/usr/include/openturns/swig/MCMC_doc.i is in libopenturns-dev 1.5-7build2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 | %feature("docstring") OT::MCMC
"Monte-Carlo Markov Chain.
Available constructor:
MCMC(*prior, conditional, observations, initialState*)
MCMC(*prior, conditional, model, parameters, observations, initialState*)
Parameters
----------
prior : :class:`~openturns.Distribution`
Prior distribution of the parameters of the underlying Bayesian statistical
model.
conditional : :class:`~openturns.Distribution`
Required distribution to define the likelihood of the underlying Bayesian
statistical model.
model : :class:`~openturns.NumericalMathFunction`
Function required to define the likelihood.
observations : 2D float sequence
Observations required to define the likelihood.
initialState : float sequence
Initial state of the Monte-Carlo Markov chain on which the Sampler is
based.
parameters : 2D float sequence
Parameters of the model to be fixed.
Notes
-----
MCMC provides a implementation of the concept of sampler, using a Monte-Carlo
Markov Chain (MCMC) algorithm starting from *initialState*. More precisely,
let :math:`t(.)` be the PDF of its target distribution and :math:`d_{\\\\theta}`
its dimension, :math:`\\\\pi(.)` be the PDF of the *prior* distribution,
:math:`f(.|\\\\vect{w})` be the PDF of the *conditional* distribution
when its parameters are set to :math:`\\\\vect{w}`, :math:`d_w` be the number of
scalar parameters of *conditional* distribution (which corresponds to the
dimension of the above :math:`\\\\vect{w}`), :math:`g(.)` be the function
corresponding to model and :math:`(\\\\vect{y}^1, \\\\dots, \\\\vect{y}^n)` be the
sample *observations* (of size :math:`n`):
In the first usage, it creates a sampler based on a MCMC algorithm whose target
distribution is defined by:
.. _PDF_target_formula:
.. math::
t(\\\\vect{\\\\theta})
\\\\quad \\\\propto \\\\quad
\\\\underbrace{~\\\\pi(\\\\vect{\\\\theta})~}_{\\\\mbox{prior}} \\\\quad
\\\\underbrace{~\\\\prod_{i=1}^n f(\\\\vect{y}^i|\\\\vect{\\\\theta})~}_{\\\\mbox{likelihood}}
In the first usage, it creates a sampler based on a MCMC algorithm whose target
distribution is defined by:
.. _second_PDF_target_formula:
.. math::
t(\\\\vect{\\\\theta})
\\\\quad \\\\propto \\\\quad
\\\\underbrace{~\\\\pi(\\\\vect{\\\\theta})~}_{\\\\mbox{prior}} \\\\quad
\\\\underbrace{~\\\\prod_{i=1}^n f(\\\\vect{y}^i|g^i(\\\\vect{\\\\theta}))~}_{\\\\mbox{likelihood}}
where the :math:`g^i: \\\\Rset^{d_{\\\\theta}} \\\\rightarrow\\\\Rset^{d_w}`
(:math:`1\\\\leq{}i\\\\leq{}n`) are such that:
.. math::
\\\\begin{array}{rcl}
g:\\\\Rset^{d_\\\\theta} & \\\\longrightarrow & \\\\Rset^{n\\\\,d_w}\\\\\\\\
\\\\vect{\\\\theta} & \\\\longmapsto &
g(\\\\vect{\\\\theta}) = \\\\Tr{(\\\\Tr{g^1(\\\\vect{\\\\theta})}, \\\\cdots, \\\\Tr{g^n(\\\\vect{\\\\theta})})}
\\\\end{array}
In fact, the first usage is a particular case of the second.
The MCMC method implemented in OpenTURNS is the Random Walk Metropolis-Hastings
algorithm. A sample can be generated only through the MCMC's derived class:
:class:`~openturns.RandomWalkMetropolisHastings`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::computeLogLikelihood
"Compute the logarithm of the likelihood w.r.t. observations.
Parameters
----------
currentState : float sequence
Current state.
Returns
-------
logLikelihood : float
Logarithm of the likelihood w.r.t. observations
:math:`(\\\\vect{y}^1, \\\\dots, \\\\vect{y}^n)`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::getBurnIn
"Get the length of the burn-in period.
Returns
-------
lenght : int
Length of the burn-in period, that is the number of first iterates of the
MCMC chain which will be thrown away when generating the sample."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::setBurnIn
"Set the length of the burn-in period.
Parameters
----------
lenght : int
Length of the burn-in period, that is the number of first iterates of the
MCMC chain which will be thrown away when generating the sample."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::getConditional
"Get the *conditional* distribution.
Returns
-------
conditional : :class:`~openturns.Distribution`
Distribution taken into account in the definition of the likelihood, whose
PDF with parameters :math:`\\\\vect{w}` corresponds to :math:`f(.|\\\\vect{w})`
in the equations of the
:ref:`target distribution's PDF <PDF_target_formula>`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::getModel
"Get the model.
Returns
-------
model : :class:`~openturns.NumericalMathFunction`
Model take into account in the definition of the likelihood, which
corresponds to :math:`g`, that is the functions :math:`g^i`
(:math:`1\\\\leq i \\\\leq n`) in the equation of the
:ref:`target distribution's PDF <second_PDF_target_formula>`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::getObservations
"Get the observations.
Returns
-------
observations : 2D float sequence
Sample taken into account in the definition of the likelihood, which
corresponds to the :math:`n`-tuple of the :math:`\\\\vect{y}^i`
(:math:`1\\\\leq i \\\\leq n`) in equations of the
:ref:`target distribution's PDF <PDF_target_formula>`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::setObservations
"Set the observations.
Parameters
----------
observations : 2D float sequence
Sample taken into account in the definition of the likelihood, which
corresponds to the :math:`n`-tuple of the :math:`\\\\vect{y}^i`
(:math:`1\\\\leq i \\\\leq n`) in the equations of the
:ref:`target distribution's PDF <PDF_target_formula>`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::getParameters
"Get the parameters.
Returns
-------
parameters : float sequence
Fixed parameters of the model :math:`g` required to define the likelihood."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::setParameters
"Set the parameters.
Parameters
----------
parameters : float sequence
Fixed parameters of the model :math:`g` required to define the likelihood."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::getPrior
"Get the *prior* distribution.
Returns
-------
prior : :class:`~openturns.Distribution`
The prior distribution of the parameter of the underlying Bayesian
statistical model, whose PDF corresponds to :math:`\\\\pi` in the equations of
the :ref:`target distribution's PDF <PDF_target_formula>`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::setPrior
"Set the *prior* distribution.
Parameters
----------
prior : :class:`~openturns.Distribution`
The prior distribution of the parameter of the underlying Bayesian
statistical model, whose PDF corresponds to :math:`\\\\pi` in the equations of
the :ref:`target distribution's PDF <PDF_target_formula>`."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::getThinning
"Get the thinning parameter.
Returns
-------
thinning : integer
Thinning parameter: storing only every :math:`k^{th}` point after the
burn-in period.
Notes
-----
When generating a sample of size :math:`q`, the number of MCMC iterations
performed is :math:`l+1+(q-1)k` where :math:`l` is the burn-in period length
and :math:`k` the thinning parameter."
// ---------------------------------------------------------------------
%feature("docstring") OT::MCMC::setThinning
"Set the thinning parameter.
Parameters
----------
thinning : integer, :math:`k \\\\geq 0`
Thinning parameter: storing only every :math:`k^{th}` point after the
burn-in period.
Notes
-----
When generating a sample of size :math:`q`, the number of MCMC iterations
performed is :math:`l+1+(q-1)k` where :math:`l` is the burn-in period length
and :math:`k` the thinning parameter."
|