def old_bootstrap_pd_stats(b, b_s, k, n_samp=int(1e3)):
'''
Calculate, by bootstrapping, statistics of preferred directions.
Parameters
----------
pd : array_like, shape (3)
preferred directions
b_s : float
standard error of lin regress coefficients
k : float
modulation depth
n_samp : int
number of samples to use for bootstrap
Returns
-------
k_s : array_like
standard errors of k, modulation depth, shape (?)
kappa : array_like
dispersion factors, shape (?)
R : array_like
length factor of pd distribution ??, shape (?)
Notes
-----
1. Angles of preferred direction cones are determined as follows.
2. Regression coefficients (`b`) are recovered from pds and modulation
depths.
3. Random populations of regression coefficients are constructed from
distributions with the same mean and standard deviation as estimated
from the regression procedure, with the same number of samples as the
original data.
4. Preferred directions are calculated from these coefficient values
(i.e. dividing by modulation depth).
'''
warn(DeprecationWarning("Doesn't calculate using covariance matrix. "
"Use ___ instead."))
assert (type(n_samp) == int) | (type(n_samp) == np.int_)
assert (type(k) == np.float_) or (type(k) == float)
assert b.shape == b_s.shape == (3,)
#pd = np.asarray(pd)
# reconstruct regression coefficients
# Now generate n_samp samples from normal populations
# (mean: b_k, sd: err_k). Will have shape (n_samp, 3).
b_rnd = np.random.standard_normal(size=(n_samp,3))
b_rnd *= b_s
b_rnd += b
pd = unitvec(b)
#io.savemat('bootstrap_b.mat', dict(b_rnd=b_rnd))
ks = norm(b_rnd, axis=1)
k_s = np.std(ks, ddof=1)
pds_rnd = b_rnd / ks[...,np.newaxis]
kappa = ss.estimate_kappa(pds_rnd, mu=pd)
R, S = ss.calc_R(pds_rnd)
return k_s, kappa, R
def test_estimate_kappa():
mus = [[0., 0., 1.],[0., 1., 0.], [1., 0., 0.]]
kappas = [1.,]
for mu, kappa in zip(mus, kappas):
n_pts = int(1e4)
tolerance = 0.1
# acceptable deviation between set kappa (hopefully),
# and estimated kappa.
# Could really do with a way to define a
# set of points with an established kappa.
P_i = vmf_rvs(mu, kappa, n_pts)
khat = estimate_kappa(P_i, mu=mu)
diff = np.abs(khat - kappa)
assert(diff < tolerance)
def bootstrap_pd_stats(b, cov, neural_data, model, ndim=3):
'''
Parameters
----------
b : ndarray
coefficients
cov : ndarray
covariance matrix
neural_data : ndarray
counts (GLM) or rates (OLS)
model : string
specification of fit model
Returns
-------
pd : ndarray
preferred directions
ca : ndarray
confidence angle of preferred direction
kd : ndarray
modulation depths
kdse : ndarray
standard errors of modulation depths
'''
# number of independent samples from original data
d = 'd' if 'd' in model else 'v'
nsamp = np.sum(~np.isnan(neural_data.sum(axis=1)))
# compressing along last axis gives number of samples per bin
# which is correct, since bootstrapping is done independently
# for each bin
# bootstrap a distribution of b values
# using mean, covariance matrix from GLM (/ OLS).
bootb = np.random.multivariate_normal(b, cov, (nsamp,))
bootdict = fit.unpack_many_coefficients(bootb, model, ndim=ndim)
if 'X' in model:
bootpd = unitvec(bootdict[d], axis=2)
# has shape nsamp, nbin, ndim
else:
bootpd = unitvec(bootdict[d], axis=1)
# has shape nsamp, ndim
# get mean pd to narrow kappa estimation
bdict = fit.unpack_coefficients(b, model, ndim=ndim)
if 'X' in model:
nbin = bdict[d].shape[0]
pd = unitvec(bdict[d], axis=1)
pdca = np.zeros((nbin))
for i in xrange(nbin):
# estimate kappa
k = ss.estimate_kappa(bootpd[:,i], mu=pd[i])
# estimate ca (preferred direction Confidence Angle)
pdca[i] = ss.measure_percentile_angle_ex_kappa(k)
# calculate the standard error of the bootstrapped PDs
kd = norm(bootdict[d], axis=2)
kdse = np.std(kd, axis=0, ddof=1)
else:
nbin = 1
pd = unitvec(bdict[d])
k = ss.estimate_kappa(bootpd, mu=pd)
pdca = ss.measure_percentile_angle_ex_kappa(k)
bootkd = norm(bootdict[d], axis=1)
kd = np.mean(bootkd, axis=0)
kdse = np.std(bootkd, axis=0, ddof=1)
return pd, pdca, kd, kdse
