Modelling of p-Value Distributions

Beta Uniform Mixture (BUM) Model

Arguments

• π0 : Contributing fraction of the uniform distribution to the full model
• α, β : Parameters of the Beta distribution, Float64, default: 0.5, 3.0

Return values

MixtureModel, as defined in the Distributions package, composed of

• a uniform distribution in the interval [0, 1], with weight/prior π₀
• a Beta distribution with parameters α and β, with weight/prior 1-π₀

Examples

julia> bum = BetaUniformMixtureModel(0.2, 0.5, 1.0);

julia> using Distributions

julia> pdf.(bum, 0.2:0.2:1.0)
5-element Array{Float64,1}:
 1.094427190999916
 0.832455532033676
 0.7163977794943224
 0.647213595499958
 0.6000000000000001

References

Pounds, S., and Morris, S.W. (2003). Estimating the occurrence of false positives and false negatives in microarray studies by approximating and partitioning the empirical distribution of p-values. Bioinformatics 19, 1236–1242.