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Liknorm's documentation

Estimates

\int_{l}^r \text{ExpFam}(\theta, g(x)) \mathcal{N} (x | \mu, \sigma^2) \mathrm d x

via deterministic numerical integration.

The values l and r are necessarily the lower and upper bound of the likelihood domain. (The user is not allowed to set it.) g(\cdot) is a link function and \theta determines the exponential-family distribution of interest:

Install

You can install it via [conda](http://conda.pydata.org/docs/index.html)

conda install -c conda-forge liknorm

or by cloning this repository and building it

git clone https://github.com/glimix/liknorm.git
cd liknorm
mkdir build
cd build
cmake ..
make
sudo make install

Usage example

Suppose you have the file

/* example.c */
#include "liknorm.h"

#include <stdio.h>

int main()
{
  double log_zeroth, mean, variance;
  double prior_var = 2.5;
  double prior_mean = -2.0;
  double nsuccesses = 2;
  double ntrials = 15;

  LikNormMachine *machine = liknorm_create_machine(500);

  liknorm_set_binomial(machine, nsuccesses, ntrials);
  liknorm_set_prior(machine, 1 / prior_var, prior_mean / prior_var);

  liknorm_integrate(machine, &log_zeroth, &mean, &variance);

  printf("%f\n", log_zeroth);
  printf("%f\n", mean);
  printf("%f\n", variance);

  liknorm_destroy_machine(machine);
}

Compiling, linking, and running it via

cc libliknorm.a example.c -o example
./example

should print:

-2.049961
-2.038184
0.524308

Functions description

.. c:function:: LikNormMachine* liknorm_create_machine(int size)

  Create a Machine instance capable of doing numerical integration.

  :param int size: Number of integration points. ``500`` points should be
                   enough. ``300`` is usually fine too.
  :return: Machine instance to perform integration.
  :rtype: LikNormMachine*


.. c:function:: void liknorm_integrate(LikNormMachine *machine, double *log_zeroth, double *mean, double *variance)

  Perform numerical integration.

  :param LikNormMachine* machine: Machine to perform integration.
  :param double* log_zeroth: Zeroth moment.
  :param double* log_mean: First moment of the normalized distribution.
  :param double* log_variance: Variance of the normalized distribution.


.. c:function:: void liknorm_destroy_machine(LikNormMachine *machine)

  Destroy a Machine instance.

  :param LikNormMachine* machine: Machine to be destroyed. Always call it before
                                 exiting your program, otherwise it will
                                 leak memory.


.. c:function:: void liknorm_set_bernoulli(LikNormMachine *machine, double k)

  Set a Bernoulli likelihood.

  :param LikNormMachine* machine: Machine to perform integration.
  :param double k: ``0`` or ``1`` indicating a Bernoulli outcome.


.. c:function:: void liknorm_set_binomial(LikNormMachine *machine, double k, double n)

  Set a Binomial likelihood.

  :param LikNormMachine* machine: Machine to perform integration.
  :param double k: Number of successes.
  :param double n: Number of trials.


.. c:function:: void liknorm_set_poisson(LikNormMachine *machine, double k)

  Set a Poisson likelihood.

  :param LikNormMachine* machine: Machine to perform integration.
  :param double k: Number of successes.


.. c:function:: void liknorm_set_exponential(LikNormMachine *machine, double x)

  Set a Exponential likelihood.

  :param LikNormMachine* machine: Machine to perform integration.
  :param double x: Time span.


.. c:function:: void liknorm_set_gamma(LikNormMachine *machine, double x, double a)

  Set a Gamma likelihood.

  :param LikNormMachine* machine: Machine to perform integration.
  :param double x: Positive outcome.
  :param double a: Shape parameter.


.. c:function:: void liknorm_set_geometric(LikNormMachine *machine, double x)

  Set a Geometric likelihood.

  :param LikNormMachine* machine: Machine to perform integration.
  :param double x: Number of trials to success.


.. c:function:: void liknorm_set_prior(LikNormMachine *machine, double tau, double eta)

  Set the natural parameters of Normal prior.

  :param LikNormMachine* machine: Machine to perform integration.
  :param double tau: It equals to :math:`\sigma^{-2}`.
  :param double eta: It equals to :math:`\mu \sigma^{-2}`.