def __init__(self, cdts, Rcut, hyp, Dist, centre_init):
"""
Constructor of the logposteriorModule
"""
rad, thet = Deg2pc(cdts, centre_init, Dist)
c, r, t, self.Rmax = TruncSort(cdts, rad, thet, Rcut)
self.pro = c[:, 2]
self.cdts = c[:, :2]
self.Dist = Dist
#------------- poisson ----------------
self.quadrants = [
0, np.pi / 2.0, np.pi, 3.0 * np.pi / 2.0, 2.0 * np.pi
]
self.poisson = st.poisson(len(r) / 4.0)
#-------------- priors ----------------
self.Prior_0 = st.norm(loc=centre_init[0], scale=hyp[0])
self.Prior_1 = st.norm(loc=centre_init[1], scale=hyp[1])
self.Prior_2 = st.uniform(loc=-0.5 * np.pi, scale=np.pi)
self.Prior_3 = st.halfcauchy(loc=0.01, scale=hyp[2])
self.Prior_4 = st.halfcauchy(loc=0.01, scale=hyp[3])
self.Prior_5 = st.halfcauchy(loc=0.01, scale=hyp[2])
self.Prior_6 = st.halfcauchy(loc=0.01, scale=hyp[3])
self.Prior_7 = st.truncexpon(b=hyp[4], loc=0.01, scale=hyp[5])
self.Prior_8 = st.truncexpon(b=hyp[4], loc=0.01, scale=hyp[5])
print("Module Initialized")
def __init__(self,cdts,Rcut,hyp,Dist,centre_init):
"""
Constructor of the logposteriorModule
"""
rad,thet = Deg2pc(cdts,centre_init,Dist)
c,r,t,self.Rmax = TruncSort(cdts,rad,thet,Rcut)
self.pro = c[:,2]
self.cdts = c[:,:2]
self.Dist = Dist
#-------------- Finds the mode of the band -------
band_all = c[:,3]
idv = np.where(np.isfinite(c[:,3]))[0]
band = c[idv,3]
kde = st.gaussian_kde(band)
x = np.linspace(np.min(band),np.max(band),num=1000)
self.mode = x[kde(x).argmax()]
print "Mode of band at ",self.mode
#---- repleace NANs by mode -----
idnv = np.setdiff1d(np.arange(len(band_all)),idv)
band_all[idnv] = self.mode
self.delta_band = band_all - self.mode
#------------- poisson ----------------
self.quadrants = [0,np.pi/2.0,np.pi,3.0*np.pi/2.0,2.0*np.pi]
self.poisson = st.poisson(len(r)/4.0)
#-------------- priors ----------------
self.Prior_0 = st.norm(loc=centre_init[0],scale=hyp[0])
self.Prior_1 = st.norm(loc=centre_init[1],scale=hyp[1])
self.Prior_2 = st.uniform(loc=-0.5*np.pi,scale=np.pi)
self.Prior_3 = st.halfcauchy(loc=0.01,scale=hyp[2])
self.Prior_4 = st.halfcauchy(loc=0.01,scale=hyp[2])
self.Prior_5 = st.truncexpon(b=hyp[3],loc=2.01,scale=hyp[4])
self.Prior_6 = st.norm(loc=hyp[5],scale=hyp[6])
print "Module Initialized"
def __init__(self, cdts, Rcut, hyp, Dist, centre):
"""
Constructor of the logposteriorModule
"""
rad, thet = Deg2pc(cdts, centre, Dist)
c, r, t, self.Rmax = TruncSort(cdts, rad, thet, Rcut)
self.pro = c[:, 2]
self.rad = r
# -------- Priors --------
self.Prior_0 = st.halfcauchy(loc=0, scale=hyp[0])
self.Prior_1 = st.halfcauchy(loc=0, scale=hyp[1])
print("Module Initialized")
def initpos(self,nwalkers):
# pick nwalkers random positions in the range
pos=[]
for i in range(len(self.rmin)):
pos.append(np.random.uniform(self.rmin[i],self.rmax[i],size=nwalkers))
pos.append(halfcauchy(scale=self.variance_prior_scale).rvs(size=nwalkers))
return np.asarray(pos).T
def __init__(self, cdts, Rmax, hyp, Dist):
"""
Constructor of the logposteriorModule
"""
self.pro = cdts[:, 2]
self.rad = cdts[:, 3]
self.Rmax = Rmax
self.Prior_0 = st.halfcauchy(loc=0, scale=hyp[0])
self.Prior_1 = st.uniform(loc=0.01, scale=hyp[1])
self.Prior_2 = st.uniform(loc=0, scale=2)
print("Module Initialized")
def setup_class(cls):
np.random.seed(42)
pdf_a = stats.halfcauchy(loc=0, scale=1)
pdf_b = stats.uniform(loc=0, scale=100)
n_a = 50
n_b = 200
params = [n_a, n_b]
X = np.concatenate([pdf_a.rvs(size=n_a),
pdf_b.rvs(size=n_b),
])[:, np.newaxis]
cls.X = X
cls.params = params
cls.pdf_a = pdf_a
cls.pdf_b = pdf_b
def setup_class(cls):
np.random.seed(42)
pdf_a = stats.halfcauchy(loc=0, scale=1)
pdf_b = stats.uniform(loc=0, scale=100)
n_a = 50
n_b = 200
params = [n_a, n_b]
X = np.concatenate([
pdf_a.rvs(size=n_a),
pdf_b.rvs(size=n_b),
])[:, np.newaxis]
cls.X = X
cls.params = params
cls.pdf_a = pdf_a
cls.pdf_b = pdf_b
def __init__(self, cdts, Rcut, hyp, Dist, centre_init):
"""
Constructor of the logposteriorModule
"""
rad, thet = Deg2pc(cdts, centre_init, Dist)
c, r, t, self.Rmax = TruncSort(cdts, rad, thet, Rcut)
self.pro = c[:, 2]
self.cdts = c[:, :2]
self.Dist = Dist
print "There are ", len(self.cdts), " observations."
# sys.exit()
#------------- poisson ----------------
self.quadrants = [
0, np.pi / 2.0, np.pi, 3.0 * np.pi / 2.0, 2.0 * np.pi
]
self.poisson = st.poisson(len(r) / 4.0)
#-------------- priors ----------------
self.Prior_0 = st.norm(loc=centre_init[0], scale=hyp[0])
self.Prior_1 = st.norm(loc=centre_init[1], scale=hyp[1])
self.Prior_2 = st.halfcauchy(loc=0.01, scale=hyp[2])
self.Prior_3 = st.truncexpon(b=hyp[3], loc=2.01, scale=hyp[4])
print "Module Initialized"
lambda probs, total_count: osp.binom(n=total_count, p=probs),
dist.BinomialLogits:
lambda logits, total_count: osp.binom(n=total_count,
p=_to_probs_bernoulli(logits)),
dist.Cauchy:
lambda loc, scale: osp.cauchy(loc=loc, scale=scale),
dist.Chi2:
lambda df: osp.chi2(df),
dist.Dirichlet:
lambda conc: osp.dirichlet(conc),
dist.Exponential:
lambda rate: osp.expon(scale=np.reciprocal(rate)),
dist.Gamma:
lambda conc, rate: osp.gamma(conc, scale=1. / rate),
dist.HalfCauchy:
lambda scale: osp.halfcauchy(scale=scale),
dist.HalfNormal:
lambda scale: osp.halfnorm(scale=scale),
dist.InverseGamma:
lambda conc, rate: osp.invgamma(conc, scale=rate),
dist.LogNormal:
lambda loc, scale: osp.lognorm(s=scale, scale=np.exp(loc)),
dist.MultinomialProbs:
lambda probs, total_count: osp.multinomial(n=total_count, p=probs),
dist.MultinomialLogits:
lambda logits, total_count: osp.multinomial(n=total_count,
p=_to_probs_multinom(logits)),
dist.MultivariateNormal:
_mvn_to_scipy,
dist.Normal:
lambda loc, scale: osp.norm(loc=loc, scale=scale),
cov = jax_dist.covariance_matrix
return osp.multivariate_normal(mean=mean, cov=cov)
_DIST_MAP = {
dist.BernoulliProbs: lambda probs: osp.bernoulli(p=probs),
dist.BernoulliLogits: lambda logits: osp.bernoulli(p=_to_probs_bernoulli(logits)),
dist.Beta: lambda con1, con0: osp.beta(con1, con0),
dist.BinomialProbs: lambda probs, total_count: osp.binom(n=total_count, p=probs),
dist.BinomialLogits: lambda logits, total_count: osp.binom(n=total_count, p=_to_probs_bernoulli(logits)),
dist.Cauchy: lambda loc, scale: osp.cauchy(loc=loc, scale=scale),
dist.Chi2: lambda df: osp.chi2(df),
dist.Dirichlet: lambda conc: osp.dirichlet(conc),
dist.Exponential: lambda rate: osp.expon(scale=np.reciprocal(rate)),
dist.Gamma: lambda conc, rate: osp.gamma(conc, scale=1./rate),
dist.HalfCauchy: lambda scale: osp.halfcauchy(scale=scale),
dist.HalfNormal: lambda scale: osp.halfnorm(scale=scale),
dist.InverseGamma: lambda conc, rate: osp.invgamma(conc, scale=rate),
dist.LogNormal: lambda loc, scale: osp.lognorm(s=scale, scale=np.exp(loc)),
dist.MultinomialProbs: lambda probs, total_count: osp.multinomial(n=total_count, p=probs),
dist.MultinomialLogits: lambda logits, total_count: osp.multinomial(n=total_count,
p=_to_probs_multinom(logits)),
dist.MultivariateNormal: _mvn_to_scipy,
dist.LowRankMultivariateNormal: _lowrank_mvn_to_scipy,
dist.Normal: lambda loc, scale: osp.norm(loc=loc, scale=scale),
dist.Pareto: lambda alpha, scale: osp.pareto(alpha, scale=scale),
dist.Poisson: lambda rate: osp.poisson(rate),
dist.StudentT: lambda df, loc, scale: osp.t(df=df, loc=loc, scale=scale),
dist.Uniform: lambda a, b: osp.uniform(a, b - a),
}
# Calculate a few first moments: mean, var, skew, kurt = halfcauchy.stats(moments='mvsk') # Display the probability density function (``pdf``): x = np.linspace(halfcauchy.ppf(0.01), halfcauchy.ppf(0.99), 100) ax.plot(x, halfcauchy.pdf(x), 'r-', lw=5, alpha=0.6, label='halfcauchy pdf') # Alternatively, the distribution object can be called (as a function) # to fix the shape, location and scale parameters. This returns a "frozen" # RV object holding the given parameters fixed. # Freeze the distribution and display the frozen ``pdf``: rv = halfcauchy() ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') # Check accuracy of ``cdf`` and ``ppf``: vals = halfcauchy.ppf([0.001, 0.5, 0.999]) np.allclose([0.001, 0.5, 0.999], halfcauchy.cdf(vals)) # True # Generate random numbers: r = halfcauchy.rvs(size=1000) # And compare the histogram: ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
import matplotlib.pyplot as plt import numpy as np from scipy.stats import halfcauchy """ Example of transformation of constrained variables. From ADVI Section 2.3 """ theta = np.linspace(0 + 1e-2, 10, 1000) zeta = np.linspace(-5, 5, 1000) pdf_original = halfcauchy(loc=0, scale=5).pdf(theta) pdf_transformed = halfcauchy(loc=0, scale=5).pdf(np.exp(zeta)) * np.exp(zeta) plt.plot(theta, pdf_original, label='p(tau)') plt.plot(zeta, pdf_transformed, label='p(log(tau))') plt.legend() plt.show()
def all_dists():
# dists param were taken from scipy.stats official
# documentaion examples
# Total - 89
return {
"alpha":
stats.alpha(a=3.57, loc=0.0, scale=1.0),
"anglit":
stats.anglit(loc=0.0, scale=1.0),
"arcsine":
stats.arcsine(loc=0.0, scale=1.0),
"beta":
stats.beta(a=2.31, b=0.627, loc=0.0, scale=1.0),
"betaprime":
stats.betaprime(a=5, b=6, loc=0.0, scale=1.0),
"bradford":
stats.bradford(c=0.299, loc=0.0, scale=1.0),
"burr":
stats.burr(c=10.5, d=4.3, loc=0.0, scale=1.0),
"cauchy":
stats.cauchy(loc=0.0, scale=1.0),
"chi":
stats.chi(df=78, loc=0.0, scale=1.0),
"chi2":
stats.chi2(df=55, loc=0.0, scale=1.0),
"cosine":
stats.cosine(loc=0.0, scale=1.0),
"dgamma":
stats.dgamma(a=1.1, loc=0.0, scale=1.0),
"dweibull":
stats.dweibull(c=2.07, loc=0.0, scale=1.0),
"erlang":
stats.erlang(a=2, loc=0.0, scale=1.0),
"expon":
stats.expon(loc=0.0, scale=1.0),
"exponnorm":
stats.exponnorm(K=1.5, loc=0.0, scale=1.0),
"exponweib":
stats.exponweib(a=2.89, c=1.95, loc=0.0, scale=1.0),
"exponpow":
stats.exponpow(b=2.7, loc=0.0, scale=1.0),
"f":
stats.f(dfn=29, dfd=18, loc=0.0, scale=1.0),
"fatiguelife":
stats.fatiguelife(c=29, loc=0.0, scale=1.0),
"fisk":
stats.fisk(c=3.09, loc=0.0, scale=1.0),
"foldcauchy":
stats.foldcauchy(c=4.72, loc=0.0, scale=1.0),
"foldnorm":
stats.foldnorm(c=1.95, loc=0.0, scale=1.0),
# "frechet_r": stats.frechet_r(c=1.89, loc=0.0, scale=1.0),
# "frechet_l": stats.frechet_l(c=3.63, loc=0.0, scale=1.0),
"genlogistic":
stats.genlogistic(c=0.412, loc=0.0, scale=1.0),
"genpareto":
stats.genpareto(c=0.1, loc=0.0, scale=1.0),
"gennorm":
stats.gennorm(beta=1.3, loc=0.0, scale=1.0),
"genexpon":
stats.genexpon(a=9.13, b=16.2, c=3.28, loc=0.0, scale=1.0),
"genextreme":
stats.genextreme(c=-0.1, loc=0.0, scale=1.0),
"gausshyper":
stats.gausshyper(a=13.8, b=3.12, c=2.51, z=5.18, loc=0.0, scale=1.0),
"gamma":
stats.gamma(a=1.99, loc=0.0, scale=1.0),
"gengamma":
stats.gengamma(a=4.42, c=-3.12, loc=0.0, scale=1.0),
"genhalflogistic":
stats.genhalflogistic(c=0.773, loc=0.0, scale=1.0),
"gilbrat":
stats.gilbrat(loc=0.0, scale=1.0),
"gompertz":
stats.gompertz(c=0.947, loc=0.0, scale=1.0),
"gumbel_r":
stats.gumbel_r(loc=0.0, scale=1.0),
"gumbel_l":
stats.gumbel_l(loc=0.0, scale=1.0),
"halfcauchy":
stats.halfcauchy(loc=0.0, scale=1.0),
"halflogistic":
stats.halflogistic(loc=0.0, scale=1.0),
"halfnorm":
stats.halfnorm(loc=0.0, scale=1.0),
"halfgennorm":
stats.halfgennorm(beta=0.675, loc=0.0, scale=1.0),
"hypsecant":
stats.hypsecant(loc=0.0, scale=1.0),
"invgamma":
stats.invgamma(a=4.07, loc=0.0, scale=1.0),
"invgauss":
stats.invgauss(mu=0.145, loc=0.0, scale=1.0),
"invweibull":
stats.invweibull(c=10.6, loc=0.0, scale=1.0),
"johnsonsb":
stats.johnsonsb(a=4.32, b=3.18, loc=0.0, scale=1.0),
"johnsonsu":
stats.johnsonsu(a=2.55, b=2.25, loc=0.0, scale=1.0),
"ksone":
stats.ksone(n=1e03, loc=0.0, scale=1.0),
"kstwobign":
stats.kstwobign(loc=0.0, scale=1.0),
"laplace":
stats.laplace(loc=0.0, scale=1.0),
"levy":
stats.levy(loc=0.0, scale=1.0),
"levy_l":
stats.levy_l(loc=0.0, scale=1.0),
"levy_stable":
stats.levy_stable(alpha=0.357, beta=-0.675, loc=0.0, scale=1.0),
"logistic":
stats.logistic(loc=0.0, scale=1.0),
"loggamma":
stats.loggamma(c=0.414, loc=0.0, scale=1.0),
"loglaplace":
stats.loglaplace(c=3.25, loc=0.0, scale=1.0),
"lognorm":
stats.lognorm(s=0.954, loc=0.0, scale=1.0),
"lomax":
stats.lomax(c=1.88, loc=0.0, scale=1.0),
"maxwell":
stats.maxwell(loc=0.0, scale=1.0),
"mielke":
stats.mielke(k=10.4, s=3.6, loc=0.0, scale=1.0),
"nakagami":
stats.nakagami(nu=4.97, loc=0.0, scale=1.0),
"ncx2":
stats.ncx2(df=21, nc=1.06, loc=0.0, scale=1.0),
"ncf":
stats.ncf(dfn=27, dfd=27, nc=0.416, loc=0.0, scale=1.0),
"nct":
stats.nct(df=14, nc=0.24, loc=0.0, scale=1.0),
"norm":
stats.norm(loc=0.0, scale=1.0),
"pareto":
stats.pareto(b=2.62, loc=0.0, scale=1.0),
"pearson3":
stats.pearson3(skew=0.1, loc=0.0, scale=1.0),
"powerlaw":
stats.powerlaw(a=1.66, loc=0.0, scale=1.0),
"powerlognorm":
stats.powerlognorm(c=2.14, s=0.446, loc=0.0, scale=1.0),
"powernorm":
stats.powernorm(c=4.45, loc=0.0, scale=1.0),
"rdist":
stats.rdist(c=0.9, loc=0.0, scale=1.0),
"reciprocal":
stats.reciprocal(a=0.00623, b=1.01, loc=0.0, scale=1.0),
"rayleigh":
stats.rayleigh(loc=0.0, scale=1.0),
"rice":
stats.rice(b=0.775, loc=0.0, scale=1.0),
"recipinvgauss":
stats.recipinvgauss(mu=0.63, loc=0.0, scale=1.0),
"semicircular":
stats.semicircular(loc=0.0, scale=1.0),
"t":
stats.t(df=2.74, loc=0.0, scale=1.0),
"triang":
stats.triang(c=0.158, loc=0.0, scale=1.0),
"truncexpon":
stats.truncexpon(b=4.69, loc=0.0, scale=1.0),
"truncnorm":
stats.truncnorm(a=0.1, b=2, loc=0.0, scale=1.0),
"tukeylambda":
stats.tukeylambda(lam=3.13, loc=0.0, scale=1.0),
"uniform":
stats.uniform(loc=0.0, scale=1.0),
"vonmises":
stats.vonmises(kappa=3.99, loc=0.0, scale=1.0),
"vonmises_line":
stats.vonmises_line(kappa=3.99, loc=0.0, scale=1.0),
"wald":
stats.wald(loc=0.0, scale=1.0),
"weibull_min":
stats.weibull_min(c=1.79, loc=0.0, scale=1.0),
"weibull_max":
stats.weibull_max(c=2.87, loc=0.0, scale=1.0),
"wrapcauchy":
stats.wrapcauchy(c=0.0311, loc=0.0, scale=1.0),
}
def p(log_tau, theta):
return norm(loc=theta, scale=SIGMA).pdf(Y1) \
* norm(loc=MU, scale=np.exp(log_tau)).pdf(theta) \
* norm(loc=0, scale=5).pdf(MU) \
* halfcauchy(loc=0, scale=5).pdf(np.exp(log_tau)) \
* np.exp(log_tau)
axs[1, 0].axhline(y=Y[2], color='black', linestyle='-')
axs[1, 0].set_xlabel(r'$\mu$')
axs[1, 0].set_ylabel(r'$\theta_{3}$')
axs[1, 0].annotate(r'$y_{3}$', xy=(-4, Y[2] + 1), xycoords='data')
axs[1, 1].scatter(np.log(mcmc_trace['mu'][1000:]), mcmc_trace['theta'][:, -2][1000:], color='tan',
alpha=0.6)
axs[1, 1].axhline(y=Y[-2], color='black', linestyle='-')
axs[1, 1].set_xlabel(r'$\mu$')
axs[1, 1].set_ylabel(r'$\theta_{7}$')
axs[1, 1].annotate(r'$y_{7}$', xy=(-4, Y[-2] + 1), xycoords='data')
# MU & THETA
mu_true_pdf = norm(loc=0, scale=5).pdf
mu_linspace = np.linspace(-15, 15, 2000)
tau_true_pdf = halfcauchy(loc=0, scale=5).pdf
tau_linspace = np.linspace(-2, 30, 2000)
f, (ax1, ax2) = plt.subplots(1, 2)
sns.kdeplot(mcmc_trace['mu'][1000:], color='steelblue', ax=ax1, label=r'kde($\mu$)')
count, bins, ignored = ax1.hist(mcmc_trace['mu'][1000:], 50, density=True, color='skyblue', alpha=0.6)
ax1.plot(mu_linspace, mu_true_pdf(mu_linspace), color='firebrick', label=r'$\mathcal{N}(0,5)$')
ax1.title.set_text(r'Distribution $\mu$')
ax1.set_xlabel(r'$\mu$')
ax1.set_ylabel(r'p($\mu$)')
ax1.legend()
sns.kdeplot(mcmc_trace['tau'][1000:], color='steelblue', ax=ax2, label=r'kde($\tau$)')
count, bins, ignored = ax2.hist(mcmc_trace['tau'][1000:], 50, density=True, color='skyblue', alpha=0.6)
ax2.plot(tau_linspace, tau_true_pdf(tau_linspace), color='firebrick', label=r'Half-Cauchy$(0,5)$')
ax2.title.set_text(r'Distribution $\tau$')
n_bs = 5
q = 95
ln_par, ln_lo, ln_up = bootstrap_fit(
stats.lognorm, resid, n_iter=n_bs, quant=q
)
hc_par, hc_lo, hc_up = bootstrap_fit(
stats.halfcauchy, resid, n_iter=n_bs, quant=q
)
gam_par, gam_lo, gam_up = bootstrap_fit(
stats.gamma, resid, n_iter=n_bs, quant=q
)
##################################################################
hc = stats.halfcauchy(*stats.halfcauchy.fit(resid))
lg = stats.lognorm(*stats.lognorm.fit(resid))
dens = KDEUnivariate(resid)
dens.fit()
ecdf = ECDF(resid)
##################################################################
# prepare X axes for plotting
ex = ecdf.x
x = np.linspace(min(resid), max(resid), 2000)
##################################################################
# Fit a Landau distribution with ROOT
if HAS_ROOT:
