def binom_interval(success, total, confint=0.95):
'''
from paulgb's binom_interval.py'''
quantile = (1 - confint) / 2.
lower = beta.ppf(quantile, success, total - success + 1)
upper = beta.ppf(1 - quantile, success + 1, total - success)
return (lower, upper)
def err(obs, total, use_beta=True, use_cache=True, for_paper=False):
""" Return uncertainty on the ratio n / total """
assert obs <= total
if total == 0.0:
return (0.0, 0.0, False)
key = str(obs) + '/' + str(total)
if use_cache and key in cached_uncertainties.errs:
return cached_uncertainties.errs[key] + (True, )
frac = float(obs) / total
if use_beta or frac == 0.0 or frac == 1.0: # still need to use beta for 0 and 1 'cause the sqrt thing below gives garbage for those cases
if for_paper: # total volume of confidence interval
vol = 0.95 # use 95% for paper
cpr = 0.5 # constant from prior (jeffreys for paper)
else:
vol = 2./3 # otherwise +/- 1 sigma
cpr = 1. # constant prior
lo = beta.ppf((1. - vol)/2, cpr + obs, cpr + total - obs)
hi = beta.ppf((1. + vol)/2, cpr + obs, cpr + total - obs)
if frac < lo: # if k/n very small (probably zero), take a one-sided c.i. with 2/3 (0.95) the mass
lo = 0.
hi = beta.ppf(vol, cpr + obs, cpr + total - obs)
if frac > hi: # same deal if k/n very large (probably one)
lo = beta.ppf(1. - vol, cpr + obs, cpr + total - obs)
hi = 1.
else: # square root shenaniganery
err = (1./(total*total)) * (math.sqrt(obs)*total - obs*math.sqrt(total))
lo = frac - err
hi = frac + err
assert lo < frac or frac == 0.0
assert frac < hi or frac == 1.0
return (lo, hi) + (False, )
def plot_beta(name, a, b, ret=None, n=None):
print(a, b)
theta = linspace(0, 1, 300)
pdf = beta.pdf(theta, a, b)
ax = axes()
ax.plot(theta, pdf / max(pdf))
if n is not None:
ax.text(0.025, 0.9, 'TRADE IDEA %d' % n)
if ret is not None:
ax.text(0.025, 0.85, 'RETURN %s 0' % ('>' if ret else '<'))
ax.set_title('P(hit rate | ideas so far)')
ax.yaxis.set_ticks([])
ax.grid()
ax.legend()
ax.xaxis.set_label_text('Hit Rate')
ax.xaxis.set_ticks(linspace(0, 1, 11))
s, e = (beta.ppf(0.025, a, b), beta.ppf(0.975, a, b))
ax.fill([s, s, e, e, s], [0, 1, 1, 0, 0], color='0.9')
gcf().set_size_inches(10, 6)
savefig(name, bbox_inches='tight')
plt.close()
return
def binomialCI(successes,attempts,alpha):
""" Calculates the upper and lower confidence intervals on binomial data using the Clopper Pearson method
Added by Doug Ollerenshaw on 02/12/2014
input:
successes = number of successes
attempts = number of attempts
alpha = confidence range (.e.g., 0.05 to return the 95% confidence interval)
output:
lower bound, upper bound
Refs:
[1] Clopper, C. and Pearson, S. The use of confidence or fiducial limits illustrated in the case of the Binomial. Biometrika 26: 404-413, 1934
[2] http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval
[3] http://www.danielsoper.com/statcalc3/calc.aspx?id=85 [an online calculator used to validate the output of this function]
"""
from scipy.stats import beta
import math
x = successes
n = attempts
# NOTE: the ppf (percent point function) is equivalent to the inverse CDF
lower = beta.ppf(alpha/2,x,n-x+1)
if math.isnan(lower):
lower = 0
upper = beta.ppf(1-alpha/2,x+1,n-x)
if math.isnan(upper):
upper = 1
return lower,upper
def confident_fail_rate(total_fail, total_pass, confidence):
"""
WE CAN NOT BE OVERLY OPTIMISTIC (0.0) ABOUT PREVIOUS SAMPLES, NOR
OVERLY PESSIMISTIC (1.0). WE MODIFY THE RATIO OF fail/total TOWARD
NEUTRAL (0.5) BY ACCOUNTING FOR SMALL total AND STILL BE WITHIN confidence
stats.beta.ppf(x, a, b) == 1 - stats.beta.ppf(1-x, b, a)
betaincinv(a, b, y) == stats.beta.ppf(y, a, b)
"""
# SMALL NAMES OF EQUAL LENGTH TO DEMONSTRATE THE SYMMETRY BELOW
confi = confidence
error = 1 - confi
# ppf() IS THE PERCENT POINT FUNCTION (INVERSE OF cdf()
max1 = MIN(beta.ppf(confi, total_fail + 1, total_pass), 1)
min1 = MAX(beta.ppf(error, total_fail, total_pass + 1), 0)
# PICK THE probability CLOSEST TO 0.5
if min1 < 0.5 and 0.5 < max1:
return 0.5
elif max1 < 0.5:
return max1
elif 0.5 < min1:
return min1
else:
assert False
def set_tpm(self, total_num_reads):
SegmentBin.set_expression(
self,
1e6*beta.ppf(0.01, self.cnts.sum()+1e-6, total_num_reads+1e-6),
1e6*beta.ppf(0.50, self.cnts.sum()+1e-6, total_num_reads+1e-6),
1e6*beta.ppf(0.99, self.cnts.sum()+1e-6, total_num_reads+1e-6))
return self
def filter_jns(jns, antistrand_jns, whitelist=set()):
filtered_junctions = defaultdict(int)
jn_starts = defaultdict( int )
jn_stops = defaultdict( int )
for (start, stop), cnt in jns.iteritems():
jn_starts[start] = max( jn_starts[start], cnt )
jn_stops[stop] = max( jn_stops[stop], cnt )
for (start, stop), cnt in jns.iteritems():
if (start, stop) not in whitelist:
val = beta.ppf(0.01, cnt+1, jn_starts[start]+1)
if val < config.NOISE_JN_FILTER_FRAC: continue
val = beta.ppf(0.01, cnt+1, jn_stops[stop]+1)
if val < config.NOISE_JN_FILTER_FRAC: continue
#val = beta.ppf(0.01, cnt+1, jn_grps[jn_grp_map[(start, stop)]]+1)
#if val < config.NOISE_JN_FILTER_FRAC: continue
try:
if ( (cnt+1.)/(antistrand_jns[(start, stop)]+1) <= 1.):
continue
except KeyError:
pass
if stop - start + 1 > config.MAX_INTRON_SIZE: continue
filtered_junctions[(start, stop)] = cnt
return filtered_junctions
def binom_interval(success, total, confint=0.95):
"""
Compute two-sided binomial confidence interval in Python. Based on R's binom.test.
"""
quantile = (1 - confint) / 2.
lower = beta.ppf(quantile, success, total - success + 1)
upper = beta.ppf(1 - quantile, success + 1, total - success)
return (lower, upper)
def bin_conj_prior():
# Constants
global bin_data, bin_mean
a, b = 2, 4
m, l = 0, 0
count = 0
u_list = []
domain = np.linspace(beta.ppf(0.01, a, b),
beta.ppf(0.99, a, b), 100)
prior = beta.pdf(domain, a, b)
fig, ax = plt.subplots(1, 1)
# Update
for i in bin_data:
# Go through data
count += 1
if i == 1:
m += 1
else:
l += 1
# Calculate mean
u = (a+m)/(a+m+l+b)
u_list.append(u)
# Calculate posterior
posterior = beta.pdf(domain, a+m, b+l)
# MSE
bin_mean_list = [] # Obtuse way to find MSE, but effective
for i in range(len(u_list)):
bin_mean_list.append(bin_mean)
mse = np.array(u_list) - np.array(bin_mean_list)
# Plot Prior
plt.figure(2)
plt.plot(domain, prior)
plt.title('Binomial - Prior')
plt.xlabel('Number of Observations')
plt.ylabel('PDF')
# Plot Posterior
plt.figure(3)
plt.title('Binomial - Posterior')
plt.xlabel('Number of Observations')
plt.ylabel('PDF')
plt.xlim(0,1)
if count % 5 == 0:
plt.plot(domain, posterior)
# Plot error
plt.figure(4)
plt.plot(mse)
plt.title('Binomial - MSE')
plt.xlabel('Number of Observations')
plt.ylabel('Error')
def clopper_pearson(x, n):
right = beta.ppf(1 - alpha / 2, x + 1, n - x)
if (np.isnan(right)):
right = 1
left = beta.ppf(alpha / 2, x, n - x + 1)
if (np.isnan(left)):
left = 0
return right - left, (left, right)
def fraction_uncertainty(obs, total):
""" Return uncertainty on the ratio n / total """
assert obs <= total
if total == 0.0:
return 0.0
lo = beta.ppf(1./6, 1 + obs, 1 + total - obs)
hi = beta.ppf(1. - 1./6, 1 + obs, 1 + total - obs)
if float(obs) / total < lo: # if k/n very small (probably zero), take a one-sided c.i. with 2/3 the mass
lo = 0.
hi = beta.ppf(2./3, 1 + obs, 1 + total - obs)
if float(obs) / total > hi: # same deal if k/n very large (probably one)
lo = beta.ppf(1./3, 1 + obs, 1 + total - obs)
hi = 1.
return (lo,hi)
def ClopperPearsonError(num_changes, num_random_bits, samples=1, alpha=.05):
num_changes = np.array(num_changes)
n = np.round(num_random_bits)
x = n - num_changes
x = x.clip(1e-12, n)
x *= samples
n *= samples
# https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Clopper-Pearson_interval
interv = np.vstack((beta.ppf(1.-alpha/2., x+1, n-x), beta.ppf(alpha/2., x, n-x+1)))
interv = n * (1. - interv) / samples
# convert to error
interv[0,:] = num_changes - interv[0,:]
interv[1,:] = interv[1,:] - num_changes
return interv
def binomial_confidence_interval(nsuccess, ntrial, conf=68.27):
""" Find a binomial confidence interval.
Uses a Bayesian method assuming a flat prior. See Cameron 2011:
http://adsabs.harvard.edu/abs/2011PASA...28..128C. This is
superior to the commonly-used Normal, Wilson and Clopper & Pearson
(AKA 'exact') approaches.
Parameters
----------
nsuccess: int
The number of successes from the trials. If 0, then return the
1-sided upper limit. If the same as ntril, return the 1-sided
lower limit.
ntrial: int
The number of trials.
conf: float (default 68.27)
Confidence level in percent (95, 90, 68.3% or similar).
Returns
-------
plo, phi : floats
The two-sided confidence interval: probabilities such that >=
observed number of successes occurs in fewer than conf% of cases
(plo), and prob such that <= number of success occurs in fewer
than conf% of cases (phi).
"""
from scipy.stats import beta
nsuccess = int(nsuccess)
ntrial = int(ntrial)
assert 0 < conf < 100
if nsuccess == 0:
alpha = 1 - conf / 100.
plo = 0.
phi = beta.ppf(1 - alpha, nsuccess + 1, ntrial - nsuccess)
elif nsuccess == ntrial:
alpha = 1 - conf / 100.
plo = beta.ppf(alpha, nsuccess, ntrial - nsuccess + 1)
phi = 1.
else:
alpha = 0.5 * (1 - conf / 100.)
plo = beta.ppf(alpha, nsuccess, ntrial - nsuccess + 1)
phi = beta.ppf(1 - alpha, nsuccess + 1, ntrial - nsuccess)
return plo, phi
def beta_confidence_intervals(ci_X, ntrials, ci=0.95):
"""
Compute confidence intervals of beta distributions.
Parameters
----------
ci_X : numpy.array
Computed confidence interval estimate from `ntrials` experiments
ntrials : int
The number of trials that were run.
ci : float, optional, default=0.95
Confidence interval to report (e.g. 0.95 for 95% confidence interval)
Returns
-------
Plow : float
The lower bound of the symmetric confidence interval.
Phigh : float
The upper bound of the symmetric confidence interval.
Examples
--------
>>> ci_X = np.random.rand(10,10)
>>> ntrials = 100
>>> Plow, Phigh = beta_confidence_intervals(ci_X, ntrials)
"""
# Compute low and high confidence interval for symmetric CI about mean.
ci_low = 0.5 - ci / 2
ci_high = 0.5 + ci / 2
# Compute for every element of ci_X.
from scipy.stats import beta
Plow = ci_X * 0.0
Phigh = ci_X * 0.0
for i in range(ci_X.shape[0]):
for j in range(ci_X.shape[1]):
Plow[i, j] = beta.ppf(ci_low,
a=ci_X[i, j] * ntrials,
b=(1 - ci_X[i, j]) * ntrials)
Phigh[i, j] = beta.ppf(ci_high,
a=ci_X[i, j] * ntrials,
b=(1 - ci_X[i, j]) * ntrials)
return Plow, Phigh
def transform(Rec):
# r1 = Rec == 0.0
# r2 = Rec == 1.0
# Rec[r1] = 0.000000001
# Rec[r2] = 0.999999999
# Rec = -np.log(1-Rec)*2.5
Rec = beta.ppf(Rec, a1, b1, loc1, sca1)
return Rec
def qBE(p: float, location: np.ndarray, scale: np.ndarray):
"""Quantile function.
"""
a = location * (1 - scale**2) / (scale**2)
b = a * (1 - location) / location
q = beta.ppf(p, a=a, b=b)
return q
def g(x): prob_xx=beta.cdf(x,alpha_param,beta_param)+z if prob_xx>1: #Numerical precision paranoia prob_xx=1 xx=beta.ppf(prob_xx,alpha_param,beta_param) prob_diff=beta.pdf(x,alpha_param,beta_param)-beta.pdf(xx,alpha_param,beta_param) #print ' x=%f, prob_xx=%f, xx=%f, prob_diff=%f'%(x,prob_xx,xx,prob_diff) return(prob_diff)
def select_bandit(self):
c = 1 - 1. / ((self.N + 1))
# percent point functions(inverse of cdf)
pps = [beta.ppf(c, a, b) for a, b in zip(self.alphas, self.betas)]
return np.argmax(pps)
def adjust_thre(x, alpha_, beta_):
'''
调整阈值：
基准分布0.99
前置分布0.9999
'''
d = beta.ppf(x, alpha_, beta_)
return x, d
def conf_int(self, conf_level=0.05):
assert self.a is not None and self.b is not None, 'Params have not been set. First run .fit()'
# Handles case where uses specifies something like 95% CI
if conf_level > 0.5:
conf_level = 1 - conf_level
left = beta.ppf(conf_level / 2, self.a, self.b)
right = beta.ppf(1 - conf_level / 2, self.a, self.b)
# Used because the ppf will never return 1, only 0.9999...
left = np.round(left, 2)
right = np.round(right, 2)
if np.isnan(left):
left = self.default_left
if np.isnan(right):
right = self.default_right
return left, right
def binomialCI(successes=None, attempts=None, alpha=0.05):
from scipy.stats import beta
import math
x = successes
n = attempts
# NOTE: the ppf (percent point function) is equivalent to the inverse CDF
lower = beta.ppf(alpha / 2, x, n - x + 1)
if math.isnan(lower):
lower = 0
upper = beta.ppf(1 - alpha / 2, x + 1, n - x)
if math.isnan(upper):
upper = 1
return lower, upper
def from_bp_to_errors(self, row):
# row has three rows : error, x, bp, and set datetime as columns
x = row["x"]
bp = row["base_process"]
a, b, loc, scale = self.s_x[x]
simulated_error = beta.ppf(bp, a, b, loc=loc,
scale=scale) # scale = 0 cause NAN
return simulated_error
def extract_scores(self, outputs):
alpha_posterior = outputs['alpha_posterior']
beta_posterior = outputs['beta_posterior']
scores = beta.ppf(0.5, alpha_posterior, beta_posterior)
scores = np.repeat(scores[:, np.newaxis], self.n_batches, axis=1)
return 1. - scores
def get_mean_accuracy(all_means, nbins=10):
"""
Bins ancestors according to mean bootstrapped posterior probability,
and then returns the mean accuracy for each bin
"""
## Add a columns of bin assignments
# bins = np.linspace(0, all_means['posterior'].max(), nbins)
bins = np.linspace(0, 1, nbins)
all_means['bin'] = np.digitize(all_means['posterior'], bins)
## Add upper bound to right-most bin
all_means.replace(to_replace={'bin':{nbins: nbins-1}}, inplace=True)
## Bin ancestors by mean bootstrapped probability, adding columns for
## whether they were the true generating ancestor, and the number of
## ancestors in each bin
bin_count = lambda x: len(x)
binned = all_means[['generator', 'bin']].pivot_table(index='bin',
aggfunc=[np.mean, bin_count], fill_value=0)
binned.columns = [['observed_prob', 'bin_count']]
binned['n_successes'] = binned['observed_prob'].values * \
binned['bin_count'].values
## Estimate means and confidence intervals as sampling from a binomial
## distribution, with a uniform prior on success rates - Done using
## a beta distribution
binned['alpha'] = binned['n_successes'] + 1
binned['beta'] = binned['bin_count'].values - binned['n_successes'].values + 1
beta_mean = lambda row: beta.mean(float(row['alpha']), float(row['beta']))
binned['posterior_mean'] = binned.apply(beta_mean, axis=1)
## Add confidence intercals
beta_025CI = lambda row: beta.ppf(0.025, float(row['alpha']), float(row['beta']))
beta_975CI = lambda row: beta.ppf(0.975, float(row['alpha']), float(row['beta']))
binned['CI2.5'] = binned.apply(beta_025CI, axis=1)
binned['CI97.5'] = binned.apply(beta_975CI, axis=1)
## Convert to values relative to mean, to fit plotting convention
binned['CI2.5'] = binned['posterior_mean'].values - binned['CI2.5'].values
binned['CI97.5'] = binned['CI97.5'].values - binned['posterior_mean'].values
## Add column with bin centre for plotting
binned['bin_centre'] = all_means[['posterior', 'bin']].groupby('bin').mean()
return binned
def choose_arm(self):
if self.HF:
T = self.t + 1
else:
T = self.horizon
d = 1 / (self.t * np.log(T)**self.c)
theta = beta.ppf(1 - d, self.alphas, self.betas)
self.t += 1
return np.argmax(theta)
def beta_lin(lower, upper, parameteralfa, parameterbeta, size):
generation_list = x_inbetween(0, 1, size)
x = []
for i in generation_list:
x.append(beta.ppf(i, parameteralfa, parameterbeta))
x = [i * (upper - lower) + lower for i in x]
return list(x)
def verify_agents(env, number_of_users, agents):
stat = {
'Agent': [],
'0.025': [],
'0.500': [],
'0.975': [],
}
for agent_id in agents:
stat['Agent'].append(agent_id)
data = deepcopy(env).generate_logs(number_of_users, agents[agent_id])
bandits = data[data['z'] == 'bandit']
successes = bandits[bandits['c'] == 1].shape[0]
failures = bandits[bandits['c'] == 0].shape[0]
stat['0.025'].append(beta.ppf(0.025, successes + 1, failures + 1))
stat['0.500'].append(beta.ppf(0.500, successes + 1, failures + 1))
stat['0.975'].append(beta.ppf(0.975, successes + 1, failures + 1))
return pd.DataFrame().from_dict(stat)
def get_probility(x, N, a=0.05):
'''
计算 N 此重复实验，事件 A 发生 x 次时，事件 A 的发生概率
Args:
x : 事件发生次数
N : 总实验次数
a : 设置显著性水平 1-a，默认 0.05
Returns:
P, E, std, (low, high)
事件 A 发生概率 P 的最概然取值、期望、以及其置信区间
'''
P = 1.0 * x / N
E = (x + 1.0) / (N + 2.0)
std = np.sqrt(E * (1 - E) / (N + 3))
low = beta.ppf(0.5 * a, x + 1, N - x + 1)
high = beta.ppf(1 - 0.5 * a, x + 1, N - x + 1)
return P, E, std, (low, high)
def display(self,names=None):
"""
Plot the posterior distributions of the bandit arms.
INPUT:
names (list) of string names of the bandit arms; defaults to None; optional
"""
for i in xrange(self.n):
a = self.arms[i][0] + 1
b = self.arms[i][1] + 1
# generate values that will define the line of the beta distribution
x = np.linspace(beta.ppf(0.01, a, b),beta.ppf(0.99, a, b),100)
l = str(i)
if names:
plt.plot(x,beta(a,b).pdf(x),label=names[i]) # plot the pdf of the beta distribution
else:
plt.plot(x,beta(a,b).pdf(x),label=l)
plt.legend(loc=2)
plt.title(str(self.arms))
plt.show()
def get_probility(x, N, a=0.05):
'''
计算 N 此重复实验，事件 A 发生 x 次时，事件 A 的发生概率
Args:
x : 事件发生次数
N : 总实验次数
a : 设置显著性水平 1-a，默认 0.05
Returns:
P, E, std, (low, high)
事件 A 发生概率 P 的最概然取值、期望、以及其置信区间
'''
P = 1.0 * x / N
E = (x + 1.0) / (N + 2.0)
std = np.sqrt(E * (1 - E) / (N + 3))
low = beta.ppf(0.5 * a, x + 1, N - x + 1)
high = beta.ppf(1 - 0.5 * a, x + 1, N - x + 1)
return P, E, std, (low, high)
def rBE(n: int, location: np.ndarray, scale: np.ndarray):
"""Random variable generation function.
"""
n = math.ceil(n)
p = np.random.uniform(0, 1, n)
a = location * (1 - scale**2) / (scale**2)
b = a * (1 - location) / location
r = beta.ppf(p, a=a, b=b)
return r
def beta_confidence_intervals(ci_X, ntrials, ci=0.95):
"""
Compute confidence intervals of beta distributions.
Parameters
----------
ci_X : numpy.array
Computed confidence interval estimate from `ntrials` experiments
ntrials : int
The number of trials that were run.
ci : float, optional, default=0.95
Confidence interval to report (e.g. 0.95 for 95% confidence interval)
Returns
-------
Plow : float
The lower bound of the symmetric confidence interval.
Phigh : float
The upper bound of the symmetric confidence interval.
Examples
--------
>>> ci_X = np.random.rand(10,10)
>>> ntrials = 100
>>> [Plow, Phigh] = beta_confidence_intervals(ci_X, ntrials)
"""
# Compute low and high confidence interval for symmetric CI about mean.
ci_low = 0.5 - ci / 2
ci_high = 0.5 + ci / 2
# Compute for every element of ci_X.
from scipy.stats import beta
Plow = ci_X * 0.0
Phigh = ci_X * 0.0
for i in range(ci_X.shape[0]):
for j in range(ci_X.shape[1]):
Plow[i, j] = beta.ppf(ci_low, a=ci_X[i, j] * ntrials, b=(1 - ci_X[i, j]) * ntrials)
Phigh[i, j] = beta.ppf(ci_high, a=ci_X[i, j] * ntrials, b=(1 - ci_X[i, j]) * ntrials)
return [Plow, Phigh]
def _bound(self, delta, n_scale=1.0):
if self._mode == 'trivial':
l = 0
u = 1
else:
# Get statistics of the samples
S = self._get_samples()
n, ns, p = len(S) * n_scale, np.sum(S), np.mean(S)
if n == 0:
return (0, 1)
# Compute the bound
if self._mode == 'jeffery':
l = beta.ppf(delta / 2, ns + 0.5, n - ns +
0.5) if (ns > 0) else 0
u = beta.ppf(1 - delta / 2, ns + 0.5, n - ns +
0.5) if (ns < n) else 1
elif self._mode == 'wilson':
z = norm.ppf(1 - delta / 2)
v = z**2 - (1 / n) + 4 * n * p * (1 - p) + (4 * p - 2)
den = 2 * (n + z**2)
i = (z * np.sqrt(v) + 1)
c = (2 * n * p + z**2)
l = max(0, (c - i) / den)
u = min(1, (c + i) / den)
elif self._mode == 'learned-miller':
S = np.sort(S)
D = np.diff(S.tolist() + [1.0])
U = np.random.random((5000, n))
U = np.sort(U, axis=1)
M = 1 - (U * D[None]).sum(1)
M = np.sort(M)
i_ub = np.ceil((1 - delta) * 5000).astype(int)
u = M[i_ub]
elif self._mode == 'bootstrap':
n_resamples = 1000
Z = (np.random.multinomial(S.shape[0],
np.ones(S.shape[0]) / S.shape[0],
n_resamples) * S[None, :]).mean(1)
l, u = np.percentile(Z,
(100 * delta / 2, 100 * (1 - delta / 2)))
else:
raise Exception('Unknown mode: %s' % self._mode)
return (l, u)
def learn(self, old_obs, act, rew, new_obs, done):
self.t += 1
if rew > 0.5:
self.successes[act] += 1
else:
self.failures[act] += 1
self.means[act] = self.successes[act]/(self.successes[act] + self.failures[act])
#update UCB bonus
self.ucb_bonus = beta.ppf(1-1/((self.t+1)*self.log_horizon**self.c), self.successes, self.failures)
def qqplot(pvals,
minuslog10p=False,
text='',
fontsize='medium',
errorbars=True,
maxy=None,
ax=None,
**kwargs):
if ax is None:
ax = plt.gca()
x = np.arange(1 / len(pvals), 1 + 1 / len(pvals),
1 / len(pvals))[:len(pvals)]
logx = -np.log10(x)
if maxy is None:
maxy = 3 * np.max(logx)
if minuslog10p:
logp = np.sort(pvals)[::-1]
else:
logp = -np.log10(np.sort(pvals))
logp[logp >= maxy] = maxy
l, r = min(np.min(logp), np.min(logx)), max(np.max(logx), np.max(logp))
if errorbars:
ranks = np.arange(1, len(logp) + 1)
cilower = -np.log10(beta.ppf(.025, ranks, len(logx) - ranks + 1))
ciupper = -np.log10(beta.ppf(.975, ranks, len(logx) - ranks + 1))
ax.fill_between(logx,
cilower,
ciupper,
facecolor='gray',
interpolate=True,
alpha=0.2,
linewidth=0)
ax.scatter(logx, logp, **kwargs)
ax.plot([l, r], [l, r], c='gray', linewidth=0.2, dashes=[1, 1])
ax.set_xlim(min(logx), 1.01 * max(logx))
ax.set_xlabel(r'$-\log_{10}(\mathrm{rank}/n)$', fontsize=fontsize)
ax.set_ylabel(r'$-\log_{10}(p)$', fontsize=fontsize)
ax.set_title(text)
plt.tight_layout()
def plot_beta_distribution():
head = 0
tail = 0
x = np.linspace(beta.ppf(0.00, 1, 1), beta.ppf(1.00, 1, 1), 200)
plt.subplot(2, 4, 1)
plt.plot(x, beta.pdf(x, 1, 1), 'r-', lw=5, label='beta pdf')
counter = 2
for outcome in outcomes:
head = head + outcome
tail = tail + (1 - outcome)
alpha, b = get_beta_posterior_parameters(head, tail)
x = np.linspace(beta.ppf(0.00, alpha, b), beta.ppf(1.00, alpha, b),
200)
plt.subplot(2, 4, counter)
plt.plot(x, beta.pdf(x, alpha, b), 'r-', lw=5, label='beta pdf')
counter += 1
# plt.axis('equal')
plt.show()
def test_beta_template():
alpha = .05
k = 5
m = 10
t = beta_template(alpha, k, m)
assert_array_almost_equal(
t,
beta.ppf(alpha, np.arange(1, k + 1),
np.array([m + 1] * k) - np.arange(1, k + 1)))
assert isinstance(t, np.ndarray)
assert len(t) == k
def select_items(self, required_num, item_score):
self.turn += 1
sample_val = [0.0] * self.K
for k in range(self.K):
z0 = beta.ppf(1.0 - 1.0 / self.turn, sum(self.S[k]),
sum(self.N[k]) - sum(self.S[k]))
sample_val[k] = z0 * item_score[k]
items = sorted([(sample_val[k], k) for k in range(self.K)],
reverse=True)
result = [items[i][1] for i in range(required_num)]
return result
def ucb(n: int, k: int, alpha: float):
"""
Computes an upper confidence bound on the probability parameter p of a binomial CDF.
Returns:
The smallest p such that Pr[Binom[n,p] <= k] <= alpha
"""
if k == n:
return 1
else:
return beta.ppf(1 - alpha, k + 1, n - k)
def test_beta_distribution():
fig, ax = plt.subplots(1, 1)
a, b = 10, 30
# Mean(‘m’), variance(‘v’), skew(‘s’), and/or kurtosis(‘k’).
mean, var, skew, kurt = beta.stats(a, b, moments='mvsk')
print(mean)
print(var)
print(skew)
print(kurt)
print(beta.pdf(0.333, a, b))
x = np.linspace(beta.ppf(0.01, a, b), beta.ppf(0.99, a, b), 100)
ax.plot(x, beta.pdf(x, a, b), 'r-', lw=5, alpha=0.6, label='beta pdf')
rv = beta(a, b)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
vals = beta.ppf([0.001, 0.5, 0.999], a, b)
np.allclose([0.001, 0.5, 0.999], beta.cdf(vals, a, b))
r = beta.rvs(a, b, size=1000)
ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
ax.legend(loc='best', frameon=False)
plt.show()
def get_initial_state(self, **kwargs):
state = {}
state['t'] = 0
state['K'] = self.K
state['successes'] = np.full(self.env.nA, self.prior_a, dtype=np.int32)
state['failures'] = np.full(self.env.nA, self.prior_b, dtype=np.int32)
state['means'] = state['successes'] / (state['successes'] +
state['failures'])
state['ucl_bonus'] = beta.ppf(1 - 1 / (state['K'] * (state['t'] + 1)),
state['successes'], state['failures'])
return state
def BBP(prior_a, prior_b, path=None):
lol = read_data()
#x = np.linspace(beta.ppf(0.01, prior_a, prior_b), beta.ppf(0.99, prior_a, prior_b), 100)
#rv = beta(prior_a, prior_b)
#plt.plot(x, rv.pdf(x))
#plt.show()
for line in lol:
x = np.linspace(beta.ppf(0.01, prior_a, prior_b),
beta.ppf(0.99, prior_a, prior_b), 100)
rv = beta(prior_a, prior_b)
plt.plot(x, rv.pdf(x))
binolike = sum(line) / len(line)
print(binolike)
print(prior_a, prior_b)
prior_a = prior_a + sum(line)
prior_b = prior_b + len(line) - sum(line)
print(prior_a, prior_b)
print("-----")
plt.show()
def inverse_beta_ml_band(z,i,N): alpha_param=i+1 beta_param=N-i+1 small=.5 if i<small: x=0 xx=beta.ppf(z,alpha_param,beta_param) elif i>N-small: x=beta.ppf(1.0-z,alpha_param,beta_param) xx=1 if np.isnan(x): print "NaN failure in beta edge case" IPython.embed() else: x_min=0 x_max=beta.ppf(1.0-z,alpha_param,beta_param) def g(x): prob_xx=beta.cdf(x,alpha_param,beta_param)+z if prob_xx>1: #Numerical precision paranoia prob_xx=1 xx=beta.ppf(prob_xx,alpha_param,beta_param) prob_diff=beta.pdf(x,alpha_param,beta_param)-beta.pdf(xx,alpha_param,beta_param) #print ' x=%f, prob_xx=%f, xx=%f, prob_diff=%f'%(x,prob_xx,xx,prob_diff) return(prob_diff) try: #print '*** (x_min,x_max)=%f,%f'%(x_min,x_max) x=brentq(g,x_min,x_max) #print ' (x)=%f\n'%(x) except: print "Failure at 'brentq'." IPython.embed() prob_xx=beta.cdf(x,alpha_param,beta_param)+z if prob_xx>1: #Numerical precision paranoia prob_xx=1 xx=beta.ppf(prob_xx,alpha_param,beta_param) larger_x=np.max((x,xx)) smaller_x=np.min((x,xx)) return((smaller_x,larger_x))
def learn(self, old_obs, act, rew, new_obs, done):
self.t += 1
if rew > 0.5:
self.successes[act] += 1
else:
self.failures[act] += 1
self.means[act] = self.successes[act] / (self.successes[act] +
self.failures[act])
#update UCL bonus
self.ucl_bonus = beta.ppf(1 - 1 / (self.K * (self.t + 1)),
self.successes, self.failures)
def plot(self, data, size, newdata=None):
data = np.array(data)
numsample = len(data)
colmean = np.mean(data, axis=0)
matcov = np.cov(data.T)
matinv = np.linalg.inv(matcov)
values = []
for sample in data:
dif = sample - colmean
value = matinv.dot(dif.T).dot(dif)
values.append(value)
cl = ((numsample - 1)**2) / numsample
lcl = cl * beta.ppf(0.00135, size / 2, (numsample - size - 1) / 2)
center = cl * beta.ppf(0.5, size / 2, (numsample - size - 1) / 2)
ucl = cl * beta.ppf(0.99865, size / 2, (numsample - size - 1) / 2)
return (values, center, lcl, ucl, self._title)
def lcb(n: int, k: int, alpha: float):
"""
Computes a lower confidence bound on the probability parameter p of a binomial CDF.
Returns:
The largest p such that Pr[Binom[n,p] >= k] <= alpha
"""
if k == 0:
return 0
else:
# Inspired by https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Clopper%E2%80%93Pearson_interval
return beta.ppf(alpha, k, n - k + 1)
def event_time(t0, x, u, exp_num):
if exp_num == 0:
lambda_ = 1 if x == 0 else 2
return -math.log(u) / lambda_ + t0
if exp_num == 1:
return beta.ppf(-math.log(u) / beta.pdf(x, 2, 2) + beta.cdf(t0, 2, 2),
2, 2)
if exp_num == 2:
return beta.ppf(-math.log(u) / beta.pdf(x, 4, 4) + beta.cdf(t0, 4, 4),
4, 4)
if exp_num == 3:
return np.exp(x - norm.ppf(u * norm.cdf(x - math.log(t0))))
if exp_num == 4:
return np.power(
-math.log(u) / (np.exp(-0.5 * math.cos(2 * math.pi * x) - 1.5)) +
np.power(t0, 1.5), 2 / 3)
def random_sample_beta_inv_cdf(cls, E, a):
"""
Sample a beta inverse CDF with expectation E and alpha param a.
The values of E and alpha will fix the value of beta.
"""
y_in = random.random()
b = a * (1.0 / E - 1.0)
# Use the percent point function - inverse CDF
x_out = beta.ppf(y_in, a, b)
x = y_in # This is the input random number, uniform between 0-1
y = x_out # This is the output weighted random number
return (x, y)
def plot(self, data, size, newdata=None):
data = np.array(data)
numsample = len(data)
colmean = np.mean(data, axis=0)
matcov = np.cov(data.T)
matinv = np.linalg.inv(matcov)
values = []
for sample in data:
dif = sample - colmean
value = matinv.dot(dif.T).dot(dif)
values.append(value)
cl = ((numsample - 1)**2) / numsample
lcl = cl * beta.ppf(0.00135, size / 2, (numsample - size - 1) / 2)
center = cl * beta.ppf(0.5, size / 2, (numsample - size - 1) / 2)
ucl = cl * beta.ppf(0.99865, size / 2, (numsample - size - 1) / 2)
return (values, center, lcl, ucl, self._title)
def Dist(stvars, value, inpt):
v = zeros(inpt)
for j in range(inpt):
if stvars[j].dist == 'NORM':
v[j] = norm.ppf(norm.cdf(value[j], 0, 1), stvars[j].param[0], stvars[j].param[1])
elif stvars[j].dist == 'LNORM':
v[j] = lognorm.ppf(norm.cdf(value[j], 0, 1), stvars[j].param[1], 0, exp(stvars[j].param[0]))
elif stvars[j].dist == 'BETA':
v[j] = beta.ppf(norm.cdf(value[j], 0, 1), stvars[j].param[0], stvars[j].param[1], stvars[j].param[2], stvars[j].param[3] - stvars[j].param[2])
elif stvars[j].dist == 'UNIF':
v[j] = uniform.ppf(norm.cdf(value[j], 0, 1), stvars[j].param[0], stvars[j].param[1])
return v
def cbox_nom(k, n): a = k b = n - k + 1 c = k + 1 d = n - k cbox = pbox() steps = cbox.steps cbox_beta = beta.ppf([xy/steps for xy in [x+1 for x in range(steps)]], [rep(a,steps),rep(c,steps)], [rep(b,steps),rep(d,steps)]) cbox.left = cbox_beta[0] cbox.right = cbox_beta[1] return cbox
def generateLatinHypercubeSampledMultipliers(self, specification_map, number_samples) :
# Construct sets of random sampled multipliers from the selected distribution for each parameter
multiplier_sets = {}
for key, specification in specification_map.items() :
# Generate stratified random probability values for distribution generation via inverse CDF
stratified_random_probabilities = ((np.array(range(number_samples)) + np.random.random(number_samples))/number_samples)
# Use stratified random probability values to generate stratified samples from selected distribution via inverse CDF
distribution = specification['distribution']
if distribution == 'uniform' :
lower = specification['settings']['lower']
base = specification['settings']['upper'] - lower
multiplier_sets[key] = uniform.ppf(stratified_random_probabilities, loc=lower, scale=base).tolist()
elif distribution == 'normal' :
mean = specification['settings']['mean']
std_dev = specification['settings']['std_dev']
multiplier_sets[key] = norm.ppf(stratified_random_probabilities, loc=mean, scale=std_dev).tolist()
elif distribution == 'triangular' :
a = specification['settings']['a']
base = specification['settings']['b'] - a
c_std = (specification['settings']['c'] - a)/base
multiplier_sets[key] = triang.ppf(stratified_random_probabilities, c_std, loc=a, scale=base).tolist()
elif distribution == 'lognormal' :
lower = specification['settings']['lower']
scale = specification['settings']['scale']
sigma = specification['settings']['sigma']
multiplier_sets[key] = lognorm.ppf(stratified_random_probabilities, sigma, loc=lower, scale=scale).tolist()
elif distribution == 'beta' :
lower = specification['settings']['lower']
base = specification['settings']['upper'] - lower
a = specification['settings']['alpha']
b = specification['settings']['beta']
multiplier_sets[key] = beta.ppf(stratified_random_probabilities, a, b, loc=lower, scale=base).tolist()
# Randomly select from sampled multiplier sets without replacement to form multipliers (dictionaries)
sampled_multipliers = []
for i in range(number_samples) :
sampled_multiplier = {}
for key, multiplier_set in multiplier_sets.items() :
random_index = np.random.randint(len(multiplier_set))
sampled_multiplier[key] = multiplier_set.pop(random_index)
sampled_multipliers.append(sampled_multiplier)
return sampled_multipliers
def is_heterozygous((n_a, n_b, gamma)): """ Determines if an allele should be considered heterozygous. Arguments: n_a (int): number of a alleles counted. Used as alpha parameter for the beta distribution n_b (int): number of b alleles counted. Used as beta parameter for the beta distribution gamma (float): parameter used for deciding heterozygosity; determined via a beta distribution with 1 - gamma confidence Returns: A boolean indicating whether or not the allele should be considered heterozygous. """ if n_a == -1 or n_b == -1: return False p_lower = gamma / 2.0 p_upper = 1 - p_lower [c_lower, c_upper] = beta.ppf([p_lower, p_upper], n_a + 1, n_b + 1) return c_lower <= 0.5 and c_upper >= 0.5
Lthr = -0.21
# how many events of L < -21% occured?
ne = np.sum(ret < Lthr)
# of what magnitude?
ev = ret[ret < Lthr]
# avgloss = np.mean(ev) # if ev is non-empty array
# prior
alpha0 = beta0 = 1
# posterior
alpha1 = alpha0 + ne
beta1 = beta0 + N - ne
pr = alpha1 / (alpha1 + beta1)
cl1 = beta.ppf(0.05, alpha1, beta1)
cl2 = beta.ppf(0.95, alpha1, beta1)
ne252 = np.round(252 / (1 / cl2))
print("ne = %g" % ne)
print("alpha', beta' = %g, %g" % (alpha1, beta1))
print("Pr(L < %3g%%) = %5.2f%%\t[%5.2f%%, %5.2f%%]" % (Lthr * 100, pr * 100, cl1 * 100, cl2 * 100))
print("E(ne) = %g" % ne252)
############################
returns = cp[1:] / cp[:-1] - 1
Lthr = -0.11
Pr = CL1 = CL2 = np.array([])
for i in range(2, len(returns)):
from app import app
from dash.dependencies import Input, Output, State
from scipy.stats import norm,bernoulli,beta,binom
# global theta value
global theta
theta = 0
n = 10 # for lambert example
# posterior dist
a = 3
b = 9
x_beta = np.linspace(beta.ppf(0.01,a,b),beta.ppf(0.99,a,b),100)
y_beta = beta.pdf(x_beta,a,b)
x1 = np.random.randn(200)
hist_data = [x1]
trace = go.Scatter(
x = x_beta,
y = y_beta
)
layout_posterior = go.Layout(
xaxis={'title': 'X'},
def binom_interval(success, total, confint=0.95):
quantile = (1 - confint) / 2.
mode = float(success)/total
lower = beta.ppf(quantile, success, total - success + 1)
upper = beta.ppf(1 - quantile, success + 1, total - success)
return (mode, lower, upper)
def CDF_error_beta(n, target_quantile, quantile_quantile):
k = target_quantile * n
return (beta.ppf(quantile_quantile, k, n + 1 - k))
def SA_FAST(driver):
# First order indicies for a given model computed with Fourier Amplitude Sensitivity Test (FAST).
# R. I. Cukier, C. M. Fortuin, Kurt E. Shuler, A. G. Petschek and J. H. Schaibly.
# Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients.
# I-III Theory/Applications/Analysis The Journal of Chemical Physics
#
# Input:
# inpt : no. of input factors
#
# Output:
# SI[] : sensitivity indices
# Other used variables/constants:
# OM[] : frequencies of parameters
# S[] : search curve
# X[] : coordinates of sample points
# Y[] : output of model
# OMAX : maximum frequency
# N : number of sample points
# AC[],BC[]: fourier coefficients
# V : total variance
# VI : partial variances
# ---------------------- Setup ---------------------------
methd = 'FAST'
method = '9'
mu = [inp.get_I_mu() for inp in driver.inputs]
I_sigma = [inp.get_I_sigma() for inp in driver.inputs]
inpt = len(driver.inputs)
input = driver.inputNames
krig = driver.krig
limstate= driver.limstate
lrflag = driver.lrflag
n_meta = driver.n_meta
nEFAST = driver.nEFAST
nSOBOL = driver.nSOBOL
nMCS = driver.nMCS
nodes = driver.nodes
order = driver.order
otpt = len(driver.outputNames)
output = driver.outputNames
p = driver.p
plotf = 0
r = driver.r
simple = driver.simple
stvars = driver.stvars
# ---------------------- Model ---------------------------
#
MI = 4#: maximum number of fourier coefficients that may be retained in
# calculating the partial variances without interferences between the assigned frequencies
#
# Frequency assignment to input factors.
OM = SETFREQ(inpt)
# Computation of the maximum frequency
# OMAX and the no. of sample points N.
OMAX = int(OM[inpt-1])
N = 2 * MI * OMAX + 1
# Setting the relation between the scalar variable S and the coordinates
# {X(1),X(2),...X(inpt)} of each sample point.
S = pi / 2.0 * (2 * arange(1,N+1) - N-1) / N
ANGLE = matrix(OM).T * matrix(S)
X = 0.5 + arcsin(sin(ANGLE.T)) / pi
# Transform distributions from standard uniform to general.
for j in range(inpt):
if stvars[j].dist == 'NORM':
X[:,j] = norm.ppf(uniform.cdf(X[:,j], 0, 1), stvars[j].param[0], stvars[j].param[1])
elif stvars[j].dist == 'LNORM':
X[:,j] = lognorm.ppf(uniform.cdf(X[:, j], 0, 1), stvars[j].param[1], 0, exp(stvars[j].param[0]))
elif stvars[j].dist == 'BETA':
X[:,j] = beta.ppf(uniform.cdf(X[:, j], 0, 1), stvars[j].param[0], stvars[j].param[1], stvars[j].param[2], stvars[j].param[3] - stvars[j].param[2])
elif stvars[j].dist == 'UNIF':
X[:,j] = uniform.ppf(uniform.cdf(X[:,j], 0, 1), stvars[j].param[0], stvars[j].param[1])
# Do the N model evaluations.
Y = zeros((N, otpt))
if krig == 1:
load("dmodel")
Y = predictor(X, dmodel)
else:
values = []
for p in range(N):
# print 'Running simulation on test',p+1,'of',N
# Y[p] = run_model(driver, array(X[p])[0])
values.append(array(X[p])[0])
Y = run_list(driver, values)
# Computation of Fourier coefficients.
AC = zeros((N, otpt))# initially zero
BC = zeros((N, otpt))# initially zero
# q = int(N / 2)-1
q = (N-1)/2
for j in range(2,N+1,2): # j is even
# print "Y[q]",Y[q]
# print "matrix(cos(pi * j * arange(1,q+) / N))",matrix(cos(pi * j * arange(1,q+1) / N))
# print "matrix(Y[q + arange(0,q)] + Y[q - arange(0,q)])",matrix(Y[q + arange(1,q+1)] + Y[q - arange(1,q+1)])
AC[j-1] = 1.0 / N * matrix(Y[q] + matrix(cos(pi * j * arange(1,q+1) / N)) * matrix(Y[q + arange(1,q+1)] + Y[q - arange(1,q+1)]))
for j in range(1,N+1,2): # j is odd
BC[j-1] = 1.0 / N * matrix(sin(pi * j * arange(1,q+1) / N)) * matrix(Y[q + arange(1,q+1)] - Y[q - arange(1,q+1)])
# Computation of the general variance V in the frequency domain.
V = 2 * (matrix(AC).T * matrix(AC) + matrix(BC).T * matrix(BC))
# Computation of the partial variances and sensitivity indices.
# Si=zeros(inpt,otpt);
Si = zeros((otpt,otpt,inpt));
for i in range(inpt):
Vi = zeros((otpt, otpt))
for j in range(1,MI+1):
idx = j * OM[i]-1
Vi = Vi + AC[idx].T * AC[idx] + BC[idx].T * BC[idx]
Vi = 2. * Vi
Si[:, :, i] = Vi / V
if lrflag == 1:
SRC, stat = SRC_regress.SRC_regress(X, Y, otpt, N)
# ---------------------- Analyze ---------------------------
Sti = []# appears right after the call to this method in the original PCC_Computation.m
# if plotf == 1:
# piecharts(inpt, otpt, Si, Sti, method, output)
if simple == 1:
Si_t = zeros((inpt,otpt))
for p in range(inpt):
Si_t[p] = diag(Si[:, :, p])
Si = Si_t.T
Results = {'FirstOrderSensitivity': Si}
if lrflag == 1:
Results.update({'SRC': SRC, 'R^2': stat})
return Results
def gridSetting(data,options,Seed):
# Initialisierung
d = np.size(options['borders'],0)
X1D = []
'''Equal steps in cumulative distribution'''
if options['gridSetType'] == 'cumDist':
Like1D = np.zeros([options['GridSetEval'], 1])
for idx in range(d):
if options['borders'][idx, 0] < options['borders'][idx,1]:
X1D.append(np.zeros([1, options['stepN'][idx]]))
local_N_eval = options['GridSetEval']
while any(np.diff(X1D[idx]) == 0):
Xtest1D = np.linspace(options['borders'][idx,0], options['borders'][idx,1], local_N_eval)
alpha = Seed[0]
beta = Seed[1]
l = Seed[2]
gamma = Seed[3]
varscale = Seed[4]
if idx == 1:
alpha = Xtest1D
elif idx == 2:
beta = Xtest1D
elif idx == 3:
l = Xtest1D
elif idx == 4:
gamma = Xtest1D
elif idx == 5:
varscale = Xtest1D
Like1D = likelihood(data, options, [alpha, beta, l, gamma, varscale])
Like1D = Like1D + np.mean(Like1D)*options['UniformWeight']
Like1D = np.cumsum(Like1D)
Like1D = Like1D/max(Like1D)
wanted = np.linspace(0,1,options['stepN'][idx])
for igrid in range(options['stepN'][idx]):
X1D[idx].append(copy.deepcopy(Xtest1D[Like1D >= wanted, 0, 'first'])) #TODO check
local_N_eval = 10*local_N_eval
else:
X1D.append(copy.deepcopy(options['borders'][idx,0]))
''' equal steps in cumulative second derivative'''
elif (options['gridSetType'] in ['2', '2ndDerivative']):
Like1D = np.zeros([options['GridSetEval'], 1])
for idx in range(d):
if options['borders'][idx,0] < options['borders'][idx,1]:
X1D.append(np.zeros([1,options['stepN'][idx]]))
local_N_eval = options['GridSetEval']
while any(np.diff(X1D[idx] == 0)):
Xtest1D = np.linspace(options['borders'][idx,0], options['borders'][idx,1], local_N_eval)
alpha = Seed[0]
beta = Seed[1]
l = Seed[2]
gamma = Seed[3]
varscale = Seed[4]
if idx == 1:
alpha = Xtest1D
elif idx == 2:
beta = Xtest1D
elif idx == 3:
l = Xtest1D
elif idx == 4:
gamma = Xtest1D
elif idx == 5:
varscale = Xtest1D
# calc likelihood on the line
Like1D = likelihood(data, options, [alpha, beta, l, gamma, varscale])
Like1D = np.abs(np.convolve(np.squeeze(Like1D), np.array([1,-2,1]), mode='same'))
Like1D = Like1D + np.mean(Like1D)*options['UniformWeight']
Like1D = np.cumsum(Like1D)
Like1D = Like1D/max(Like1D)
wanted = np.linspace(0,1,options['stepN'][idx])
for igrid in range(options['stepN'][idx]):
X1D[idx].append(copy.deepcopy(Xtest1D[Like1D >= wanted, 0, 'first'])) #ToDo
local_N_eval = 10*local_N_eval
if local_N_eval > 10**7:
X1D[idx] = np.unique(np.array(X1D)) # TODO check
break
else:
X1D.append(options['borders'][idx,0])
''' different choices for the varscale '''
''' We use STD now directly as parametrisation'''
elif options['gridSetType'] in ['priorlike', 'STD', 'exp', '4power']:
for i in range(4):
if options['borders'](i,0) < options['borders'](i,1):
X1D.append(np.linspace(options['borders'][i,0], options['borders'][i,1], options['stepN'][i]))
else:
X1D.append(copy.deepcopy(options['borders'][id,0]))
if options['gridSetType'] == 'priorlike':
maximum = b.cdf(options['borders'][4,1],1,options['betaPrior'])
minimum = b.cdf(options['borders'][4,0],1,options['betaPrior'])
X1D.append(b.ppf(np.linspace(minimum, maximum, options['stepN'][4]), 1, options['betaPrior']))
elif options['gridSetType'] == 'STD':
maximum = np.sqrt(options['borders'][4,1])
minimum = np.sqrt(options['borders'][4,0])
X1D.append((np.linspace(minimum, maximum, options['stepN'][4]))**2)
elif options['gridSetType'] == 'exp':
p = np.linspace(1,1,options['stepN'][4])
X1D.append(np.log(p)/np.log(.1)*(options['borders'][4,1] - options['borders'][4,0]) + options['borders'][4,0])
elif options['gridSetType'] == '4power':
maximum = np.sqrt(options['borders'][4,1])
minimum = np.sqrt(options['borders'][4,0])
X1D.append((np.linspace(minimum, maximum, options['stepN'][4]))**4)
return X1D
def binom_interval(success, total, conf=0.95):
quantile = (1 - conf) / 2.
lower = beta.ppf(quantile, success, total - success + 1)
upper = beta.ppf(1 - quantile, success + 1, total - success)
return (lower, upper)