def __init__(self, log_pdf, xlo, xhi, nx, step='linear'):
"""
Initialize the HPDGrid1D object.
:Parameters:
log_pdf : float function of scalar argument
Function returning log pdf value log_pdf(x)
xlo, xhi : float
Range spanned by logpdf
nx : int
Number of points in the logpdf grid
step : 'linear' OR 'lin' OR 'logarithmic' OR 'log'
'linear' for a grid linear in x; 'log' for a grid linear in log(x)
"""
self.log_pdf = log_pdf
xlo, xhi = float(xlo), float(xhi)
self.xlo, self.xhi = xlo, xhi
self.nx = nx
if step == 'linear' or step=='lin':
self.linstep = True
self.xvals = array( [x for x in lin_stepper(xlo, xhi, self.nx)] )
self.dx = (xhi-xlo)/(self.nx-1)
elif step=='log' or step=='logarithmic':
self.linstep = False
self.xvals = [x for x in log_stepper(xlo, xhi, self.nx)]
self.dx = log(xhi/xlo)/(self.nx-1)
else:
raise ValueError, 'Invalid step type!'
logpdf = zeros(nx, float)
for i, x in enumerate(self.xvals):
logpdf[i] = log_pdf(x)
self.logpdf = logpdf
self.max = logpdf.max()
self.spdf = exp(logpdf-self.max) # scaled PDF
# For log steps, change variables to log(x).
if not self.linstep:
for i, x in enumerate(self.xvals):
self.spdf[i] = self.spdf[i]*x
# Find the overall normalization for spdf.
self.snorm = qgt1d(self.spdf, self.spdf.min())*self.dx
# lml is the log marginal likelihood if logpdf = prior*like.
self.lml = log(self.snorm) + self.max
self.probs = []
self.deltas = []
self.levels = []
self.bounds = []
def __init__(self, logpdf, xlo, xhi, step='linear'):
"""
Initialize the HPDGrid1D object.
:Parameters:
logpdf : float array
Array of log pdf values
xlo, xhi : float
Range spanned by logpdf
step : 'linear' OR 'lin' OR 'logarithmic' OR 'log'
'linear' for a grid linear in x; 'log' for a grid linear in log(x)
"""
if len(logpdf.shape) != 1:
raise ValueError, 'logpdf array must be 1-d!'
self.logpdf = logpdf
self.xlo, self.xhi = xlo, xhi
self.nx = logpdf.shape[0]
if step == 'linear' or step=='lin':
self.linstep = True
self.xvals = array( [x for x in lin_stepper(xlo, xhi, self.nx)] )
self.dx = (xhi-xlo)/(self.nx-1.)
elif step=='log' or step=='logarithmic':
self.linstep = False
self.xvals = [x for x in log_stepper(xlo, xhi, self.nx)]
self.dx = log(xhi/xlo)/(self.nx-1)
else:
raise ValueError, 'Invalid step type!'
self.max = logpdf.max()
self.spdf = exp(logpdf-self.max) # scaled PDF
# For log steps, change variables to log(x).
if not self.linstep:
for i, x in enumerate(self.xvals):
self.spdf[i] = self.spdf[i]*x
# Find the overall normalization for spdf.
self.snorm = qgt1d(self.spdf, self.spdf.min())*self.dx
# lml is the log marginal likelihood if logpdf = prior*like.
self.lml = log(self.snorm) + self.max
self.probs = []
self.deltas = []
self.levels = []
self.bounds = []
def fracgt(self, logratio):
"""
The fraction of the posterior with log density > maximum + logratio.
"""
ratio = exp(logratio)
return qgt1d(self.spdf, ratio)*self.dx/self.snorm