Detailed Description

vonMisesSufficient

Probability density function and -log(p) of von Mises distribution of N iid von Mises observations, provided through their sufficient statistics. This is much more efficient than multiplying N von Mises densities.

$f(\chi|N, R_0, \chi_{exp}, \kappa) = \frac{\exp \left(R_0 \kappa \cos (\chi - \chi_{exp})\right)} {2\pi I_0(\kappa)^N}$

where

$R = \sqrt{\left(\sum_{i=1}^N \cos \chi_{exp}^i\right)^2 + \left(\sum_{i=1}^N \cos \chi_{exp}^i\right)^2}$

$\exp (i \chi_{exp}) = \frac{1}{R} \sum_{j=1}^N \exp(i \chi_{exp}^j)$

If $N=1$ and $\mu_1=\mu_2$ this reduces to the original von Mises distribution with known mean and concentration.

Note:: derivative with respect to the mean $\chi_{exp}$ is not provided.

Inheritance diagram for IMP::isd::vonMisesSufficient:

List of all members.

Public Member Functions
	vonMisesSufficient (double chi, unsigned N, double R0, double chiexp, double kappa)
	vonMisesSufficient (double chi, Floats obs, double kappa)
virtual double	density () const
virtual double	evaluate () const
virtual double	evaluate_derivative_kappa () const
virtual double	evaluate_derivative_x () const
double	get_chiexp ()
double	get_kappa ()
double	get_N ()
double	get_R0 ()
double	get_x ()
void	set_chiexp (double chiexp)
void	set_kappa (double kappa)
void	set_N (unsigned N)
void	set_R0 (double R0)
void	set_x (double x)
Public Member Functions inherited from IMP::base::Object
std::size_t	__hash__ () const
virtual std::string	get_type_name () const =0
	Return a string identifying the type of the object.
virtual IMP::base::VersionInfo	get_version_info () const =0
	Get information about the module and version of the object.
void	set_check_level (CheckLevel l)
void	set_log_level (LogLevel l)
	Set the logging level used in this object.
void	set_was_used (bool tf) const
void	show (std::ostream &out=std::cout) const
const std::string &	get_name () const
void	set_name (std::string name)

Static Public Member Functions
static vonMisesSufficient *	get_from (IMP::base::Object *o)
static Floats	get_sufficient_statistics (Floats data)
	Compute sufficient statistics from a list of observations.

Additional Inherited Members
Protected Member Functions inherited from IMP::base::Object
	Object (std::string name)

Constructor & Destructor Documentation

IMP::isd::vonMisesSufficient::vonMisesSufficient	(	double	chi,
		unsigned	N,
		double	R0,
		double	chiexp,
		double	kappa
	)

compute von Mises given the sufficient statistics

Parameters:

[in]	chi
[in]	N	number of observations
[in]	R0	component of N observations on the x axis ( )
[in]	chiexp	mean ( $\chi_{exp}$ )
[in]	kappa	concentration

IMP::isd::vonMisesSufficient::vonMisesSufficient	(	double	chi,
		Floats	obs,
		double	kappa
	)

compute von Mises given the raw observations this is equivalent to calling get_sufficient_statistics and then the other constructor.

Parameters:

[in]	chi
[in]	obs	a list of observed angles (in radians).
[in]	kappa	concentration

Member Function Documentation

static Floats IMP::isd::vonMisesSufficient::get_sufficient_statistics ( Floats data )

static

Compute sufficient statistics from a list of observations.

See Mardia and El-Atoum, "Bayesian inference for the von Mises-Fisher distribution ", Biometrika, 1967.

Returns:: the number of observations, (the component on the x axis) and $\chi_{exp}$

The documentation for this class was generated from the following files:

vonMisesSufficient.h
isd/__init__.py

Detailed Description

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

Member Function Documentation