Bayesian Entropy Estimate

Description

Computing the Maximul Likelihood Entropy Estimate of cellCounts.

Usage

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entropyBayes(cellCounts, unit = unit,
            priorHyperParam = priorHyperParam)

Arguments

cellCounts

an integer vector (or matrix) representing the number of times each particular count is obtained.

unit

the unit in which entropy is measured. One of "bit" (log2, default), "ban" (log10) or "nat" (natural units).

priorHyperParam

the prior distribution type for the Bayes estimation. One of "Jeffreys" (default, Jeffreys Prior, Krichevsky and Trofimov Estimator), "BLUnif" (Bayes-Laplace uniform Prior, Holste Estimator), "Perks" (Perks Prior, Schurmann and Grassberger Estimator), or "MiniMax" (MiniMax Prior), can be abbreviated.

Value

The entropyBayes function returns the value of the entropy of that gene H(X) (or pair of genes H(X,Y)).

Author(s)

Luciano Garofano lucianogarofano88@gmail.com, Stefano Maria Pagnotta, Michele Ceccarelli

References

Jeffreys H. (1946). An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London, vol. 186 no. 1007 pp. 453-461.

Krichevsky R.E., Trofimov V.K. (1981). The performance of universal encoding. IEEE Transactions on Information Theory, vol. 27 pp. 199-207.

Holste D., Hertzel H. (1998). Bayes' estimators of generalized entropies. Journal of Physics A, vol. 31 pp. 2551-2566.

Perks W. (1947). Some observations on inverse probability including a new indifference rule. Journal of the Institute of Actuaries, vol. 73 pp. 285-334.

Schurmann T., Grassberg P. (1996). Entropy estimation of symbol sequences. Chaos, vol. 6 pp. 414-427.

Trybula S. (1958). Some problems of simultaneous minimax estimation. The Annals of Mathematical Statistics, vol. 29 pp. 245-253.

See Also

entropyML, entropyMM, entropyCS, entropyShrink

Examples

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simData <- simulatedData(p = 50, n = 100, mu = 100, sigma = 0.25,
                        ppower = 0.73, noise = FALSE)
cellCounts <- table(simData$counts[1, ])
eBJ <- entropyBayes(cellCounts, unit = "nat", priorHyperParam = "Jeffreys")
eBB <- entropyBayes(cellCounts, unit = "nat", priorHyperParam = "BLUnif")
eBP <- entropyBayes(cellCounts, unit = "nat", priorHyperParam = "Perks")
eBM <- entropyBayes(cellCounts, unit = "nat", priorHyperParam = "MiniMax")