object Probability extends Error
The Probability object provides methods for operating on univariate and
bivariate probability distributions of discrete random variables 'X' and 'Y'.
A probability distribution is specified by its probability mass functions (pmf)
stored either as a "probability vector" for a univariate distribution or
a "probability matrix" for a bivariate distribution.
joint probability matrix: pxy(i, j) = P(X = x_i, Y = y_j) marginal probability vector: px(i) = P(X = x_i) conditional probability matrix: px_y(i, j) = P(X = x_i|Y = y_j)
In addition to computing joint, marginal and conditional probabilities, methods for computing entropy and mutual information are also provided. Entropy provides a measure of disorder or randomness. If there is little randomness, entropy will close to 0, while when randomness is high, entropy will be close to, e.g., 'log2 (px.dim)'. Mutual information provides a robust measure of dependency between random variables (contrast with correlation).
- See also
scalation.stat.StatVector
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def
condProbX_Y(pxy: MatriD): MatriD
Given a joint probability matrix 'pxy', compute the "conditional probability" for random variable 'X' given random variable 'Y', i.e, P(X = x_i|Y = y_j).
Given a joint probability matrix 'pxy', compute the "conditional probability" for random variable 'X' given random variable 'Y', i.e, P(X = x_i|Y = y_j).
- pxy
the joint probability matrix
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def
condProbY_X(pxy: MatriD): MatriD
Given a joint probability matrix 'pxy', compute the "conditional probability" for random variable 'Y' given random variable 'X', i.e, P(Y = y_j|X = x_i).
Given a joint probability matrix 'pxy', compute the "conditional probability" for random variable 'Y' given random variable 'X', i.e, P(Y = y_j|X = x_i).
- pxy
the joint probability matrix
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def
entropy(pxy: MatriD, px_y: MatriD): Double
Given a joint probability matrix 'pxy' and a conditional probability matrix 'py_x', compute the "conditional entropy" of random variable 'X' given random variable 'Y'.
Given a joint probability matrix 'pxy' and a conditional probability matrix 'py_x', compute the "conditional entropy" of random variable 'X' given random variable 'Y'.
- pxy
the joint probability matrix
- px_y
the conditional probability matrix
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def
entropy(pxy: MatriD): Double
Given a joint probability matrix 'pxy', compute the "joint entropy" of random variables 'X' and 'Y'.
Given a joint probability matrix 'pxy', compute the "joint entropy" of random variables 'X' and 'Y'.
- pxy
the joint probability matrix
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def
entropy(px: VectoD): Double
Given a probability vector 'px', compute the "entropy" of random variable 'X'.
Given a probability vector 'px', compute the "entropy" of random variable 'X'.
- px
the probability vector
- See also
http://en.wikipedia.org/wiki/Entropy_%28information_theory%29
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def
entropy_k(px: VectoD): Double
Given a probability vector 'px', compute the "base-k entropy" of random variable 'X'.
Given a probability vector 'px', compute the "base-k entropy" of random variable 'X'.
- px
the probability vector
- See also
http://en.wikipedia.org/wiki/Entropy_%28information_theory%29
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final
def
flaw(method: String, message: String): Unit
- Definition Classes
- Error
-
def
isProbability(pxy: MatriD): Boolean
Determine whether the matrix 'pxy' is a legitimate joint "probability matrix".
Determine whether the matrix 'pxy' is a legitimate joint "probability matrix". The elements of the matrix must be non-negative and add to one.
- pxy
the probability matrix
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def
isProbability(px: VectoD): Boolean
Determine whether the vector 'px' is a legitimate "probability vector".
Determine whether the vector 'px' is a legitimate "probability vector". The elements of the vector must be non-negative and add to one.
- px
the probability vector
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def
jointProbXY(px: VectoD, py: VectoD): MatriD
Given two independent random variables 'X' and 'Y', compute their "joint probability", which is the outer product of their probability vectors 'px' and 'py', i.e., P(X = x_i, Y = y_j).
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def
margProbX(pxy: MatriD): VectoD
Given a joint probability matrix 'pxy', compute the "marginal probability" for random variable 'X', i.e, P(X = x_i).
Given a joint probability matrix 'pxy', compute the "marginal probability" for random variable 'X', i.e, P(X = x_i).
- pxy
the probability matrix
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def
margProbY(pxy: MatriD): VectoD
Given a joint probability matrix 'pxy', compute the "marginal probability" for random variable 'Y', i.e, P(Y = y_j).
Given a joint probability matrix 'pxy', compute the "marginal probability" for random variable 'Y', i.e, P(Y = y_j).
- pxy
the probability matrix
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def
muInfo(pxy: MatriD): Double
Given a joint probability matrix 'pxy', compute the mutual information for random variables 'X' and 'Y'.
Given a joint probability matrix 'pxy', compute the mutual information for random variables 'X' and 'Y'.
- pxy
the probability matrix