|
|
Entwicklerinformationen
|
| libranlip-dev | generates random variates with multivariate Lipschitz density | Mehr ... |
RanLip generates random variates with an arbitrary multivariate
Lipschitz density.
.
While generation of random numbers from a variety of distributions is
implemented in many packages (like GSL library
http://www.gnu.org/software/gsl/ and UNURAN library
http://statistik.wu-wien.ac.at/unuran/), generation of random variate
with an arbitrary distribution, especially in the multivariate case, is
a very challenging task. RanLip is a method of generation of random
variates with arbitrary Lipschitz-continuous densities, which works in
the univariate and multivariate cases, if the dimension is not very
large (say 3-10 variables).
.
Lipschitz condition implies that the rate of change of the function (in
this case, probability density p(x)) is bounded:
.
|p(x)-p(y)| .
From this condition, we can build an overestimate of the density, so
called hat function h(x)>=p(x), using a number of values of p(x) at some
points. The more values we use, the better is the hat function. The
method of acceptance/rejection then works as follows: generatea random
variate X with density h(x); generate an independent uniform on (0,1)
random number Z; if p(X)<=Z h(X), then return X, otherwise repeat all
the above steps.
.
RanLip constructs a piecewise constant hat function of the required
density p(x) by subdividing the domain of p (an n-dimensional rectangle)
into many smaller rectangles, and computes the upper bound on p(x)
within each of these rectangles, and uses this upper bound as the value
of the hat function. |
| libranlip1c2 | generates random variates with multivariate Lipschitz density | Mehr ... |
RanLip generates random variates with an arbitrary multivariate
Lipschitz density.
.
While generation of random numbers from a variety of distributions is
implemented in many packages (like GSL library
http://www.gnu.org/software/gsl/ and UNURAN library
http://statistik.wu-wien.ac.at/unuran/), generation of random variate
with an arbitrary distribution, especially in the multivariate case, is
a very challenging task. RanLip is a method of generation of random
variates with arbitrary Lipschitz-continuous densities, which works in
the univariate and multivariate cases, if the dimension is not very
large (say 3-10 variables).
.
Lipschitz condition implies that the rate of change of the function (in
this case, probability density p(x)) is bounded:
.
|p(x)-p(y)| .
From this condition, we can build an overestimate of the density, so
called hat function h(x)>=p(x), using a number of values of p(x) at some
points. The more values we use, the better is the hat function. The
method of acceptance/rejection then works as follows: generatea random
variate X with density h(x); generate an independent uniform on (0,1)
random number Z; if p(X)<=Z h(X), then return X, otherwise repeat all
the above steps.
.
RanLip constructs a piecewise constant hat function of the required
density p(x) by subdividing the domain of p (an n-dimensional rectangle)
into many smaller rectangles, and computes the upper bound on p(x)
within each of these rectangles, and uses this upper bound as the value
of the hat function. |
|
|
|
