def discrete_uniform(x, lower=0, upper=1):
""" Discrete Uniform distribution log-likelihood.
:param x: *int, np.array[int].*
:param lower: (optional) *int, float.* Lower bound, default is 0.
:param upper: (optional) *int, float.* Upper bound, default is 1.
.. math ::
\log{P(x; a, b)} = -n\log(b-a)
"""
if fails_constraints(x >= lower, x <= upper):
return -np.inf
if isinstance(x, np.ndarray):
if x.dtype != np.int_:
raise ValueError(
'x must be integers, function received {}'.format(x))
else:
return -np.size(x) * np.log(upper - lower)
elif isinstance(x, numbers.Integral):
return -np.log(upper - lower)
else:
return -np.inf
def poisson(x, rate=1):
""" Poisson distribution log-likelihood.
:param x: *int, float, np.array.* Event count.
:param rate: (optional) *int, float, np.array.* Rate parameter, :math:`\lambda > 0`. Defaults to 1.
.. math ::
\log{P(x; \lambda)} \propto x \log{\lambda} - \lambda
"""
if fails_constraints(rate > 0):
return -np.inf
if np.size(rate) != 1 and len(x) != len(rate):
raise ValueError('If rate is a vector, x must be the same size as rate.'
' We got x={}, rate={}'.format(x, rate))
return np.sum(x*np.log(rate)) - np.size(x)*rate
def poisson(x, rate=1):
""" Poisson distribution log-likelihood.
:param x: *int, float, np.array.* Event count.
:param rate: (optional) *int, float, np.array.* Rate parameter, :math:`\lambda > 0`. Defaults to 1.
.. math ::
\log{P(x; \lambda)} \propto x \log{\lambda} - \lambda
"""
if outofbounds(rate > 0):
return -np.inf
if np.size(rate) != 1 and len(x) != len(rate):
raise ValueError('If rate is a vector, x must be the same size as rate.'
' We got x={}, rate={}'.format(x, rate))
return np.sum(x*np.log(rate)) - np.size(x)*rate
def uniform(x, lower=0, upper=1):
""" Uniform distribution log-likelihood. Bounds are inclusive.
:param x: *int, float, np.array.*
:param lower: (optional) *int, float.* Lower bound, default is 0.
:param upper: (optional) *int, float.* Upper bound, default is 1.
.. math ::
\log{P(x; a, b)} = -n\log(b-a)
"""
if fails_constraints(x >= lower, x <= upper):
return -np.inf
return -np.size(x) * np.log(upper - lower)
def uniform(x, lower=0, upper=1):
""" Uniform distribution log-likelihood. Bounds are inclusive.
:param x: *int, float, np.array.*
:param lower: (optional) *int, float.* Lower bound, default is 0.
:param upper: (optional) *int, float.* Upper bound, default is 1.
.. math ::
\log{P(x; a, b)} = -n\log(b-a)
"""
if outofbounds(x >= lower, x <= upper):
return -np.inf
return -np.size(x) * np.log(upper-lower)
def exponential(x, rate=1):
""" Log likelihood of the exponential distribution.
:param x: *int, float, np.array.*
:param rate: (optional) *int, float, np.array.* Rate parameter, :math:`\lambda > 0`. Defaults to 1.
.. math ::
\log{P(x; \lambda)} \propto \log{\lambda} - \lambda x
"""
if outofbounds(rate > 0):
return -np.inf
if np.size(rate) != 1 and len(x) != len(rate):
raise ValueError('If rate is a vector, x must be the same size as rate.'
' We got x={}, rate={}'.format(x, rate))
return np.sum(np.log(rate) - rate*x)
def exponential(x, rate=1):
""" Log likelihood of the exponential distribution.
:param x: *int, float, np.array.*
:param rate: (optional) *int, float, np.array.* Rate parameter, :math:`\lambda > 0`. Defaults to 1.
.. math ::
\log{P(x; \lambda)} \propto \log{\lambda} - \lambda x
"""
if fails_constraints(x > 0, rate > 0):
return -np.inf
if np.size(rate) != 1 and len(x) != len(rate):
raise ValueError('If rate is a vector, x must be the same size as rate.'
' We got x={}, rate={}'.format(x, rate))
return np.sum(np.log(rate) - rate*x)
def normal(x, mu=0, sig=1):
""" Normal distribution log-likelihood.
:param x: *int, float, np.array.*
:param mu: (optional) *int, float, np.array.*
Location parameter of the normal distribution. Defaults to 0.
:param sig: (optional) *int, float.*
Standard deviation of the normal distribution, :math:`\sigma > 0`.
Defaults to 1.
.. math::
\log{P(x; \mu, \sigma)} \propto -\log{\sigma} \
- \\frac{(x - \mu)^2}{2 \sigma^2}
"""
if np.size(mu) != 1 and len(x) != len(mu):
raise ValueError('If mu is a vector, x must be the same size as mu.'
' We got x={}, mu={}'.format(x, mu))
return np.sum(-np.log(sig) - (x - mu)**2/(2*sig**2))
def normal(x, mu=0, sig=1):
""" Normal distribution log-likelihood.
:param x: *int, float, np.array.*
:param mu: (optional) *int, float, np.array.*
Location parameter of the normal distribution. Defaults to 0.
:param sig: (optional) *int, float.*
Standard deviation of the normal distribution, :math:`\sigma > 0`.
Defaults to 1.
.. math::
\log{P(x; \mu, \sigma)} \propto -\log{\sigma} \
- \\frac{(x - \mu)^2}{2 \sigma^2}
"""
if np.size(mu) != 1 and len(x) != len(mu):
raise ValueError('If mu is a vector, x must be the same size as mu.'
' We got x={}, mu={}'.format(x, mu))
return np.sum(-np.log(sig) - (x - mu)**2 / (2 * sig**2))
def discrete_uniform(x, lower=0, upper=1):
""" Discrete Uniform distribution log-likelihood.
:param x: *int, np.array[int].*
:param lower: (optional) *int, float.* Lower bound, default is 0.
:param upper: (optional) *int, float.* Upper bound, default is 1.
.. math ::
\log{P(x; a, b)} = -n\log(b-a)
"""
if outofbounds(x >= lower, x <= upper):
return -np.inf
if isinstance(x, np.ndarray):
if x.dtype != np.int_:
raise ValueError('x must be integers, function received {}'.format(x))
else:
return -np.size(x) * np.log(upper-lower)
elif isinstance(x, int) or isinstance(x, np.int_):
return -np.log(upper-lower)
else:
return -np.inf
def size(self):
return State([(var, np.size(self[var])) for var in self])
def size(self):
return State([(var, np.size(self[var])) for var in self])
