def build_model(historic_prices: pd.DataFrame, base_days: int, vault: Vault, config: Config) -> pd.DataFrame:
pct_changes = historic_prices.price.pct_change().dropna().values[-base_days * 24:]
with pm.Model() as model:
mu = pm.Normal("mu", mu=0, sigma=0.1)
sd = pm.HalfNormal("sd", sigma=0.1)
obs = pm.Normal("obs", mu=mu, sigma=sd, observed=pct_changes)
trace = pm.sample(5000, cores=config.SAMPLING_CORES, tune=5000)
mus = np.random.choice(trace.get_values('mu'), size=config.N_POSTERIOR_SAMPLES, replace=True)
sds = np.random.choice(trace.get_values('sd'), size=config.N_POSTERIOR_SAMPLES, replace=True)
posterior_samples = np.random.normal(mus, sds, size=(config.MODEL_HORIZON_DAYS*24, config.N_POSTERIOR_SAMPLES))
posterior_samples = np.transpose(posterior_samples)
posterior_growths = np.cumsum(posterior_samples, axis=1)
latest_known_price = historic_prices.loc[historic_prices.index.max()].price
price_projections = to_float((1 + posterior_growths) * latest_known_price, vault.decimals)
hpd_95 = pm.hpd(price_projections, hdi_prob=0.95)
hpd_50 = pm.hpd(price_projections, hdi_prob=0.5)
model = pd.DataFrame.from_dict(
{
'hpd_95_lower': hpd_95[:,0],
'hpd_95_upper': hpd_95[:,1],
'hpd_50_lower': hpd_50[:,0],
'hpd_50_upper': hpd_50[:,1]
}
)
index = pd.DatetimeIndex(pd.date_range(historic_prices.index.max() + pd.DateOffset(hours=1), periods=config.MODEL_HORIZON_DAYS*24, freq='H'))
model = model.set_index(index).resample('1D').nearest()
model['vault'] = vault.name
model['base_days'] = base_days
return model
def generate_ebbinghaus_data_figure_3():
fig, (ax1, ax2) = plt.subplots(ncols=1, nrows=2)
fig.set_size_inches(5.5, 4.5)
# plot 1
ax1.plot(delay, savings, marker='o', linestyle='--')
ax1.plot(delay, np.median(np.exp(mu), axis=0), color='red', linestyle='-')
ax1.set_title('c. Log-log plot (blue) and power law model estimates (red)')
ax1.set_xlabel('Delay (log hours)')
ax1.set_xscale('log', basex=10)
ax1.set_ylabel('Savings (log \\%)')
ax1.set_yscale('log', basey=10)
ax1.grid(b=True, which='minor', color='w', linewidth=1.0)
# plot 2
yerr = [
np.median(np.exp(mu), axis=0) - pm.hpd(np.exp(mu))[:, 0],
pm.hpd(np.exp(mu))[:, 1] - np.median(np.exp(mu), axis=0)
]
ax2.errorbar(savings,
np.median(np.exp(mu), axis=0),
yerr=yerr,
marker='o',
linestyle='')
ax2.plot(np.linspace(0, 100, 10),
np.linspace(0, 100, 10),
color='red',
linestyle=':')
ax2.set_title('Power law model: Observed vs. predicted savings')
ax2.set_xlabel('Observed savings (\\%)')
ax2.set_ylabel('Predicted savings (\\%)')
ax2.grid(b=True, which='minor', color='w', linewidth=1.0)
# clean up and save
plt.tight_layout(pad=0.5, w_pad=0.2, h_pad=0.7)
plt.savefig('./figures/ebbinghaus_data_3.eps')
plt.savefig('./figures/ebbinghaus_data_3.png')
plt.savefig('./figures/ebbinghaus_data_3.pdf')
def generate_log_freq_figure():
fig, (ax1, ax2) = plt.subplots(ncols=1, nrows=2)
fig.set_size_inches(5.5, 5.5)
# plot 1
ax1.plot(freq, rt, marker='o', linestyle='')
ax1.plot(freq, mu.mean(axis=0), color='red', linestyle='-')
ax1.set_title('Observed (blue) \& predicted (red) RTs\
against log frequency')
ax1.set_xlabel('Log frequency (log of \# tokens/1 million words)')
ax1.set_xscale('log', basex=10)
ax1.set_ylabel('RTs (s)')
ax1.grid(b=True, which='minor', color='w', linewidth=1.0)
# plot 2
yerr=[mu.mean(axis=0)-pm.hpd(mu)[:,0],\
pm.hpd(mu)[:,1]-mu.mean(axis=0)]
ax2.errorbar(rt, mu.mean(axis=0), yerr=yerr,\
marker='o', linestyle='')
ax2.plot(np.linspace(0.5, 0.7, 10),
np.linspace(0.5, 0.7, 10),
color='red',
linestyle=':')
ax2.set_title('Log frequency model: Observed vs. predicted RTs')
ax2.set_xlabel('Observed RTs (s)')
ax2.set_ylabel('Predicted RTs (s)')
ax2.grid(b=True, which='minor', color='w', linewidth=1.0)
# clean up and save
plt.tight_layout(pad=0.5, w_pad=0.2, h_pad=1.9)
plt.savefig('./figures/log_freq_model_figure.eps')
plt.savefig('./figures/log_freq_model_figure.png')
plt.savefig('./figures/log_freq_model_figure.pdf')
def plot_fits_w_estimates(y_obs, ppc, ax=None, legend=False):
""" Plot Fits with Uncertainty Estimates"""
iy = np.argsort(y_obs)
ix = np.arange(iy.size)
lik_mean = ppc.mean(axis=0)
lik_hpd = pm.hpd(ppc)
lik_hpd_05 = pm.hpd(ppc, alpha=0.5)
r2 = r2_score(y_obs, lik_mean)
mae = mean_absolute_error(y_obs, lik_mean)
if ax is None:
_, ax = pl.subplots(figsize=(12, 8))
ax.scatter(ix,
y_obs.values[iy],
label='observed',
edgecolor='k',
s=40,
color='w',
marker='d',
zorder=2)
ax.scatter(ix,
lik_mean[iy],
label='model mean -- $r^2$=%.2f -- mae=%.2f' % (r2, mae),
edgecolor='k',
s=40,
color='w',
zorder=3)
ax.fill_between(ix,
y1=lik_hpd_05[iy, 0],
y2=lik_hpd_05[iy, 1],
color='gray',
label='model output 50%CI',
zorder=1,
linestyle='-',
lw=2,
edgecolor='k')
ax.fill_between(
ix,
y1=lik_hpd[iy, 0],
y2=lik_hpd[iy, 1],
color='k',
alpha=0.75,
label='model output 95%CI',
zorder=0,
)
if legend:
ax.legend(loc='upper left')
return ax
def mcmc_stats(runs, burnin, prob, batch):
"""
入力
runs: モンテカルロ標本
burnin: バーンインの回数
prob: 区間確率 (0 < prob < 1)
batch: 乱数系列の分割数
出力
事後統計量のデータフレーム
"""
traces = runs[burnin:, :]
n = traces.shape[0] // batch
k = traces.shape[1]
alpha = 100 * (1.0 - prob)
post_mean = np.mean(traces, axis=0)
post_median = np.median(traces, axis=0)
post_sd = np.std(traces, axis=0)
mc_err = pm.mc_error(traces, batches=batch)
ci_lower = np.percentile(traces, 0.5 * alpha, axis=0)
ci_upper = np.percentile(traces, 100 - 0.5 * alpha, axis=0)
hpdi = pm.hpd(traces, 1.0 - prob)
rhat = [pm.gelman_rubin(traces[:, i].reshape((n, batch), order='F')) \
for i in range(k)]
stats = np.vstack((post_mean, post_median, post_sd, mc_err,
ci_lower, ci_upper, hpdi.T, rhat)).T
stats_string = ['平均', '中央値', '標準偏差', '近似誤差',
'信用区間（下限）', '信用区間（上限）',
'HPDI（下限）', 'HPDI（上限）', '$\\hat R$']
param_string = ['平均 $\\mu$', '分散 $\\sigma^2$']
return pd.DataFrame(stats, index=param_string, columns=stats_string)
def plot_model_ppc_stats(self,
ppc,
y_obs,
alpha_level1=0.05,
alpha_level2=0.5,
ax=None):
if ax is None:
_, ax = pl.subplots()
iy = np.argsort(y_obs)
ix = np.arange(iy.size)
ppc_mean = ppc.mean(axis=0)
ax.scatter(ix,
y_obs.values[iy],
label='observed',
edgecolor='k',
s=50,
color='steelblue')
ax.scatter(ix,
ppc_mean[iy],
label='prediction mean',
edgecolor='k',
s=50,
color='red')
if alpha_level2:
lik_hpd_2 = pm.hpd(ppc, alpha=alpha_level2)
ax.fill_between(
ix,
y1=lik_hpd_2[iy, 0],
y2=lik_hpd_2[iy, 1],
alpha=0.5,
color='k',
label=f'prediction {1-alpha_level2:.2f}%CI',
)
if alpha_level1:
lik_hpd_1 = pm.hpd(ppc, alpha=alpha_level1)
ax.fill_between(
ix,
y1=lik_hpd_1[iy, 0],
y2=lik_hpd_1[iy, 1],
alpha=0.5,
color='k',
label=f'prediction {1-alpha_level1:.2f}%CI',
)
ax.legend(loc='best')
return ax
def compare_parameters_hierarchical(model,
parameters=['v', 'gamma', 's', 'tau'],
comparisons=None):
"""Compute comparisons of group level parameters between groups / conditions.
Args:
model (glambox.GLAM): Fitted GLAM instance
parameters (list, optional): List of parameters. Defaults to ['v', 'gamma', 's', 'tau'].
comparisons (list of tuples, optional): List of comparisons to perform. Must be a list of tuples, e.g., `[('A', 'B'), ('A', 'C')]`. Defaults to None.
Returns:
pandas.DataFrame: Distribution statistics of group level parameter differences.
"""
if comparisons is None:
comparisons = []
n_params = len(parameters)
n_comps = len(comparisons)
comparison_df = []
for p, parameter in enumerate(parameters):
# Comparisons
for c, comparison in enumerate(comparisons):
comparison_string = '{}-{}'.format(*comparison)
df_pc = pd.DataFrame(dict(parameter=parameter, comparison=comparison_string),
index=[0])
# Check if parameter has dependence
if model.design[parameter]['dependence'] is not None:
# Then, if both conditions are present, compute posterior of the difference
c0_present = (comparison[0] in model.design[parameter]['conditions'])
c1_present = (comparison[1] in model.design[parameter]['conditions'])
if c0_present & c1_present:
difference = (
model.trace[0].get_values(parameter + '_' +
comparison[0] + '_mu') -
model.trace[0].get_values(parameter + '_' +
comparison[1] + '_mu'))
hpd_lower, hpd_upper = hpd(difference, alpha=0.05)
df_pc['hpd_2.5'] = hpd_lower
df_pc['hpd_97.5'] = hpd_upper
df_pc['mean'] = np.mean(difference)
df_pc['p>0'] = np.mean(difference > 0)
else:
# Otherwise, state that at least one condition is not present.
df_pc['warning'] = 'At least one condition is missing.'
else:
# Or that the parameter has no dependencies.
df_pc['warning'] = 'Parameter has no dependencies.'
comparison_df.append(df_pc)
comparison_df = pd.concat(comparison_df, sort=False).reset_index(drop=True)
return comparison_df
def getAngelRate(data, n_sample=10000, n_chain=3, ax=None):
# データの整理
data_0 = data.query('campaign != 1')
data_1 = data.query('campaign == 1')
d = np.array([[
sum(data_0['angel'] == 0),
sum(data_0['angel'] == 1),
sum(data_0['angel'] == 2)
],
[
sum(data_1['angel'] == 0),
sum(data_1['angel'] == 1),
sum(data_1['angel'] == 2)
]])
weight = np.array([[1.0, 1.0, 1.0], [1.0, 0.0, 2.0]])
# パラメータ推定
with pm.Model() as model:
alpha = [1., 1., 1.] # hyper-parameter of DirichletDist.
pi = pm.Dirichlet('pi', a=np.array(alpha))
for i in np.arange(d.shape[0]):
piw = pi * weight[i]
m = pm.Multinomial('m_%s' % (i),
n=np.sum(d[i]),
p=piw,
observed=d[i])
trace = pm.sample(n_sample, chains=n_chain)
np.savetxt('trace_pi.csv', trace['pi'], delimiter=',')
# Silver
hpd_l, hpd_u = pm.hpd(trace['pi'][:, 1])
print('Silver : 95% HPD : {}-{}'.format(hpd_l, hpd_u))
print('Silver ExpectedValue : {}'.format(trace['pi'][:, 1].mean()))
# Gold
hpd_l, hpd_u = pm.hpd(trace['pi'][:, 2])
print('Gold : 95% HPD : {}-{}'.format(hpd_l, hpd_u))
print('Gold ExpectedValue : {}'.format(trace['pi'][:, 2].mean()))
# save fig
if ax is not None:
pm.plot_posterior(trace['pi'][:, 0], ax=ax[0])
pm.plot_posterior(trace['pi'][:, 1], ax=ax[1])
pm.plot_posterior(trace['pi'][:, 2], ax=ax[2])
ax[0].set_title('Nothing')
ax[1].set_title('SilverAngel')
ax[2].set_title('GoldAngel')
return trace
def compare_parameters_individual(model,
parameters,
comparisons=None):
if comparisons is None:
comparisons = []
n_params = len(parameters)
n_comps = len(comparisons)
subjects = model.data['subject'].unique().astype(int)
summaries = [summary(trace) for trace in model.trace]
comparison_df = []
for p, parameter in enumerate(parameters):
# Comparisons
for c, comparison in enumerate(comparisons):
comparison_string = '{}-{}'.format(*comparison)
df_pc = pd.DataFrame(dict(subject=subjects, parameter=parameter, comparison=comparison_string),
index=subjects)
# Check if parameter has dependence
if model.design[parameter]['dependence'] is not None:
# Then, if both conditions are present, plot posterior of the difference
c0_present = (
comparison[0] in model.design[parameter]['conditions'])
c1_present = (
comparison[1] in model.design[parameter]['conditions'])
if c0_present & c1_present:
differences = np.array([(model.trace[i].get_values(parameter + '_' + comparison[0]) -
model.trace[i].get_values(parameter + '_' + comparison[1]))
for i in subjects])[:, :, 0, 0]
means = np.mean(differences, axis=1)
hpdlower, hpdupper = hpd(differences.T, alpha=0.05).T
plarger0 = np.mean(differences > 0, axis=1)
df_pc['mean'] = means
df_pc['hpd_2.5'] = hpdlower
df_pc['hpd_97.5'] = hpdupper
df_pc['p>0'] = plarger0
else:
# Otherwise, state that at least one condition is not present.
df_pc['warning'] = 'At least one condition is missing.'
else:
# Or that the parameter has no dependencies.
df_pc['warning'] = 'Parameter has no dependencies.'
comparison_df.append(df_pc)
comparison_df = pd.concat(comparison_df, sort=False).sort_values('subject').reset_index(drop=True)
return comparison_df
def visualize_posteriors(samples, param_names):
'''
Function visualizes the approximate posteriors for all parameters based on the generated samples.
Returns posterior means, precision and HDI for all parameters.
'''
fig, axes = plt.subplots(1,samples.shape[-1], figsize=(15,6))
hdi = []; means = []
for c, vals in enumerate(samples.reshape(-1,samples.shape[-1]).T):
mean = np.round(np.mean(vals),3); hdi_low, hdi_high = np.round(pymc3.hpd(vals),3) # calc mean and HDI of params
means.append(mean); hdi.append([hdi_low, hdi_high])
axes[c].axvline(x=hdi_low, c='r'); axes[c].axvline(x=hdi_high, c='r')
sns.distplot(vals, bins=50, ax=axes[c]) # create histogramms for params with approx. density plots
axes[c].set_title("{0} mean: {1} \n HDI_low: {2} - HDI_high: {3}".format(param_names[c],np.round(mean, 3),
np.round(hdi_low,3), np.round(hdi_high,3)))
fig.suptitle('Posterior Distributions', fontsize=20)
fig.tight_layout(rect=[0, 0.03, 1, 0.90])
return np.asarray(means), np.asarray(hdi)
def plot_counterfactual(data,
trace,
variables,
parameters,
intercept='a',
hpdi=0.10,
xlab='',
ylab=''):
"""
x = predictor of interest
intercept = The string used to denote the intercept (i.e., alpha, or beta_0). Defaults to 'a'
variables and parameters are lists that must be in the same order (corresponding data column + coefficient).
The first value in each list should be the predictor of interest. Do not include the intercept term.
"""
# Calculate value of x term (predictor of interest)
x = data[variables[0]]
x_coef = parameters[0]
x_space = np.linspace(x.min(), x.max(), 50)
x_value = trace[x_coef] * x_space[:, None]
# Calculate value of other variables, holding them to the mean value.
controls = np.array(data[variables[1]].mean())
for item in variables[2:]:
controls = np.hstack((controls, [data[item].mean()]))
control_coefficients = []
for item in parameters[1:]:
control_coefficients.append(trace[item])
control_values = np.dot(controls, control_coefficients)
# Calculate the predicted mean.
mu_predicted = trace[intercept] + x_value + control_values
mu_hpd = pm.hpd(mu_predicted.T, alpha=hpdi)
plt.plot(x_space, mu_predicted.mean(1), 'k')
plt.plot(x_space, mu_hpd[:, 0], 'k--')
plt.plot(x_space, mu_hpd[:, 1], 'k--')
plt.xlabel(xlab)
plt.ylabel(ylab)
def plot_model_fits2(self,
y_obs,
y_pred=None,
title=None,
ax=None,
ci=0.95):
if y_pred is None:
y_pred = self.trace_.get_values('mu')
y_obs = y_obs.values
mask = np.logical_not(np.isnan(y_obs))
y_obs = y_obs[mask]
y_pred_mean = np.mean(y_pred, axis=0)[mask]
y_pred_hpd = pm.hpd(y_pred, alpha=1 - ci)[mask]
xi = np.arange(y_obs.size)
iy = np.argsort(y_obs)
if ax is None:
_, ax = pl.subplots(figsize=(12, 8), )
ax.set_title(title)
ax.plot(xi,
y_obs[iy],
marker='.',
ls='',
markeredgecolor='darkblue',
markersize=13,
label='observed')
ax.plot(xi,
y_pred_mean[iy],
marker='o',
color='indigo',
ls='',
markeredgecolor='k',
alpha=0.5,
label='predicted avg.')
ax.fill_between(xi,
y_pred_hpd[iy, 0],
y_pred_hpd[iy, 1],
color='k',
alpha=0.5,
label=f'{ci*100}%CI on pred.')
ax.legend(loc='best')
return ax
def _summarize_one_variable(ppc_samples, variable):
"""
Provide mean and hpd summaries of given variable.
:param ppc_samples: pymc3 ppc samples
:param variable: key of dict ppc_samples
:return: DataFrame, (variable_mean, variable_hpd_lower, variable_hpd_upper), n rows = n columns in ppcs_samples[variable]
which should correspond to number of input data points
"""
# row = sample, column = original data point
sample_array = ppc_samples[variable]
hpds = pm.hpd(sample_array, alpha=.3)
d = dict()
# collect all samples into one field per input row
# more elegant way?
d[f'{variable}_samples'] = list(sample_array.T)
d[f'{variable}_hpd_lower'] = hpds[:, 0]
d[f'{variable}_hpd_upper'] = hpds[:, 1]
d[f'{variable}_mean'] = np.mean(sample_array, axis=0)
return (pd.DataFrame(d))
def hdi(self, var_name: str, credible_mass: float = 0.95):
"""Calculate the highest posterior density interval (HDI)
This function calculates a *credible interval* which contains the
``credible_mass`` most likely values of the parameter, given the data.
Also known as an HPD interval.
Parameters
----------
var_name : str
Name of variable.
credible_mass : float
The HDI will cover credible_mass * 100% of the probability mass.
Default: 0.95, i.e. a 95% HDI.
Returns
-------
(float, float)
The endpoints of the HPD
"""
check_credible_mass(credible_mass)
return tuple(pm.hpd(self.trace[var_name], alpha=(1 - credible_mass)))
def plot_regression_line(x, y, mu, hdpi=0.1, xlab='', ylab=''):
'''
x: The predictor variable
y: The response variable
mu: The mu value from the PyMC3 model trace. (eg., trace['mu'])
hdpi: The alpha value for the HDPI. 0.1 corresponds to the 90% interval
Plots a scatter plot of the data and then the regression line with the HDPI interval shaded.
'''
mu_hpd = pm.hpd(mu, alpha=hdpi)
plt.scatter(x, y, alpha=0.5)
plt.plot(x, mu.mean(0), 'C2') # MAP line (column-wise mean of mu)
# HPDI fill-in
index = np.argsort(x)
plt.fill_between(x[index],
mu_hpd[:, 0][index],
mu_hpd[:, 1][index],
color='C2',
alpha=0.25)
plt.xlabel(str(xlab))
plt.ylabel(str(ylab))
def stats(self) -> pd.DataFrame:
"""Stats task result."""
import pymc3 as pm
idxes = [col for col in self.trace.columns if not col.startswith('RAW')]
means = []
sds = []
hpd_2_5s = []
hpd_97_5s = []
cols = ['mean', 'sd', 'hpd_2.5', 'hpd_97.5']
data = [means, sds, hpd_2_5s, hpd_97_5s]
for var_name in idxes:
d_i = self.trace[var_name]
means.append(np.mean(d_i))
sds.append(np.std(d_i))
hpd_2_5, hpd_97_5 = pm.hpd(d_i)
hpd_2_5s.append(hpd_2_5)
hpd_97_5s.append(hpd_97_5)
df = pd.DataFrame({col: data[i] for i, col in enumerate(cols)}, index=idxes, columns=cols)
return df
# out_pai = pm.Deterministic('out_pai', mu + beta * dag_time + gamma1 * z1 + gamma2 * z2 + gamma3 * z3 + gamma4 * z4)
Observed = pm.Binomial("Observed", dag_sum, out_pai,
observed=dag_fault) # 观测值
# start = pm.find_MAP()
step = pm.Metropolis()
trace = pm.sample(10000, step=step)
chain = trace
# logistic(chain, locals())
varnames = ['gamma1', 'mu', 'beta', 'out_pai']
varnames1 = ['out_pai']
pm.traceplot(chain, varnames)
plt.show()
sig0 = pm.hpd(trace['out_pai'], alpha=0.6)[0]
sig = pm.hpd(trace['out_pai'], alpha=0.6)[1]
sig1 = pm.hpd(trace['out_pai'], alpha=0.6)[2]
sig2 = pm.hpd(trace['out_pai'], alpha=0.6)[3]
sig3 = pm.hpd(trace['out_pai'], alpha=0.6)[4]
sig4 = pm.hpd(trace['out_pai'], alpha=0.6)[5]
plt.figure()
ax = sns.distplot(sig0)
ax = sns.distplot(sig1)
ax = sns.distplot(sig2)
ax = sns.distplot(sig3)
ax = sns.distplot(sig4)
ax = sns.distplot(sig)
plt.show()
# Make a summary dataframe
# Because this is pretty gaussian, median is pretty much the same
# as the mean, although we might as well compute it since we have the distribution
# one standard deviation covers 68% of the distribution, might be better to
# keep 95% HPD
# get strain names first
strains = [*df_mcmc.columns]
# dataframe to store summary statistics
df_summary = pd.DataFrame(index=['median', '_hpd', 'hpd_', 'mean','std'],
columns=strains)
for strain in strains:
# median
df_summary.loc['median', strain] = np.median(df_mcmc[strain])
# 95% highest posterior density
df_summary.loc[['_hpd', 'hpd_'], strain] = pm.hpd(df_mcmc[strain], alpha=0.05)
# mean
df_summary.loc['mean', strain] = np.mean(df_mcmc[strain])
# standard deviation
df_summary.loc['std', strain] = np.std(df_mcmc[strain])
# plot sample histograms
for strain in strains:
plt.hist(df_mcmc[strain], bins=100, normed=True, histtype='step', linewidth=2)
plt.xlabel('prob. of dauer, $p$')
plt.ylabel(r'$P(p\mid d, n)$')
plt.legend(strains, loc='upper center');
sns.despine()
plt.tight_layout()
#plt.savefig('./output/probdistrib_dauer.pdf', transparent=True, bbox_inches='tight')
plt.close('all')
trace_0 = pm.sample(5000)
chain_0 = trace_0[1000:]
varnames = ['alpha', 'beta', 'bd']
pm.traceplot(chain_0, varnames)
plt.savefig('img505.png', dpi=300, figsize=(5.5, 5.5))
plt.figure()
pm.summary(chain_0, varnames)
theta = chain_0['theta'].mean(axis=0)
idx = np.argsort(x_0)
plt.plot(x_0[idx], theta[idx], color='b', lw=3)
plt.axvline(chain_0['bd'].mean(), ymax=1, color='r')
bd_hpd = pm.hpd(chain_0['bd'])
plt.fill_betweenx([0, 1], bd_hpd[0], bd_hpd[1], color='r', alpha=0.5)
plt.plot(x_0, y_0, 'o', color='k')
theta_hpd = pm.hpd(chain_0['theta'])[idx]
plt.fill_between(x_0[idx],
theta_hpd[:, 0],
theta_hpd[:, 1],
color='b',
alpha=0.5)
plt.xlabel(x_n, fontsize=16)
plt.ylabel(r'$\theta$', rotation=0, fontsize=16)
plt.savefig('img506.png', dpi=300, figsize=(5.5, 5.5))
plt.figure()
plt.savefig('img408.png')
plt.clf()
plt.plot(x, alpha_m + beta_m * x, c='k', label='y ={:.2f} + {:.2f} * x'.format(alpha_m, beta_m))
idx = np.argsort(x)
x_ord = x[idx]
sig = pm.hpd(trace_n['mu'], alpha=0.02)[idx]
plt.fill_between(x_ord, sig[:, 0], sig[:, 1], color='gray')
plt.xlabel('$x$', fontsize=16)
plt.ylabel('$y$', fontsize=16, rotation=0)
plt.savefig('img409.png')
"""
ppc = pm.sample_ppc(trace_n, samples=100000, model=model)
idx = np.argsort(x)
x_ord = x[idx]
#plt.plot(x, y, 'b.')
plt.plot(x,
alpha_m + beta_m * x,
c='k',
label='y = {:.2f} + {:.2f} * x'.format(alpha_m, beta_m))
sig0 = pm.hpd(ppc['y_pred'], alpha=0.5)[idx]
sig1 = pm.hpd(ppc['y_pred'], alpha=0.05)[idx]
plt.fill_between(x_ord, sig0[:, 0], sig0[:, 1], color='gray', alpha=1)
plt.fill_between(x_ord, sig1[:, 0], sig1[:, 1], color='gray', alpha=0.5)
plt.xlabel('$x$', fontsize=16)
plt.ylabel('$y$', fontsize=16, rotation=0)
plt.savefig('img410.png')
def hpd_range(x):
hpd = pm.hpd(x)
return hpd[1] - hpd[0]
num_already_found = np.mean(
[num_true_hits - i.shape[0] for i in normalized_ranks_holder[idx]])
num_remaining = n_hits_pulled - num_already_found
num_needed = desired_num_hits - num_already_found
fraction_required = num_needed / num_remaining
#expected performance on undocked ligands:
trace = estimate_holder[idx][0]
mu = trace['mu']
nu = trace['nu']
sig = trace['sig']
samples = t(nu, mu, sig).ppf(fraction_required)
#this is the fraction of remaining ligands we need to dock to reach the goal.
hpd = expit(pm.hpd(samples))
time_hpd = hpd * (n_ligands_to_pull - size) + size
time_days = time_hpd / 60 / 60 / 24
time_mean = expit(samples.mean()) * (n_ligands_to_pull - size) + size
time_mean = time_mean / 60 / 60 / 24
print(time_mean)
df.loc[count] = [
time_mean, time_hpd[0], time_hpd[1], size, desired_num_hits
]
count += 1
import altair as alt
#now plot :)
yl = pm.Bernoulli('yl', p=theta, observed=y_0)
trace_0 = pm.sample(5000)
chain_0 = trace_0[1000:]
varnames = ['alpha', 'beta', 'bd']
pm.traceplot(chain_0, varnames)
plt.savefig('img505b.png')
pm.summary(trace_0, varnames)
#print(chain_0['theta'])
plt.figure()
theta = chain_0['theta'].mean(axis=0)
idx = np.argsort(x_0)
plt.plot(x_0[idx], theta[idx], color='b', lw=3)
plt.axvline(chain_0['bd'].mean(), ymax=1, color='r')
bd_hpd = pm.hpd(chain_0['bd'])
plt.fill_betweenx([0, 1], bd_hpd[0], bd_hpd[1], color='r', alpha=0.5)
plt.plot(x_0, y_0, 'o', color='k')
theta_hpd = pm.hpd(chain_0['theta'])[idx]
plt.fill_between(x_0[idx],
theta_hpd[:, 0],
theta_hpd[:, 1],
color='b',
alpha=0.5)
plt.xlabel(x_n, fontsize=16)
plt.ylabel(r'$\theta$', rotation=0, fontsize=16)
plt.savefig('img506b.png')
alpha = pm.Normal(name='alpha', mu=mean_data, sd=std_data)
beta = pm.Normal(name='beta', mu=0, sd=10, shape=4)
sigma = pm.Uniform(name='sigma', lower=0, upper=std_data)
mu = pm.Deterministic('mu', alpha + beta[0] * data_s + beta[1] * data_s2 + beta[2] * data_s3 + beta[3] * data_s4)
ret = pm.Normal(name='returns', mu=mu, sd=sigma, observed=ror)
trace_model = pm.sample(1000, tune=2000)
print(pm.summary(trace_model, ['alpha', 'beta', 'sigma']))
pm.traceplot(trace_model, varnames=['alpha', 'beta', 'sigma'])
plt.title('model parameters')
plt.show()
mu_pred = trace_model['mu']
idx = np.argsort(data_s)
mu_hpd = pm.hpd(mu_pred, alpha=0.11)[idx]
ret_pred = pm.sample_ppc(trace_model, 10000, model)
ret_pred_hpd = pm.hpd(ret_pred['returns'], alpha=0.11)[idx]
for r in ror:
plt.plot(r)
plt.plot(ret_pred_hpd)
plt.show()
for r in ror:
# plt.scatter(data_s, r, c='C0', alpha=0.3)
plt.plot(data_s[idx], r, c='C0', alpha=0.3)
plt.fill_between(data_s[idx], mu_hpd[:, 0], mu_hpd[:, 1], color='C2', alpha=0.25)
plt.fill_between(data_s[idx], ret_pred_hpd[:, 0], ret_pred_hpd[:, 1], color='C2', alpha=0.25)
plt.show()
f.close()
# Save the trace to the output folder as a numpy array, for later reference
# Save every 10th sample from the trace, to avoid any autocorrelation issues
np.save("palatability_regression_trace.npy", tr[::10]["coeff_pal"])
# Convert the trace to a dataframe, and save that too
# Save every 10th sample from the trace, to avoid any autocorrelation issues
tr_df = pm.trace_to_dataframe(tr[::10])
tr_df.to_csv("palatability_regression_trace.csv")
# Plot the results of the palatability regression analysis
# First just plot the mean regression coefficients for every laser condition, across time
fig = plt.figure()
mean_coeff = np.mean(tr[::10]["coeff_pal"], axis = 0)
hpd_coeff = pm.hpd(tr[::10]["coeff_pal"], alpha = 0.05)
for condition in range(unique_lasers[0].shape[0]):
plt.plot(x[analyze_indices], mean_coeff[:, condition], linewidth = 3.0, label = "Dur:{}ms, Lag:{}ms".format(unique_lasers[0][condition][0], unique_lasers[0][condition][1]))
plt.legend()
plt.xlabel("Time post taste delivery (ms)")
plt.ylabel("Mean posterior regression coefficient")
fig.savefig("palatability_regression_coefficients_mean.png", bbox_inches = "tight")
plt.close("all")
# Now plot the mean and SD of the regression coefficients for every laser condition, across time
fig = plt.figure()
for condition in range(unique_lasers[0].shape[0]):
plt.plot(x[analyze_indices], np.mean(tr[::10]["coeff_pal"], axis = 0)[:, condition], linewidth = 3.0, label = "Dur:{}ms, Lag:{}ms".format(unique_lasers[0][condition][0], unique_lasers[0][condition][1]))
plt.fill_between(x[analyze_indices], hpd_coeff[:, condition, 0], hpd_coeff[:, condition, 1], alpha = 0.5)
plt.legend()
plt.xlabel("Time post taste delivery (ms)")
plt.ylabel("Mean posterior regression coefficient")
from sklearn.model_selection import train_test_split
import os
import pandas as pd
data_file = 'btc.data.csv'
if not os.path.isfile(data_file):
data = data_reader.get_data_yahoo('BTC-USD')
data.to_csv(data_file)
data = pd.read_csv(data_file)
print(data.Open.head())
print(data.Open.tail())
print(data.Open.iloc[-1])
hpd = pm.hpd(data.Open, alpha=0.05)
print('[%f %f]' % (hpd[0], hpd[1]))
# _, (ax0, ax1) = plt.subplots(2, 1)
# sns.kdeplot(data.Open, ax=ax0)
# ax1.plot(data.Open)
# plt.show()
data = data.as_matrix(columns=['Open'])
print(data.shape)
standard_scaler = StandardScaler()
standard_scaler.fit(data)
d = standard_scaler.transform(data)
# d = standard_scaler.inverse_transform(d)
f.close()
# Save the trace to the output folder as a numpy array, for later reference
# Save every 10th sample from the trace, to avoid any autocorrelation issues
np.save("palatability_regression_trace.npy", tr[::10]["coeff_pal"])
# Convert the trace to a dataframe, and save that too
# Save every 10th sample from the trace, to avoid any autocorrelation issues
tr_df = pm.trace_to_dataframe(tr[::10])
tr_df.to_csv("palatability_regression_trace.csv")
# Plot the results of the palatability regression analysis
# First just plot the mean regression coefficients for every laser condition, across time
fig = plt.figure()
mean_coeff = np.mean(tr[::10]["coeff_pal"], axis=0)
hpd_coeff = pm.hpd(tr[::10]["coeff_pal"], alpha=0.05)
for condition in range(unique_lasers[0].shape[0]):
plt.plot(x[analyze_indices],
mean_coeff[:, condition],
linewidth=3.0,
label="Dur:{}ms, Lag:{}ms".format(unique_lasers[0][condition][0],
unique_lasers[0][condition][1]))
plt.legend()
plt.xlabel("Time post taste delivery (ms)")
plt.ylabel("Mean posterior regression coefficient")
fig.savefig("palatability_regression_coefficients_mean.png",
bbox_inches="tight")
plt.close("all")
# Now plot the mean and SD of the regression coefficients for every laser condition, across time
fig = plt.figure()
for condition in range(unique_lasers[0].shape[0]):
start = pm.find_MAP()
step = pm.NUTS(scaling=start)
trace_1 = pm.sample(5000, step=step, start=start)
chain_1 = trace_1[100:]
varnames = ['alpha', 'beta']
pm.traceplot(chain_1)
plt.show()
idx = np.argsort(x_1[:, 0])
bd = chain_1['bd'].mean(0)[idx]
plt.scatter(x_1[:, 0], x_1[:, 1], c=y_1)
plt.plot(x_1[:, 0][idx], bd, color='r')
bd_hpd = pm.hpd(chain_1['bd'])[idx]
plt.fill_between(x_1[:, 0][idx],
bd_hpd[:, 0],
bd_hpd[:, 1],
color='r',
alpha=0.5)
plt.xlabel(x_n[0], fontsize=16)
plt.ylabel(x_n[1], fontsize=16)
plt.show()
corr = iris[iris['species'] != 'virginica'].corr()
mask = np.tri(*corr.shape).T
sns.heatmap(corr.abs(), mask=mask, annot=True)
plt.show()
ax2.set_xlabel('Observed probabilities')
ax2.set_ylabel('Predicted probabilities')
ax2.grid(b=True, which='minor', color='w', linewidth=1.0)
# clean up and save
plt.tight_layout(pad=0.5, w_pad=0.2, h_pad=0.7)
plt.savefig('../figures/lex_dec_model_pyactr_no_imaginal.eps')
plt.savefig('../figures/lex_dec_model_pyactr_no_imaginal.png')
plt.savefig('../figures/lex_dec_model_pyactr_no_imaginal.pdf')
#plt.show()
generate_lex_dec_pyactr_no_imaginal_figure()
decay_posterior = trace["decay"]
decay_posterior.mean()
pm.hpd(decay_posterior)
threshold_posterior = trace["threshold"]
threshold_posterior.mean()
pm.hpd(threshold_posterior)
noise_posterior = trace["noise"]
noise_posterior.mean()
pm.hpd(noise_posterior)
latency_factor_posterior = trace["lf"]
latency_factor_posterior.mean()
pm.hpd(latency_factor_posterior)
latency_exponent_posterior = trace["le"]
latency_exponent_posterior.mean()
# Save these findings in a table specific to this unit
unit_table = hf5.create_table('/laser_effects_bayesian/unit_summaries', 'unit{:d}'.format(chosen_units[unit]), description = laser_effects)
# Now run through the tastes and laser conditions
for laser in range(diff.shape[0]):
for taste in range(diff.shape[1]):
# Get a new row for this taste and laser condition
this_condition_results = unit_table.row
# Fill in the taste and laser conditions
this_condition_results['laser'] = laser + 1
this_condition_results['taste'] = taste + 1
# First check if the control firing was close to zero for this taste/laser combo (comparing it to a sufficiently small number because the control firing rate is always > 0 by definition)
if pm.hpd(bayesian_results[laser, taste, :, 0], alpha = sig_level)[0] <= 1e-4:
this_condition_results['control_zero'] = 1.0
else:
this_condition_results['control_zero'] = 0.0
# Then check if the laser condition has no effect on firing (the diff HPD will overlap zero)
diff_hpd = pm.hpd(diff[laser, taste, :], alpha = sig_level)
if diff_hpd[0] * diff_hpd[1] < 0:
this_condition_results['unchanged'] = 1.0
this_condition_results['enhanced'] = 0.0
this_condition_results['suppressed'] = 0.0
# Firing is enhanced if the diff (control-laser) lies consistently below zero
elif diff_hpd[0] < 0 and diff_hpd[1] < 0:
this_condition_results['unchanged'] = 0.0
this_condition_results['enhanced'] = 1.0
this_condition_results['suppressed'] = 0.0
org_beta111 = post_beta111 * faults_sd / year_std
org_beta00 = post_beta00 * faults_sd + faults_m - (
post_beta111 * faults_sd * year_m / year_std) - (post_beta2 * faults_sd *
tem_m / tem_std)
#
beta_plot = chain2['beta'][:, 0]
beta1_plot = chain2['beta1'][:, 0]
beta2_plot = chain2['beta2']
# # 后验
plt.figure(figsize=(10, 10))
idx = np.argsort(elec_year)
x_ord = elec_year[idx]
ppc = pm.sample_ppc(chain2, samples=500, model=unpooled_model)
sig_y = pm.hpd(ppc['Observed'][0:42], alpha=0.05)[idx]
sig_y1 = pm.hpd(ppc['Observed'][42:91], alpha=0.05)[idx]
# plt.fill_between(x_ord, sig_y[:, 0], sig_y[:, 1], color='gray', alpha=0.4)
# plt.fill_between(x_ord, sig_y1[:, 0], sig_y1[:, 1], color='red', alpha=0.3)
#
# # sig_y0 = pm.hpd(ppc['Observed'][1], alpha=0.5)[idx]
# # sig_y11 = pm.hpd(ppc['Observed'][1], alpha=0.05)[idx]
# # plt.fill_between(x_ord, sig_y[:, 0], sig_y[:, 1], color='gray', alpha=1)
# # plt.fill_between(x_ord, sig_y1[:, 0], sig_y1[:, 1], color='gray', alpha=0.5)
# idd = range(0, len(chain2['beta2']), 100)
plt.figure(figsize=(5, 3), facecolor=(1, 1, 1))
ax = plt.subplot(1, 1, 1)
# j, k1 = 0, 6
# for jx in range(7):
# k1 = 6
def process_one_etf(top, result_df):
print(top)
bah_investor = compute_bah([top],period,cash_sum)
print('invested:' + str(bah_investor.invested_history[-1]))
print('value gained:' + str(bah_investor.history[-1]))
print('returns:' + str(bah_investor.ror_history[-1]))
investors = []
while len(investors) < MAX_RUNS:
investor = run_bah_sim([top],period,cash_sum)
if len(investor.ror_history) == 0:
continue
investors.append(investor)
print('%d:%f:%f:%f' % (len(investors), investor.invested, investor.history[-1], investor.ror_history[-1]))
returns_bah = [investor.ror_history[-1] for investor in investors]
returns_bah = np.array(returns_bah)
# returns_bah = np.sort(returns_bah)
print('original:%f' % bah_investor.ror_history[-1])
print('observed:%f +/- %f' % (np.mean(returns_bah), np.std(returns_bah)))
with pm.Model() as model:
mu = pm.Normal('mu', mu=np.mean(returns_bah), sd=np.std(returns_bah))
sigma = pm.Uniform('sigma', lower=0., upper=np.std(returns_bah))
mean_returns = pm.Normal('mean_returns', mu=mu, sd=sigma, observed=np.array(returns_bah))
trace_model = pm.sample(1000, tune=2000)
samples_bah = pm.sample_ppc(trace_model, size=10000, model=model)
hpd89_bah = pm.hpd(samples_bah['mean_returns'], alpha=0.11)
print('mean 89 percentile:' + str(np.mean(hpd89_bah)))
investors = []
while len(investors) < MAX_RUNS:
investor = compute_one_etf([top],period,cash_sum)
if investor.cash == investor.invested:
continue
if len(investor.ror_history) == 0:
continue
investors.append(investor)
print('%d:%f:%f:%f' % (len(investors), investor.invested, investor.history[-1], investor.ror_history[-1]))
returns_chaos = [investor.ror_history[-1] for investor in investors]
returns_chaos = np.array(returns_chaos)
# returns_chaos = np.sort(returns_chaos)
print('original:%f' % (bah_investor.ror_history[-1]))
print('observed:%f +/- %f' % (np.mean(returns_chaos), np.std(returns_chaos)))
with pm.Model() as model:
mu = pm.Normal('mu', mu=np.mean(returns_chaos), sd=np.std(returns_chaos))
sigma = pm.Uniform('sigma', lower=0., upper=np.std(returns_chaos))
mean_returns = pm.Normal('mean_returns', mu=mu, sd=sigma, observed=np.array(returns_chaos))
trace_model = pm.sample(1000, tune=2000)
samples_chaos = pm.sample_ppc(trace_model, size=10000, model=model)
hpd89_chaos = pm.hpd(samples_chaos['mean_returns'], alpha=0.11)
print('mean 89 percentile:' + str(np.mean(hpd89_chaos)))
validity_chaos = np.count_nonzero(np.abs(returns_chaos - bah_investor.ror_history[-1]) < 0.05) / len(
returns_chaos) * 100.
validity_bah = np.count_nonzero(np.abs(returns_bah - bah_investor.ror_history[-1]) < 0.05) / len(returns_bah) * 100.
result_df = result_df.append({
'ticket': top,
'original_returns': bah_investor.ror_history[-1],
'hpd89_bah': np.mean(hpd89_bah),
'hpd89_chaos': np.mean(hpd89_chaos),
'validity_bah': validity_bah,
'validity_chaos': validity_chaos}, ignore_index=True)
report = Report(top,
bah_investor,
returns_bah,
hpd89_bah,
samples_bah['mean_returns'],
returns_chaos,
hpd89_chaos,
samples_chaos['mean_returns'])
report.gen_report()
result_df.to_csv(result_csv, index=False)
return result_df
