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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
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Inherited from |
| Method Details |
Args:
- alpha -- The parameters of the Dirichlet prior distribution.
A vector of non-negative real numbers.
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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)
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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
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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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