
if helpers.issparse(portions):
bb = [sum_multiply(portions[:, jj], betas * overvars) for jj in range(numalphas)]
else:
bb = [sum(betas * portions[:, jj] / stdvars) for jj in range(numalphas)]
print "Begin inversion...", invsigma.shape
sigma = np.linalg.inv(invsigma)
alphas = np.dot(sigma, np.transpose(bb))
return MultivariateNormal(alphas, sigma)
def lincombo_hiernorm_taubybeta(betas, stderrs, portions, maxtaus=None, guess_range=False, draws=100):
betas, stdvars, portions = helpers.check_arguments(betas, stderrs, portions)
numalphas = portions.shape[1]
print "Sampling taus..."
observed_tau = 2 * np.sqrt(np.var(betas) + max(stderrs)**2)
if observed_tau == 0:
return None, None, None
if maxtaus is None:
maxtaus = pooling.estimated_maxlintaus(betas, stderrs, portions)
print "Using maximum tau =", maxtaus, "vs.", observed_tau
if maxtaus[0] > 0:
probability_prior_taus = MultivariateUniform([0, 0], maxtaus)
# Prepare to sample from from p(taus | betas)
# Create pdf for p(taus | betas)
def pdf(*taus): # taus is [tau0s, tau1s]
transtaus = np.transpose(taus) # [[tau0, tau1], ...]
values = []
for ii in range(len(taus[0])):
## Observation taus
obstaus = transtaus[ii][0] + transtaus[ii][1] * np.abs(np.array(betas))
# Requires alphas, but is invarient to them
values.append(probability_tau([np.mean(betas)] * numalphas, transtaus[ii], obstaus, betas, stdvars, portions, probability_prior_taus))
return values
dist = MultivariateSampled(pdf, 2)
if guess_range:
mins, maxs = dist.guess_ranges([0, 0], maxtaus, draws * 10)
else:
mins = [0, 0]
maxs = maxtaus
print mins, maxs
dist.prepare_draws(mins, maxs, count=draws)
else:
# maxtau == 0
dist = MultivariateDelta(np.zeros(2))
print "Sampling alphas..."
taus2obstaus = lambda taus: taus[0] + taus[1] * np.abs(np.array(betas))
return sample_posterior(betas, stderrs, portions, dist, taus2obstaus, draws)
def sample_posterior(yy, stderrs, XX, taudist, draws=100):
yy, stdvars, XX = helpers.check_arguments(yy, stderrs, XX)
# Draw samples from posterior
alltau = []
allmus = []
allbetahats = []
for ii in range(draws):
tau = taudist.rvs(size=1)
alltau.append(tau)
# Sample from p(mus | tau, yy)
mus = mu_given_tau(yy, stdvars, XX, tau).rvs(size=1)
allmus.append(mus)
# Sample from p(betahat | tau, yy)
betahats = betahat_given_tau(yy, stdvars, XX, tau).rvs(size=1)
allbetahats.append(betahats)
return alltau, allmus, allbetahats
def sample_posterior(betas, stderrs, portions, taudist, taus2obstaus, draws=100):
betas, stdvars, portions = helpers.check_arguments(betas, stderrs, portions)
# Draw samples from posterior
alltaus = []
allalphas = []
allbetahats = []
for ii in range(draws):
taus = np.ravel(taudist.rvs(size=1))
alltaus.append(taus)
obstaus = taus2obstaus(taus)
# Sample from p(alphas | taus, betas)
alphas = alpha_given_taus(betas, stdvars, portions, obstaus).rvs(size=1)
allalphas.append(alphas)
# Sample from p(betahat | taus, betas)
betahats = betahat_given_taus(betas, stdvars, portions, obstaus).rvs(size=1)
allbetahats.append(betahats)
return alltaus, allalphas, allbetahats
