def lnprob(theta, Deltam, nsne, xi, redshiftterm):
A, M, sigma, pv = theta
if (A <= 0 or sigma < 0 or pv < 0):
return -numpy.inf
C = A * numpy.array(xi)
numpy.fill_diagonal(
C,
C.diagonal() + sigma**2 / nsne + (pv * redshiftterm)**2)
mterm = Deltam - M
C = matrix(C)
W = matrix(mterm)
try:
lapack.posv(C, W, uplo='U')
except ArithmeticError:
return -np.inf
logdetC = 2 * numpy.log(numpy.array(C).diagonal()).sum()
lp = -0.5 * (logdetC + blas.dot(matrix(mterm), W)) + cauchy.logpdf(
sigma, loc=0.08, scale=0.5) + cauchy.logpdf(
pv, loc=0, scale=600 / 3e5)
if not numpy.isfinite(lp):
return -np.inf
return lp
def pdf(cls, x: Numeric, alpha: float, beta: float, gamma=1., delta=0., pm=0):
cls._check_parameters(alpha, beta, gamma, pm)
delta, gamma = cls._form_parameters(alpha, delta, gamma, beta, pm)
x = (x - delta) / gamma
if alpha == 2:
ans = norm.logpdf(x, 0, np.sqrt(2))
if np.array(ans).size == 1:
ans = np.ravel([ans])
elif alpha == 1 and beta == 0:
ans = cauchy.logpdf(x)
if np.array(ans).size == 1:
ans = np.ravel([ans])
elif alpha == 1: # beta not 0
if isinstance(x, (float, int)):
ans = np.array([_pdf_f2(x, beta)])
else:
ans = np.array([_pdf_f2(e, beta) for e in x])
else: # alpha != 1
bt = beta * tanpi2(alpha)
zeta = -bt
theta0 = min(max(-PI2, np.arctan(bt) / alpha), PI2)
if bt == 0:
zeta_tol = 4e-10
elif 1 - abs(beta) < 0.01 or alpha < 0.01:
zeta_tol = 2e-9
else:
zeta_tol = 5e-5
if isinstance(x, (float, int)):
ans = np.array([_pdf_f1(x, alpha, beta, zeta, theta0, zeta_tol)])
else:
ans = np.array([_pdf_f1(e, alpha, beta, zeta, theta0, zeta_tol) for e in x])
infs = ans == 0
if np.any(ans):
d = cls._pareto_pdf(x, alpha, beta)
ans[infs] = d[infs] / gamma
if np.any(~infs):
ans[~infs] /= gamma
return float(ans) if ans.size == 1 else ans
def compute_noise_loglike(physics, det):
"""
Compute the log-likelihood that the detection was generated by noise.
"""
assert (det.time > 0 and det.time < physics.T and det.amp > 0)
loglike = 0
loglike += -log(physics.T) # detection time
loglike += -log(360) # detection azimuth
loglike += -log(compute_slowness(0) - compute_slowness(180)) # slowness
# detection amplitude
loglike += cauchy.logpdf(log(det.amp), physics.mu_f[det.stanum],
physics.theta_f[det.stanum])
return loglike
def compute_noise_loglike(physics, det):
"""
Compute the log-likelihood that the detection was generated by noise.
"""
assert (det.time > 0 and det.time < physics.T and det.amp > 0)
loglike = 0
loglike += -log(physics.T) # detection time
loglike += -log(360) # detection azimuth
loglike += -log(compute_slowness(0) - compute_slowness(180)) # slowness
# detection amplitude
loglike += cauchy.logpdf(log(det.amp),
physics.mu_f[det.stanum], physics.theta_f[det.stanum])
return loglike
def calc_pred_p(self, pred_labels):
neg_logl = cauchy.logpdf(pred_labels, *self.wt_distr)
pos_logl = cauchy.logpdf(pred_labels, *self.mut_distr)
return 1 / (1 + np.exp(np.clip(neg_logl - pos_logl, -100, 100)))
def __call__(self, u: np.ndarray, y: float) -> np.ndarray:
return cauchy.logpdf(x=u, loc=y, scale=self.scale)
def sample_and_plot(sess, kld, kl_from_pq, kl_from_cob, p_samples, q_samples,
m_samples, log_ratio_p_q, log_ratio_p_m, mu_1, mu_2,
scale_p, scale_q, mu_3, scale_m):
kl_ratio_store = []
log_ratio_store = []
log_r_p_from_m_direct_store = []
feed_dict = {}
kl_ratio, kl_true, kl_cob, p_s, q_s, m_s, lpq, lpq_from_cob_dre_direct = sess.run(
[
kld, kl_from_pq, kl_from_cob, p_samples, q_samples, m_samples,
log_ratio_p_q, log_ratio_p_m
],
feed_dict=feed_dict)
'''Save ratio estimates'''
data_dir = "../data/sym/" + str(scale_p) + "-" + str(scale_q) + str(
scale_m) + "/"
if not os.path.exists(data_dir):
os.makedirs(data_dir)
f = open(data_dir + "KLD" + ".txt", "a")
f.write("GT for mu_3 = " + str(mu_3) + ": " + str(kl_ratio) +
"\nGT-est: " + str(kl_true) + "\nCoB: " + str(kl_cob) +
"\n----------\n")
f.close()
log_ratio_store.append(lpq)
log_r_p_from_m_direct_store.append(lpq_from_cob_dre_direct)
pickle.dump(
log_r_p_from_m_direct_store,
open(data_dir + "log_r_p_from_m_direct_store" + str(mu_3) + ".p",
"wb"))
pickle.dump(m_s, open(data_dir + "xs" + str(mu_3) + ".p", "wb"))
pickle.dump(log_ratio_store,
open(data_dir + "log_ratio_store" + str(mu_3) + ".p", "wb"))
xs = m_s
fig, [ax1, ax2, ax3, ax4] = plt.subplots(1, 4, figsize=(13, 4))
ax1.hist(p_s, density=True, histtype='stepfilled', alpha=0.8, label='P')
ax1.hist(q_s, density=True, histtype='stepfilled', alpha=0.8, label='Q')
ax1.hist(m_s, density=True, histtype='stepfilled', alpha=0.8, label='M')
ax1.legend(loc='best', frameon=False)
ax1.set_xlim([-5, 5])
ax2.scatter(xs,
log_ratio_store[0],
label='True p/q',
alpha=0.9,
s=10.,
c='b')
ax2.scatter(xs,
log_r_p_from_m_direct_store[-1][:, 0] -
log_r_p_from_m_direct_store[-1][:, 1],
label='CoB p/q',
alpha=0.9,
s=10.,
c='r')
ax2.scatter(xs,
-log_ratio_store[0],
label='True q/p',
alpha=0.9,
s=10.,
c='b')
ax2.scatter(xs,
log_r_p_from_m_direct_store[-1][:, 1] -
log_r_p_from_m_direct_store[-1][:, 0],
label='CoB q/p',
alpha=0.9,
s=10.,
c='r')
ax2.set_xlabel("Samples")
ax2.set_ylabel("Log Ratio")
ax2.legend(loc='best')
ax2.set_xlim([-6, 10])
ax2.set_ylim([-1000, 1000])
pm = [
np.squeeze(
norm.logpdf(x, mu_1, scale_p) - cauchy.logpdf(x, mu_3, scale_m))
for x in xs
]
qm = [
np.squeeze(
norm.logpdf(x, mu_2, scale_q) - cauchy.logpdf(x, mu_3, scale_m))
for x in xs
]
ax4.scatter(xs, pm, label='True p/m', alpha=0.9, s=10., c='b')
ax4.scatter(xs,
log_r_p_from_m_direct_store[-1][:, 0] -
log_r_p_from_m_direct_store[-1][:, 2],
label='CoB p/m',
alpha=0.9,
s=10.,
c='r')
ax4.scatter(xs, qm, label='True q/m', alpha=0.9, s=10., c='y')
ax4.scatter(xs,
log_r_p_from_m_direct_store[-1][:, 1] -
log_r_p_from_m_direct_store[-1][:, 2],
label='CoB q/m',
alpha=0.9,
s=10.,
c='g')
ax4.set_xlabel("Samples")
ax4.set_ylabel("Log Ratio")
ax4.legend(loc='best')
ax4.set_xlim([-6, 10])
ax4.set_ylim([-1000, 1000])
rat = log_r_p_from_m_direct_store[-1][:, 0] - log_r_p_from_m_direct_store[
-1][:, 1]
d = [np.squeeze(norm.logpdf(x, mu_2, scale_q)) for x in xs]
b = [np.squeeze(norm.logpdf(x, mu_1, scale_p)) for x in xs]
ax3.scatter(xs, b, label='True P', alpha=0.9, s=5.)
ax3.scatter(xs, rat + d, label='P', alpha=0.9, s=5.)
ax3.set_xlabel("Samples")
ax3.set_ylabel("Log P(x)")
ax3.legend(loc='best')
ax3.set_xlim([-6, 10])
ax3.set_ylim([-600, 400])
plt.savefig(data_dir + str(mu_3) + ".jpg")
def cauchy_adj_log_pdf(x, loc, scale):
if isinstance(x, float): correction = np.log(np.pi)
else: correction = len(x) * np.log(np.pi)
return np.sum(cauchy.logpdf(x, loc, scale)) + correction
def fitDist(ys, func, xlabel, varNames, params, plot, x=np.arange(-2, 2,
0.01)):
vals, bins = np.histogram(ys, bins=x, normed=True)
bins = bins[:-1]
popt, _ = curve_fit(func, bins, vals)
outputString = ", ".join(
["params[\"%s\"]"] * len(popt)) + " = " + ", ".join(["%f"] * len(popt))
for varName, val in zip(varNames, popt):
params[varName] = val
if func == funcHypsec:
fitLabel = "hypsec fit"
elif func == funcNorm:
fitLabel = "normal fit"
elif func == funcGamma:
fitLabel = "gamma fit"
else:
fitLabel = "distribution fit"
print(" " + outputString % tuple(varNames + list(popt)))
if plot:
import matplotlib.pyplot as plt
plt.figure()
plt.title("Curve fit for " + " ".join(varNames), fontsize=14)
plt.bar(bins,
vals,
width=bins[1] - bins[0],
label='observed distribution')
plt.plot(bins, func(bins, *popt), 'g', label=fitLabel, linewidth=2.0)
if func == funcHypsec:
poptNormal, _ = curve_fit(funcNorm, bins, vals)
plt.plot(bins,
funcNorm(bins, *poptNormal),
'r',
label='normal fit (for comparison)',
linewidth=2.0,
alpha=0.5)
if False:
funcStudentT = lambda x, df, mu, sigma: t.pdf(
x, df=df, loc=mu, scale=sigma)
poptStudentT, _ = curve_fit(funcStudentT, bins, vals)
print(poptStudentT)
funcCauchy = lambda x, mu, sigma: cauchy.pdf(
x, loc=mu, scale=sigma)
poptCauchy, _ = curve_fit(funcCauchy, bins, vals)
print(poptCauchy)
plt.plot(bins,
funcStudentT(bins, *poptStudentT),
'm',
label='student-t fit',
linewidth=2.0)
plt.plot(bins,
funcCauchy(bins, *poptCauchy),
'c',
label='cauchy fit',
linewidth=2.0)
funcLogStudentT = lambda x, df, mu, sigma: t.logpdf(
x, df=df, loc=mu, scale=sigma)
funcLogNorm = lambda x, mu, sigma: norm.logpdf(
x, loc=mu, scale=sigma)
funcLogCauchy = lambda x, mu, sigma: cauchy.logpdf(
x, loc=mu, scale=sigma)
plt.ylabel("relative frequency", fontsize=14)
plt.xlabel(xlabel, fontsize=14)
plt.legend()
plt.figure()
plt.plot(bins,
funcLogHypsec(bins, *popt),
'g',
label='hypsec log fit',
linewidth=2.0)
plt.plot(bins,
funcLogNorm(bins, *poptNormal),
'r',
label='normal log fit',
linewidth=2.0)
plt.plot(bins,
funcLogStudentT(bins, *poptStudentT),
'm',
label='student-t log fit',
linewidth=2.0)
plt.plot(bins,
funcLogCauchy(bins, *poptCauchy),
'c',
label='cauchy log fit',
linewidth=2.0)
plt.ylabel("relative frequency", fontsize=14)
plt.xlabel(xlabel, fontsize=14)
plt.legend()
plt.tight_layout()
def pdf(cls, x, alpha, beta, gamma=1., delta=0., pm=0, log=False):
"""
Returns density for stable DF
Parameters
----------
x: {array_like, scalar}
Numeric vector of quantiles.
alpha: float
Value of the index parameter alpha in the interval = (0, 2]
beta: float
Skewness parameter in the range [-1, 1]
gamma: float
Scale parameter
delta: float
Location (or ‘shift’) parameter delta.
pm: {0, 1, 2}
Type of parameterization, an integer in {0, 1, 2}. Defaults to 0, 'S0' parameterization.
log: bool
If True, returns the log of the density
Returns
-------
{array_like, scalar}
Numeric vectors of density
"""
cls._check_parameters(alpha, beta, gamma, pm)
delta, gamma = cls._parameterize(alpha, delta, gamma, beta, pm)
if isinstance(x, abc.Iterable):
x = np.asarray(x)
x = (x - delta) / gamma
if alpha == 2:
ans = norm.logpdf(x, 0, np.sqrt(2)) if log else norm.pdf(
x, 0, np.sqrt(2))
elif alpha == 1 and beta == 0:
ans = cauchy.logpdf(x) if log else cauchy.pdf(x)
elif alpha == 1: # beta not 0
if isinstance(x, (complex, float, int)):
ans = np.array([pdf.aux_f2(x, beta, log)])
else:
ans = np.array([pdf.aux_f2(e, beta, log)
for e in x.ravel()]).reshape(x.shape)
else: # alpha != 1
if isinstance(x, (complex, float, int)):
ans = np.array([pdf.aux_f1(x, alpha, beta, log)])
else:
ans = np.array([
pdf.aux_f1(e, alpha, beta, log) for e in x.ravel()
]).reshape(x.shape)
if ans.size == 1:
ans = ans.ravel()
infs = ans == 0
if np.any(ans):
d = pdf.pareto(x, alpha, beta, log)[infs]
ans[infs] = (d - np.log(gamma)) if log else (d / gamma)
if np.any(~infs):
d = ans[~infs]
ans[~infs] = (d - np.log(gamma)) if log else (d / gamma)
return ans.item(0) if ans.size == 1 else ans
def sample_and_plot(sess, kld, p_samples, q_samples, m_samples, log_ratio_p_q, log_ratio_p_m, mu_1, mu_2, scale_p, scale_q, mu_3, scale_m):
kl_ratio_store=[]
log_ratio_store=[]
log_r_p_from_m_direct_store=[]
feed_dict = {}
kl_ratio, p_s, q_s, m_s, lpq, lpq_from_cob_dre_direct = sess.run([kld, p_samples, q_samples, m_samples,
log_ratio_p_q, log_ratio_p_m],
feed_dict=feed_dict)
kl_ratio_store.append(kl_ratio)
log_ratio_store.append(lpq)
log_r_p_from_m_direct_store.append(lpq_from_cob_dre_direct)
xs = m_s
fig, [ax1,ax2,ax3, ax4] = plt.subplots(1, 4,figsize=(13,4))
ax1.hist(p_s, density=True, histtype='stepfilled', alpha=0.8, label='P')
ax1.hist(q_s, density=True, histtype='stepfilled', alpha=0.8, label='Q')
ax1.hist(m_s, density=True, histtype='stepfilled', alpha=0.8, label='M')
ax1.legend(loc='best', frameon=False)
ax1.set_xlim([-5,5])
ax2.scatter(xs,log_ratio_store[0],label='True p/q',alpha=0.9,s=10.,c='b')
ax2.scatter(xs,log_r_p_from_m_direct_store[-1][:,0]-log_r_p_from_m_direct_store[-1][:,1],label='CoB p/q',alpha=0.9,s=10.,c='r')
ax2.scatter(xs,-log_ratio_store[0],label='True q/p',alpha=0.9,s=10.,c='b')
ax2.scatter(xs,log_r_p_from_m_direct_store[-1][:,1]-log_r_p_from_m_direct_store[-1][:,0],label='CoB q/p',alpha=0.9,s=10.,c='r')
ax2.set_xlabel("Samples")
ax2.set_ylabel("Log Ratio")
ax2.legend(loc='best')
ax2.set_xlim([-4,6])
ax2.set_ylim([-1000,1000])
pm = [np.squeeze(norm.logpdf(x,mu_1,scale_p)-cauchy.logpdf(x,mu_3,scale_m)) for x in xs]
qm = [np.squeeze(norm.logpdf(x,mu_2,scale_q)-cauchy.logpdf(x,mu_3,scale_m)) for x in xs]
ax4.scatter(xs,pm,label='True p/m',alpha=0.9,s=10.,c='b')
ax4.scatter(xs,log_r_p_from_m_direct_store[-1][:,0]-log_r_p_from_m_direct_store[-1][:,2],label='CoB p/m',alpha=0.9,s=10.,c='r')
ax4.scatter(xs,qm,label='True q/m',alpha=0.9,s=10.,c='y')
ax4.scatter(xs,log_r_p_from_m_direct_store[-1][:,1]-log_r_p_from_m_direct_store[-1][:,2],label='CoB q/m',alpha=0.9,s=10.,c='g')
ax4.set_xlabel("Samples")
ax4.set_ylabel("Log Ratio")
ax4.legend(loc='best')
ax4.set_xlim([-4,6])
ax4.set_ylim([-1000,1000])
rat = log_r_p_from_m_direct_store[-1][:,0]-log_r_p_from_m_direct_store[-1][:,1]
d = [np.squeeze(norm.logpdf(x,mu_2,scale_q)) for x in xs]
b = [np.squeeze(norm.logpdf(x,mu_1,scale_p)) for x in xs]
ax3.scatter(xs,b,label='True P',alpha=0.9,s=5.)
ax3.scatter(xs,rat+d,label='P',alpha=0.9,s=5.)
ax3.set_xlabel("Samples")
ax3.set_ylabel("Log P(x)")
ax3.legend(loc='best')
ax3.set_xlim([-4.,4])
ax3.set_ylim([-600,400])
def sample_and_plot(sess, kl_p_q, kl_cob, kld, p_samples, q_samples, m_samples, log_ratio_p_q, log_ratio_p_m, mu_1, mu_2, scale_p, scale_q, mu_3, scale_m, training=True):
kl_ratio_store=[]
log_ratio_store=[]
log_r_p_from_m_direct_store=[]
feed_dict = {}
encoder_m = ratios_critic(m_samples)
encoder_p = ratios_critic(p_samples)
kl_ratio, kl_cob, kl_true, p_s, q_s, xs, enc_m, enc_p, lpq, lpq_from_cob_dre_direct= sess.run([kl_p_q, kl_cob, kld,
p_samples, q_samples, m_samples, encoder_m, encoder_p,
log_ratio_p_q, log_ratio_p_m],
feed_dict=feed_dict)
log_ratio_store.append(lpq)
log_r_p_from_m_direct_store.append(lpq_from_cob_dre_direct)
fig, [ax1,ax2,ax3, ax4] = plt.subplots(1, 4,figsize=(13,4))
ax1.hist(p_s, density=True, histtype='stepfilled', alpha=0.8, label='P')
ax1.hist(q_s, density=True, histtype='stepfilled', alpha=0.8, label='Q')
ax1.hist(xs, density=True, histtype='stepfilled', alpha=0.8, label='M')
ax1.legend(loc='best', frameon=False)
ax1.set_xlim([-5,5])
ax2.scatter(xs,log_ratio_store[0],label='True p/q',alpha=0.9,s=10.,c='b')
ax2.scatter(xs,log_r_p_from_m_direct_store[-1][:,0]-log_r_p_from_m_direct_store[-1][:,1],label='CoB p/q',alpha=0.9,s=10.,c='r')
ax2.scatter(xs,-log_ratio_store[0],label='True q/p',alpha=0.9,s=10.,c='b')
ax2.scatter(xs,log_r_p_from_m_direct_store[-1][:,1]-log_r_p_from_m_direct_store[-1][:,0],label='CoB q/p',alpha=0.9,s=10.,c='r')
ax2.set_xlabel("Samples")
ax2.set_ylabel("Log Ratio")
ax2.legend(loc='best')
ax2.set_xlim([-4,6])
ax2.set_ylim([-1000,1000])
pm = [np.squeeze(norm.logpdf(x,mu_1,scale_p)-cauchy.logpdf(x,mu_3,scale_m)) for x in xs]
qm = [np.squeeze(norm.logpdf(x,mu_2,scale_q)-cauchy.logpdf(x,mu_3,scale_m)) for x in xs]
ax4.scatter(xs,pm,label='True p/m',alpha=0.9,s=10.,c='b')
ax4.scatter(xs,log_r_p_from_m_direct_store[-1][:,0]-log_r_p_from_m_direct_store[-1][:,2],label='CoB p/m',alpha=0.9,s=10.,c='r')
ax4.scatter(xs,qm,label='True q/m',alpha=0.9,s=10.,c='y')
ax4.scatter(xs,log_r_p_from_m_direct_store[-1][:,1]-log_r_p_from_m_direct_store[-1][:,2],label='CoB q/m',alpha=0.9,s=10.,c='g')
ax4.set_xlabel("Samples")
ax4.set_ylabel("Log Ratio")
ax4.legend(loc='best')
ax4.set_xlim([-4,6])
ax4.set_ylim([-1000,1000])
rat = log_r_p_from_m_direct_store[-1][:,0]-log_r_p_from_m_direct_store[-1][:,1]
d = [np.squeeze(norm.logpdf(x,mu_2,scale_q)) for x in xs]
b = [np.squeeze(norm.logpdf(x,mu_1,scale_p)) for x in xs]
ax3.scatter(xs,b,label='True P',alpha=0.9,s=5.)
ax3.scatter(xs,rat+d,label='P',alpha=0.9,s=5.)
ax3.set_xlabel("Samples")
ax3.set_ylabel("Log P(x)")
ax3.legend(loc='best')
ax3.set_xlim([-4.,4])
ax3.set_ylim([-600,400])
plt.show()
print('KL : ',kl_true)
print('KL from samples : ',kl_ratio)
print('KL from CoB: ', kl_cob)
n_posterior_samples
candidate_ws = []
candidate_bs = []
if training:
print(f"Taking {n_posterior_samples} samples from posterior distributions on weights\n")
w_draw = layer.kernel_posterior.sample()
else:
print(f"Taking {n_posterior_samples} samples from prior distributions on weights\n")
w_draw = layer.kernel_prior.sample()
b_draw = layer.bias_posterior.sample()
for mc in range(n_posterior_samples):
w_, b_ = sess.run([w_draw, b_draw])
candidate_ws.append(w_)
candidate_bs.append(b_)
candidate_ws = np.array(candidate_ws).astype(np.float32)
candidate_bs = np.array(candidate_bs).astype(np.float32)
post, post_pred,post_std = log_ratio_predictive(enc_m, candidate_ws.T, candidate_bs.T)
kl_post,_,_ = log_ratio_predictive(enc_p, candidate_ws.T, candidate_bs.T)
x_sorted = []
m_sorted = []
s_sorted = []
p_sorted = []
[(x_sorted.append(a),m_sorted.append(b), s_sorted.append(c), p_sorted.append(d)) for a,b,c,d in sorted(zip(xs,post_pred, post_std, post))]
fig1, ax = plt.subplots()
plt.plot(x_sorted, norm.logpdf(x_sorted,mu_1,scale_p)-norm.logpdf(x_sorted,mu_2,scale_q),label='True log_prob',c='r')
# plt.plot(x_sorted, m_sorted,label='BC_Bayes_e',alpha=0.7)
quan = [np.abs(np.quantile(p_, .05)-np.quantile(p_, .95)) for p_ in p_sorted]
plt.errorbar(x_sorted, m_sorted, yerr = quan,label='BC_Bayes_e')
# plt.scatter(x_sorted,norm.logpdf(x_sorted,mu_1,scale_p)-norm.logpdf(x_sorted,mu_2,scale_q),label='True log_prob',alpha=0.99,s=5.)
plt.xlabel("Samples")
plt.ylabel("Log Ratio")
plt.legend(loc='upper right')
plt.xlim(-4,4)
plt.ylim(-400,1000)
plt.show()
fig1, ax = plt.subplots(figsize=(30,4))
plt.plot(norm.logpdf(x_sorted[100:400],mu_1,scale_p)-norm.logpdf(x_sorted[100:400],mu_2,scale_q),label='True log_prob',alpha=0.99)
plt.plot(m_sorted[100:400],label='BC_Bayes_e',alpha=0.7)
plt.boxplot(p_sorted[100:400],widths=0.05,notch=True,labels=x_sorted[100:400], showfliers=False, showbox=False, showcaps=False)
plt.xlabel("Samples")
plt.ylabel("Log Ratio")
plt.legend(loc='upper right')
plt.xticks(rotation = -65)
plt.locator_params(axis='x', nbins=100)
plt.ylim(-400,1000)
plt.show()
fig1, ax = plt.subplots()
print(kl_post.shape)
plt.boxplot(kl_post.mean(0),widths=0.5,notch=True, showfliers=False)
# plt.boxplot(kl_post.mean(0),widths=0.5,notch=True, showfliers=False)
plt.ylabel("KLD")
def nll(params):
return -sum(
cauchy.logpdf(data['delta_food'], loc=params[0], scale=params[2]) +
cauchy.logpdf(data['delta_money'], loc=params[1], scale=params[2]) +
cauchy.logpdf(data['delta_music'], loc=params[1], scale=params[2]))
