def bayesian_random_effects(data, labels, group, n_samples=2000, n_burnin=500):
import pymc as pm
#preparing the data
donors = data[group].unique()
donors_lookup = dict(zip(donors, range(len(donors))))
data['donor_code'] = data[group].replace(donors_lookup).values
n_donors = len(data[group].unique())
donor_idx = data['donor_code'].values
#setting up the model
with pm.Model() as hierarchical_model:
# Hyperpriors for group nodes
group_intercept_mean = pm.Normal('group intercept (mean)', mu=0., sd=100**2)
group_intercept_variance = pm.Uniform('group intercept (variance)', lower=0, upper=100)
group_slope_mean = pm.Normal('group slope (mean)', mu=0., sd=100**2)
group_slope_variance = pm.Uniform('group slope (variance)', lower=0, upper=100)
individual_intercepts = pm.Normal('individual intercepts', mu=group_intercept_mean, sd=group_intercept_variance, shape=n_donors)
individual_slopes = pm.Normal('individual slopes', mu=group_slope_mean, sd=group_slope_variance, shape=n_donors)
# Model error
residuals = pm.Uniform('residuals', lower=0, upper=100)
expression_est = individual_slopes[donor_idx] * data[labels[0]].values + individual_intercepts[donor_idx]
# Data likelihood
expression_like = pm.Normal('expression_like', mu=expression_est, sd=residuals, observed=data[labels[1]])
start = pm.find_MAP()
step = pm.NUTS(scaling=start)
hierarchical_trace = pm.sample(n_samples, step, start=start, progressbar=True)
mean_slope = hierarchical_trace['group slope (mean)'][n_burnin:].mean()
zero_percentile = percentileofscore(hierarchical_trace['group slope (mean)'][n_burnin:], 0)
print "Mean group level slope was %g (zero was %g percentile of the posterior distribution)"%(mean_slope, zero_percentile)
pm.summary(hierarchical_trace[n_burnin:], vars=['group slope (mean)'])
pm.traceplot(hierarchical_trace[n_burnin:])
selection = donors
fig, axis = plt.subplots(2, 3, figsize=(12, 6), sharey=True, sharex=True)
axis = axis.ravel()
xvals = np.linspace(data[labels[0]].min(), data[labels[0]].max())
for i, c in enumerate(selection):
c_data = data.ix[data[group] == c]
c_data = c_data.reset_index(drop = True)
z = list(c_data['donor_code'])[0]
for a_val, b_val in zip(hierarchical_trace['individual intercepts'][n_burnin::10][z], hierarchical_trace['individual slopes'][n_burnin::10][z]):
axis[i].plot(xvals, a_val + b_val * xvals, 'g', alpha=.1)
axis[i].plot(xvals, hierarchical_trace['individual intercepts'][n_burnin:][z].mean() + hierarchical_trace['individual slopes'][n_burnin:][z].mean() * xvals,
'g', alpha=1, lw=2.)
axis[i].hexbin(c_data[labels[0]], c_data[labels[1]], mincnt=1, cmap=plt.cm.YlOrRd_r)
axis[i].set_title(c)
axis[i].set_xlabel(labels[0])
axis[i].set_ylabel(labels[1])
plt.show()
return mean_slope, zero_percentile
def run_banova():
y = 10+hstack((np.random.randn(100),np.random.randn(100)+1,
np.random.randn(100)+2))
y = y-y.mean()
y = y/y.std()
x = concatenate(([1.0]*100,[0.0]*200))
X = vstack((x, np.roll(x,100), np.roll(x,200)))
m = oneway_banova(y.astype(float),X.astype(float))
start = {'offset': 0.0,
'alphas': array([0,1,2.])}
with m:
step = pm.Metropolis()
#step = pm.NUTS()
trace = pm.sample(150000, step, start, tune=1500, njobs=1, progressbar=True)
pm.traceplot(trace[::2])
show()
def bayesian_regression():
import warnings
warnings.simplefilter("ignore")
import pymc as pm
import numpy as np
np.random.seed(1000)
import matplotlib.pyplot as plt
%matplotlib inline
#PYMC3
x = np.linspace(0, 10, 500)
y = 4 + 2 * x + np.random.standard_normal(len(x)) * 2
reg = np.polyfit(x, y, 1)
plt.figure(figsize=(8, 4))
plt.scatter(x, y, c=y, marker="v")
plt.plot(x, reg[1] + reg[0] * x, lw=2.0)
plt.colorbar()
plt.grid(True)
plt.xlabel("x")
plt.ylabel("y")
reg
with pm.Model() as model:
# model specifications in PyMC3
# are wrapped in a with statement
# define priors
alpha = pm.Normal("alpha", mu=0, sd=20)
beta = pm.Normal("beta", mu=0, sd=20)
sigma = pm.Uniform("sigma", lower=0, upper=10)
# define linear regression
y_est = alpha + beta * x
# define likelihood
likelihood = pm.Normal("y", mu=y_est, sd=sigma, observed=y)
# inference
start = pm.find_MAP()
# find starting value by optimization
step = pm.NUTS(state=start)
# instantiate MCMC sampling algorithm
trace = pm.sample(100, step, start=start, progressbar=False)
# draw 100 posterior samples using NUTS sampling
trace[0]
fig = pm.traceplot(trace, lines={"alpha": 4, "beta": 2, "sigma": 2})
plt.figure(figsize=(8, 8))
plt.figure(figsize=(8, 4))
plt.scatter(x, y, c=y, marker="v")
plt.colorbar()
plt.grid(True)
plt.xlabel("x")
plt.ylabel("y")
for i in range(len(trace)):
plt.plot(x, trace["alpha"][i] + trace["beta"][i] * x)
pass
def foo(self, discrete):
student_ids = []
timestep_ids = []
y = []
ids = collections.defaultdict(itertools.count().next)
for t in range(0, len(self)):
student_ids += [ids[o.id] for o in self[t]]
timestep_ids += [t for o in self[t]]
y += [o.value for o in self[t]]
n_students = len(set(student_ids))
n_timesteps = len(self)
print student_ids, "!", n_students
with pm.Model() as hierarchical_model:
# Hyperpriors for group nodes
mu_student = pm.Normal('mu_student', mu=0., sd=100**2)
sigma_student = pm.Uniform('sigma_student', lower=0, upper=100)
#mu_timestep = pm.Normal('mu_beta', mu=0., sd=100**2)
#sigma_timestep = pm.Uniform('sigma_beta', lower=0, upper=100)
student = pm.Normal('student', mu=mu_student, sd=sigma_student, shape=n_students) #random effect
timestep = pm.Normal('timestep', mu=0, sd=100**2, shape=n_timesteps) #fixed effect
# Model error
eps = pm.Uniform('eps', lower=0, upper=100)
theta = student[student_ids] + timestep[timestep_ids]
# Data likelihood
if discrete:
ll = pm.Bernoulli('theta', p=self.invlogit(theta), observed=y)
else:
ll = pm.Normal('theta', mu=theta, sd=eps, observed=y)
with hierarchical_model:
print "Find MAP..."
start = pm.find_MAP()
#if discrete:
# step = pm.BinaryMetropolis(scaling=start)
# else:
print "NUTS..."
step = pm.NUTS(scaling=start)
print "Samples..."
hierarchical_trace = pm.sample(2000, step, start=start, progressbar=False)
print "done..."
print "Plot..."
pl.figure(figsize=(10,10))
f = pm.traceplot(hierarchical_trace[500:])
f.savefig("a.png")
return hierarchical_trace
def run_best():
a = np.random.randn(10)
b = np.random.randn(10)+2
print 'A:', a.mean(), a.std()
print 'B:', b.mean(), b.std()
x_eval = np.linspace(-10,10,100)
m = best('A', a, 'B', b)
start = {'A Mean': b.mean(),
'A Std': a.std(),
'B Mean': a.mean(),
'B Std': b.std(),
'Nu-1': 100}
with m:
step = pm.Metropolis(blocked=False)
trace = pm.sample(10000, step, start, tune=1000, njobs=3, progressbar=False)
pm.traceplot(trace)
show()
return m, trace
ndims = 2
nobs = 20
xtrue = np.random.normal(scale=2., size=1)
ytrue = np.random.normal(loc=np.exp(xtrue), scale=1, size=(ndims, 1))
zdata = np.random.normal(loc=xtrue + ytrue, scale=.75, size=(ndims, nobs))
with pm.Model() as model:
x = pm.Normal('x', mu=0., sd=1)
y = pm.Normal('y', mu=pm.exp(x), sd=2., shape=(ndims, 1)) # here, shape is telling us it's a vector rather than a scalar.
z = pm.Normal('z', mu=x + y, sd=.75, observed=zdata) # shape is inferred from zdata
with model:
start = pm.find_MAP()
print("MAP found:")
print("x:", start['x'])
print("y:", start['y'])
print("Compare with true values:")
print("ytrue", ytrue)
print("xtrue", xtrue)
with model:
step = pm.NUTS()
with model:
trace = pm.sample(3000, step, start)
pm.traceplot(trace);
xtrue=np.random.normal(scale=2., size=1.)
ytrue = np.random.normal(loc=np.exp(xtrue), scale=1, size=(ndims, 1))
zdata = np.random.normal(loc=xtrue + ytrue, scale=.75, size=(ndims, nobs))
with pm.Model() as model:
x = pm.Normal('x', mu=0., sd=1)
y = pm.Normal('y', mu=pm.exp(x), sd=2., shape=(ndims, 1)) # here, shape is telling us it's a vector rather than a scalar.
z = pm.Normal('z', mu=x + y, sd=.75, observed=zdata) # shape is inferred from zdata
with model:
start = pm.find_MAP()
print("MAP found:")
print("x:", start['x'])
print("y:", start['y'])
print("Compare with true values:")
print("ytrue", ytrue)
print("xtrue", xtrue)
with model:
step = pm.NUTS()
with model:
trace = pm.sample(3000, step, start)
pm.traceplot(trace)
def realdata():
import warnings
warnings.simplefilter("ignore")
import zipline
import pytz
import datetime as dt
data = zipline.data.load_from_yahoo(stocks=["GLD", "GDX"],
end=dt.datetime(2014, 3, 15, 0, 0, 0, 0, pytz.utc)).dropna()
data.info()
data.plot(figsize=(8, 4))
data.ix[-1] / data.ix[0] - 1
data.corr()
data.index
import matplotlib as mpl
mpl_dates = mpl.dates.date2num(data.index)
mpl_dates
plt.figure(figsize=(8, 4))
plt.scatter(data["GDX"], data["GLD"], c=mpl_dates, marker="o")
plt.grid(True)
plt.xlabel("GDX")
plt.ylabel("GLD")
plt.colorbar(ticks=mpl.dates.DayLocator(interval=250),
format=mpl.dates.DateFormatter("%d %b %y"))
with pm.Model() as model:
alpha = pm.Normal("alpha", mu=0, sd=20)
beta = pm.Normal("beta", mu=0, sd=20)
sigma = pm.Uniform("sigma", lower=0, upper=50)
y_est = alpha + beta * data["GDX"].values
likelihood = pm.Normal("GLD", mu=y_est, sd=sigma,
observed=data["GLD"].values)
start = pm.find_MAP()
step = pm.NUTS(state=start)
trace = pm.sample(100, step, start=start, progressbar=False)
fig = pm.traceplot(trace)
plt.figure(figsize=(8, 8))
plt.figure(figsize=(8, 4))
plt.scatter(data["GDX"], data["GLD"], c=mpl_dates, marker="o")
plt.grid(True)
plt.xlabel("GDX")
plt.ylabel("GLD")
for i in range(len(trace)):
plt.plot(data["GDX"], trace["alpha"][i] + trace["beta"][i] * data
["GDX"])
plt.colorbar(ticks=mpl.dates.DayLocator(interval=250),
format=mpl.dates.DateFormatter("%d %b %y"))
model_randomwalk = pm.Model()
with model_randomwalk:
# std of random walk best sampled in log space
sigma_alpha, log_sigma_alpha = \
model_randomwalk.TransformedVar("sigma_alpha",
pm.Exponential.dist(1. / .02, testval=.1),
pm.logtransform)
sigma_beta, log_sigma_beta = \
model_randomwalk.TransformedVar("sigma_beta",
pm.Exponential.dist(1. / .02, testval=.1),
pm.logtransform)
from pymc.distributions.timeseries import GaussianRandomWalk
# to make the model simpler, we will apply the same coefficients
# to 50 data points at a time
subsample_alpha = 50
subsample_beta = 50
with model_randomwalk:
alpha = GaussianRandomWalk("alpha", sigma_alpha**-2,
shape=len(data) / subsample_alpha)
beta = GaussianRandomWalk("beta", sigma_beta**-2,
shape=len(data) / subsample_beta)
# make coefficients have the same length as prices
alpha_r = np.repeat(alpha, subsample_alpha)
beta_r = np.repeat(beta, subsample_beta)
len(data.dropna().GDX.values)
with model_randomwalk:
# define regression
regression = alpha_r + beta_r * data.GDX.values[:1950]
# assume prices are normally distributed
# the mean comes from the regression
sd = pm.Uniform("sd", 0, 20)
likelihood = pm.Normal("GLD",
mu=regression,
sd=sd,
observed=data.GLD.values[:1950])
import scipy.optimize as sco
with model_randomwalk:
# first optimize random walk
start = pm.find_MAP(vars=[alpha, beta], fmin=sco.fmin_l_bfgs_b)
# sampling
step = pm.NUTS(scaling=start)
trace_rw = pm.sample(100, step, start=start, progressbar=False)
np.shape(trace_rw["alpha"])
part_dates = np.linspace(min(mpl_dates), max(mpl_dates), 39)
fig, ax1 = plt.subplots(figsize=(10, 5))
plt.plot(part_dates, np.mean(trace_rw["alpha"], axis=0), "b", lw=2.5, label="alpha")
for i in range(45, 55):
plt.plot(part_dates, trace_rw["alpha"][i], "b-.", lw=0.75)
plt.xlabel("date")
plt.ylabel("alpha")
plt.axis("tight")
plt.grid(True)
plt.legend(loc=2)
ax1.xaxis.set_major_formatter(mpl.dates.DateFormatter("%d %b %y") )
ax2 = ax1.twinx()
plt.plot(part_dates, np.mean(trace_rw["beta"], axis=0), "r", lw=2.5, label="beta")
for i in range(45, 55):
plt.plot(part_dates, trace_rw["beta"][i], "r-.", lw=0.75)
plt.ylabel("beta")
plt.legend(loc=4)
fig.autofmt_xdate()
plt.figure(figsize=(10, 5))
plt.scatter(data["GDX"], data["GLD"], c=mpl_dates, marker="o")
plt.colorbar(ticks=mpl.dates.DayLocator(interval=250),
format=mpl.dates.DateFormatter("%d %b %y"))
plt.grid(True)
plt.xlabel("GDX")
plt.ylabel("GLD")
x = np.linspace(min(data["GDX"]), max(data["GDX"]))
for i in range(39):
alpha_rw = np.mean(trace_rw["alpha"].T[i])
beta_rw = np.mean(trace_rw["beta"].T[i])
plt.plot(x, alpha_rw + beta_rw * x, color=plt.cm.jet(256 * i / 39))
pass
def run_appc_rt_model():
'''
Run appc model and load data for it...
'''
return sample_model_appc(get_appc_rt_model(), 500000, observed=['Data_context', 'Data_nocontext', ])
def get_multi_trace(model, data, chains=1):
sd, traces = [], []
if chains == 1:
sd += [dict((k, data[k][:]) for k in data.keys())]
for chain in range(chains):
sd += [dict((k, data[k]['chain%i' % chain][:]) for k in data.keys())]
for i, s in enumerate(sd):
t = pm.backends.NDArray('', model)
t.samples = s
t.chain = i+1
traces += [t]
return pm.backends.base.MultiTrace(traces)
if __name__ == '__main__':
import sys
filename = sys.argv[1]
# t = run_test_case() #run_fixdur()
t = run_appc_subject_model()
save(t, filename)
pm.traceplot(t, vars=[v for v in t.varnames if not v.startswith('DNP')])
plt.show()
discriminability = Normal('Discriminability', mu=md, tau=taud, shape=num_observers)
bias = Normal('Bias', mu=mc, tau=tauc, shape=num_observers)
hi = phi( 0.5*(discriminability-bias))
fi = phi(-0.5*(discriminability-bias))
counts_signal = Binomial('Signal trials', num_trials, hi, observed=signal_responses)
counts_noise = Binomial('Noise trials', num_trials, fi, observed=noise_responses)
return model
def run_sig():
signal_responses = binom.rvs(100, 0.69, size=1)
noise_responses = binom.rvs(100, 0.30, size=1)
m = sig_detect(signal_responses, noise_responses, 1, 100)
with m:
#step = pm.Metropolis(blocked=False)
step = pm.HamiltonianMC()
start = pm.find_MAP()
#start = {'Pr. mean discrim.':0.0, 'Pr. mean bias':0.0,
# 'taud':0.001, 'tauc':0.001}
trace = pm.sample(5000, step, start, tune=500, njobs=2)
return trace[1000:]
if __name__ == '__main__':
t = run_fixdur()
save(t, 'fixdur_trace.hdf5')
pm.traceplot(t)
show()
# Entire Set # <markdowncell> # **(Run as individual)** # <codecell> ## run sampling traces_ind_all = OrderedDict() traces_ind_all['all'] = get_traces_individual(df[xy['x']], df[xy['y']], max_iter=10000) # <codecell> ## view parameters p = pm.traceplot(traces_ind_all['all'],figsize=(18,1.5*3)) plt.show(p) # <markdowncell> # ### Plot regression # <codecell> plot_reg_bayes(df,xy,traces_ind_all,None,burn_ind=2000) # <markdowncell> # **Try Quadratic** # <codecell>
# The trace object can be indexed by the variables in the model, returning an array with the first index being the sample index # and the other indexes the shape of the parameter. Thus for this example: # In[8]: trace[y].shape # Out[8]: # (3000, 2, 1) # `traceplot` is a summary plotting function for a trace. # In[9]: pm.traceplot(trace) # Out[9]: # image file: # ## PyMC Internals # # ### Model # # The `Model` class has very simple internals: just a list of unobserved variables (`Model.vars`) and a list of factors which go into computing the posterior density (`Model.factors`) (see model.py for more). # # A Python "`with model:`" block has `model` as the current model. Many functions, like `find_MAP` and `sample`, must be in such a block to work correctly by default. They look in the current context for a model to use. You may also explicitly specify the model for them to use. This allows us to treat the current model as an implicit parameter to these functions. # # ### Distribution Classes #
### Now we calculate the expected flux from SED Model
y_hat = FluxFromTheory(lTs,lMs,ldMenvbyMs,lRenv,ThetaCav,lMdbyMs,lRdo,lRdi,Zdisc,Bdisc,lalphad,lroCav,lroAmp,Inc,Av)/distance**2
#Data likelihood
y_like = pm.Normal('y_like',mu= y_hat, sd=ObservedDataSigma, observed=ObservedData)
# y_like = pm.T('y_like',mu= y_hat, nu=T_nu, lam=T_lam, observed=ObservedData) # T distribution for robustness
# Inference...
# start = pm.find_MAP() # Find starting value by optimization
start = {'lTs':0.5,'lMs':0.5,'ldMenvbyMs':0.8,'lRenv':0.5,'ThetaCav':0.5,'lMdbyMs':0.8,'lRdo':0.5,'lRdi':0.5,'Zdisc':0.5,'Bdisc':0.5,'lalphad':0.5,'lroCav':0.5,'lroAmp':0.5,'Inc':1,'Av':2.5,'distance':0.9}
# step = pm.NUTS(state=start) # Instantiate MCMC sampling algorithm
step = pm.Metropolis([lTs,lMs,ldMenvbyMs,lRenv,ThetaCav,lMdbyMs,lRdo,lRdi,Zdisc,Bdisc,lalphad,lroCav,lroAmp,Inc,Av,distance])
# step1 = pm.Slice([x,w,z])
# step2 = pm.Metropolis([z])
trace = pm.sample(1000, step, start=start, progressbar=True) # draw 1000 posterior samples using Sampling
# trace = pm.sample(10000, [step1,step2], start=start, progressbar=True) # draw 1000 posterior samples using Sampling
print('The trace plot')
fig = pm.traceplot(trace, model.vars[:-1]);
fig.show()
raw_input('enter to close..')
# fig = pm.traceplot(trace, lines={'x': 16, 'w': 12, 'z':3.6})
# fig.show()
# print TESTFindFromGrid(start['x'],start['w'],start['z'])
# print ydata
# print TESTFindFromGrid(np.mean(trace['x']),np.mean(trace['w']),np.mean(trace['z']))
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
data=pd.read_csv("http://hosho.ees.hokudai.ac.jp/~kubo/stat/iwanamibook/fig/hbm/data7a.csv")
#種子の数yごとに集計、グラフとして表示すると
plt.bar(range(9),data.groupby('y').sum().id)
data.groupby('y').sum().T
#dataの制限
Y=np.array(data.y)[:6]
import numpy as np
import pymc as pm import theano.tensor as T
def invlogit(v):
return T.exp(v)/(T.exp(v)+1)
with pm.Model() as model_hier:
s=pm.Uniform('s',0,1.0E+2)
beta=pm.Normal('beta',0,1.0E+2)
r=pm.Normal('r',0,s,shape=len(Y))
q=invlogit(beta+r)
y=pm.Binomial('y',8,q,observed=Y)
step = pm.Slice([s,beta,r])
trace_hier = pm.sample(10000, step)
with model_hier:
pm.traceplot(trace_hier, model_hier.vars)
alpha = pm.Normal('alpha', mu=0, sd=20)
beta = pm.Normal('beta', mu=0, sd=20)
sigma = pm.Uniform('sigma', lower=0, upper=10)
# define linear regression
y_est = alpha + beta * x
# define likelihood
likelihood = pm.Normal('y', mu=y_est, sd=sigma, observed=y)
# inference
start = pm.find_MAP()
# find starting value by optimization
step = pm.NUTS(state=start)
# instantiate MCMC sampling algorithm
trace = pm.sample(100, step, start=start, progressbar=False)
# draw 100 posterior samples using NUTS sampling
fig = pm.traceplot(trace, lines={'alpha': 4, 'beta': 2, 'sigma': 2})
plt.figure(figsize=(8, 8))
# GUI
# 出现NotImplementedError，被调用却没被实现,需要用到pyqt4
# 使用Anaconda新版本会强制安装pyqt5，如不兼容则卸载重装pyqt4
import numpy as np
import traits.api as trapi
import traitsui.api as trui
class short_rate(trapi.HasTraits):
name = trapi.Str
rate = trapi.Float
time_list = trapi.Array(dtype=np.float, shape=(1, 5))
disc_list = trapi.Array(dtype=np.float, shape=(1, 5))
import pymc as pm
from pymc.distributions.timeseries import GaussianRandomWalk
from scipy.sparse import csc_matrix
from scipy import optimize
with pm.Model() as model:
sigma, log_sigma = model.TransformedVar('sigma', pm.Exponential.dist(1./.02, testval=.1),
pm.logtransform)
nu = pm.Exponential('nu', 1./10)
s = GaussianRandomWalk('s', sigma**-2, shape=len(nreturns))
r = pm.T('r', nu, lam=pm.exp(-2*s), observed=nreturns)
with model:
start = pm.find_MAP(vars=[s], fmin=optimize.fmin_l_bfgs_b)
step = pm.NUTS(scaling=start)
trace = pm.sample(2000, step, start,progressbar=False)
plt.plot(trace[s][::10].T,'b', alpha=.03)
plt.title('log volatility')
with model:
pm.traceplot(trace, model.vars[:2])
exps=np.exp(trace[s][::10].T)
plt.plot(returns[:600][::-1])
plt.plot( exps, 'r', alpha=.03);
plt.plot(-exps, 'r', alpha=.03);
plt.show()
alpha = pm.Normal('alpha', mu=0, sd=20)
beta = pm.Normal('beta', mu=0, sd=20)
sigma = pm.Uniform('sigma', lower=0)
y = pm.Normal('y', mu=beta*X + alpha, sd=sigma, observed=Y)
start = pm.find_MAP()
step = pm.NUTS(state=start)
with model:
if(multicore):
trace = pm.sample(itenum, step, start=start,
njobs=chainnum, random_seed=range(chainnum), progress_bar=False)
else:
ts=[pm.sample(itenum, step, chain=i, progressbar=False) for i in range(chainnum)]
trace=merge_traces(ts)
if(saveimage):
pm.traceplot(trace).savefig("simple_linear_trace.png")
print "Rhat="+str(pm.gelman_rubin(trace))
t1=time.clock()
print "elapsed time="+str(t1-t0)
#trace
if(not multicore):
trace=ts[0]
with model:
pm.traceplot(trace,model.vars)
pm.forestplot(trace)
import pickle as pkl
with open("simplelinearregression_model.pkl","w") as fpw:
# trace = pm.sample(5000, [step1, step2], start=start, progressbar=False) ## Check the results. burnin = 2000 # posterior samples to discard thin = 10 # posterior samples to discard ## Print summary for each trace #pm.summary(trace[burnin::thin]) #pm.summary(trace) ## Check for mixing and autocorrelation pm.autocorrplot(trace[burnin::thin], vars =[mu, kappa]) #pm.autocorrplot(trace, vars =[mu, kappa]) ## Plot KDE and sampled values for each parameter. pm.traceplot(trace[burnin::thin]) #pm.traceplot(trace) # Create arrays with the posterior sample theta1_sample = trace['theta'][:,0][burnin::thin] theta2_sample = trace['theta'][:,1][burnin::thin] theta3_sample = trace['theta'][:,2][burnin::thin] mu_sample = trace['mu'][burnin::thin] kappa_sample = trace['kappa'][burnin::thin] fig = plt.figure(figsize=(12,12)) # Scatter plot hyper-parameters plt.subplot(4, 3, 1) plt.scatter(mu_sample, kappa_sample, marker='o') plt.xlim(0,1)
getParameters=True,
getEnergy=True)
class Step(object):
def __init__(self, var):
self.var = var.name
def step(self, point):
new = point.copy()
#new[self.var] = 10 + np.random.rand() # Normal samples
state = point['state']
sigma = point['sigma']
new[self.var] = propagate(simulation, state, temperature, sigma,
epsilon)
return new
with pymc.Model() as model:
sigma = pymc.Uniform("sigma", 0.535, 0.565)
state = pymc.Flat('state')
step1 = pymc.step_methods.NUTS(vars=[sigma])
step2 = Step(state) # not sure how to limit this to one variable
trace = pymc.sample(10, [step1, step2])
pymc.traceplot(trace[:])
show()
def foo(self, discrete):
student_ids = []
timestep_ids = []
y = []
ids = collections.defaultdict(itertools.count().next)
for t in range(0, len(self)):
student_ids += [ids[o.id] for o in self[t]]
timestep_ids += [t for o in self[t]]
y += [o.value for o in self[t]]
n_students = len(set(student_ids))
n_timesteps = len(self)
print student_ids, "!", n_students
with pm.Model() as hierarchical_model:
# Hyperpriors for group nodes
mu_student = pm.Normal('mu_student', mu=0., sd=100**2)
sigma_student = pm.Uniform('sigma_student', lower=0, upper=100)
#mu_timestep = pm.Normal('mu_beta', mu=0., sd=100**2)
#sigma_timestep = pm.Uniform('sigma_beta', lower=0, upper=100)
student = pm.Normal('student',
mu=mu_student,
sd=sigma_student,
shape=n_students) #random effect
timestep = pm.Normal('timestep',
mu=0,
sd=100**2,
shape=n_timesteps) #fixed effect
# Model error
eps = pm.Uniform('eps', lower=0, upper=100)
theta = student[student_ids] + timestep[timestep_ids]
# Data likelihood
if discrete:
ll = pm.Bernoulli('theta', p=self.invlogit(theta), observed=y)
else:
ll = pm.Normal('theta', mu=theta, sd=eps, observed=y)
with hierarchical_model:
print "Find MAP..."
start = pm.find_MAP()
#if discrete:
# step = pm.BinaryMetropolis(scaling=start)
# else:
print "NUTS..."
step = pm.NUTS(scaling=start)
print "Samples..."
hierarchical_trace = pm.sample(2000,
step,
start=start,
progressbar=False)
print "done..."
print "Plot..."
pl.figure(figsize=(10, 10))
f = pm.traceplot(hierarchical_trace[500:])
f.savefig("a.png")
return hierarchical_trace
# trace = pm.sample(5000, [step1, step2], start=start, progressbar=False) ## Check the results. burnin = 2000 # posterior samples to discard thin = 10 # posterior samples to discard ## Print summary for each trace #pm.summary(trace[burnin::thin]) #pm.summary(trace) ## Check for mixing and autocorrelation pm.autocorrplot(trace[burnin::thin], vars=[mu, kappa]) #pm.autocorrplot(trace, vars =[mu, kappa]) ## Plot KDE and sampled values for each parameter. pm.traceplot(trace[burnin::thin]) #pm.traceplot(trace) # Create arrays with the posterior sample theta1_sample = trace['theta'][:, 0][burnin::thin] theta2_sample = trace['theta'][:, 1][burnin::thin] theta3_sample = trace['theta'][:, 2][burnin::thin] mu_sample = trace['mu'][burnin::thin] kappa_sample = trace['kappa'][burnin::thin] fig = plt.figure(figsize=(12, 12)) # Scatter plot hyper-parameters plt.subplot(4, 3, 1) plt.scatter(mu_sample, kappa_sample, marker='o') plt.xlim(0, 1)
s['p'],
map_est['p'],
model.logp(map_est)))
# By default `basinhopping` uses a gradient minimization technique,
# `fmin_bfgs`, resulting in inaccurate predictions many times. If we force
# `basinhoping` to use a non-gradient technique we get much better results
with model:
for i in range(n+1):
s = {'p': 0.5, 'surv_sim': i}
map_est = mc.find_MAP(start=s, vars=model.vars,
fmin=bh, minimizer_kwargs={"method": "Powell"})
print('surv_sim: %i->%i, p: %f->%f, LogP:%f'%(s['surv_sim'],
map_est['surv_sim'],
s['p'],
map_est['p'],
model.logp(map_est)))
# Confident in our MAP estimate we can sample from the posterior, making sure
# we use the `Metropolis` method for our discrete variables.
with model:
step1 = mc.step_methods.HamiltonianMC(vars=[p])
step2 = mc.step_methods.Metropolis(vars=[surv_sim])
with model:
trace = mc.sample(25000, [step1, step2], start=map_est)
mc.traceplot(trace);
print('surv_sim: %i->%i, p: %f->%f, LogP:%f' %
(s['surv_sim'], map_est['surv_sim'], s['p'], map_est['p'],
model.logpc(map_est)))
# By default `basinhopping` uses a gradient minimization technique,
# `fmin_bfgs`, resulting in inaccurate predictions many times. If we force
# `basinhoping` to use a non-gradient technique we get much better results
with model:
for i in range(n + 1):
s = {'p': 0.5, 'surv_sim': i}
map_est = mc.find_MAP(start=s,
vars=model.vars,
fmin=bh,
minimizer_kwargs={"method": "Powell"})
print('surv_sim: %i->%i, p: %f->%f, LogP:%f' %
(s['surv_sim'], map_est['surv_sim'], s['p'], map_est['p'],
model.logpc(map_est)))
# Confident in our MAP estimate we can sample from the posterior, making sure
# we use the `Metropolis` method for our discrete variables.
with model:
step1 = mc.step_methods.HamiltonianMC(vars=[p])
step2 = mc.step_methods.Metropolis(vars=[surv_sim])
with model:
trace = mc.sample(25000, [step1, step2], start=map_est)
mc.traceplot(trace)
# and the other indexes the shape of the parameter. Thus for this example: # In[8]: trace[y].shape # Out[8]: # (3000, 2, 1) # `traceplot` is a summary plotting function for a trace. # In[9]: pm.traceplot(trace); # Out[9]: # image file: # ## PyMC Internals # # ### Model # # The `Model` class has very simple internals: just a list of unobserved variables (`Model.vars`) and a list of factors which go into computing the posterior density (`Model.factors`) (see model.py for more). # # A Python "`with model:`" block has `model` as the current model. Many functions, like `find_MAP` and `sample`, must be in such a block to work correctly by default. They look in the current context for a model to use. You may also explicitly specify the model for them to use. This allows us to treat the current model as an implicit parameter to these functions. # # ### Distribution Classes
import pymc as pm
from pymc.distributions.timeseries import GaussianRandomWalk
from scipy.sparse import csc_matrix
from scipy import optimize
with pm.Model() as model:
sigma, log_sigma = model.TransformedVar(
'sigma', pm.Exponential.dist(1. / .02, testval=.1), pm.logtransform)
nu = pm.Exponential('nu', 1. / 10)
s = GaussianRandomWalk('s', sigma**-2, shape=len(nreturns))
r = pm.T('r', nu, lam=pm.exp(-2 * s), observed=nreturns)
with model:
start = pm.find_MAP(vars=[s], fmin=optimize.fmin_l_bfgs_b)
step = pm.NUTS(scaling=start)
trace = pm.sample(2000, step, start, progressbar=False)
plt.plot(trace[s][::10].T, 'b', alpha=.03)
plt.title('log volatility')
with model:
pm.traceplot(trace, model.vars[:2])
exps = np.exp(trace[s][::10].T)
plt.plot(returns[:600][::-1])
plt.plot(exps, 'r', alpha=.03)
plt.plot(-exps, 'r', alpha=.03)
plt.show()