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Package weblogolib :: Module logomath :: Class Dirichlet

Class Dirichlet

source code

object --+
         |
        Dirichlet

The Dirichlet probability distribution. The Dirichlet is a continuous 
multivariate probability distribution across non-negative unit length
vectors. In other words, the Dirichlet is a probability distribution of 
probability distributions. It is conjugate to the multinomial
distribution and is widely used in Bayesian statistics.

The Dirichlet probability distribution of order K-1 is 

 p(theta_1,...,theta_K) d theta_1 ... d theta_K = 
    (1/Z) prod_i=1,K theta_i^{alpha_i - 1} delta(1 -sum_i=1,K theta_i)

The normalization factor Z can be expressed in terms of gamma functions:

  Z = {prod_i=1,K Gamma(alpha_i)} / {Gamma( sum_i=1,K alpha_i)}  

The K constants, alpha_1,...,alpha_K, must be positive. The K parameters, 
theta_1,...,theta_K are nonnegative and sum to 1.

Status:
    Alpha
Instance Methods
 
__init__(self, alpha)
Args: - alpha -- The parameters of the Dirichlet prior distribution.		 source code
 
sample(self)
Return a randomly generated probability vector.		 source code
 
mean(self) source code
 
covariance(self) source code
 
mean_x(self, x) source code
 
variance_x(self, x) source code
 
mean_entropy(self)
Calculate the average entropy of probabilities sampled from this Dirichlet distribution.		 source code
 
variance_entropy(self)
Calculate the variance of the Dirichlet entropy.		 source code
 
mean_relative_entropy(self, pvec) source code
 
variance_relative_entropy(self, pvec) source code
 
interval_relative_entropy(self, pvec, frac) source code

Inherited from object: __delattr__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __str__

Properties

Inherited from object: __class__

Method Details

__init__(self, alpha)
(Constructor)

source code  

Args:
    - alpha  -- The parameters of the Dirichlet prior distribution.
                A vector of non-negative real numbers.
Overrides: object.__init__

sample(self)

source code  
Return a randomly generated probability vector.

Random samples are generated by sampling K values from gamma
distributions with parameters a=lpha_i, b=1, and renormalizing. 

Ref:
    A.M. Law, W.D. Kelton, Simulation Modeling and Analysis (1991).
Authors:
    Gavin E. Crooks <gec@compbio.berkeley.edu> (2002)

mean_entropy(self)

source code  
Calculate the average entropy of probabilities sampled
from this Dirichlet distribution. 

Returns:
    The average entropy.
    
Ref:
    Wolpert & Wolf, PRE 53:6841-6854 (1996) Theorem 7
    (Warning: this paper contains typos.)
Status:
    Alpha
Authors:
    GEC 2005

variance_entropy(self)

source code  
Calculate the variance of the Dirichlet entropy. 

Ref:
    Wolpert & Wolf, PRE 53:6841-6854 (1996) Theorem 8
    (Warning: this paper contains typos.)

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