admix (version 2.4.2)

decontaminated_density: Probability density function of the unknown component

Description

Estimate the decontaminated density of the unknown component in the admixture model under study, after inversion of the admixture cumulative distribution function. Recall that an admixture model follows the cumulative distribution function (CDF) L, where L = p*F + (1-p)*G, with g a known CDF and p and f unknown quantities.

Usage

decontaminated_density(sample1, estim.p, admixMod)

Value

An object of class 'decontaminated_density', containing 3 attributes: 1) the data under study; 2) the type of support for the underlying distribution (either discrete or continuous, useful for plots); 3) the decontaminated density function.

Arguments

sample1

Sample under study.

estim.p

The estimated weight, related to the proportion of the unknown component distribution in the admixture model studied.

admixMod

An object of class 'admix_model', containing useful information about known distribution(s) and parameter(s).

Author

Xavier Milhaud

Details

The decontaminated density is obtained by inverting the admixture density, given by l = p*f + (1-p)*g, to isolate the unknown component f after having estimated p.

Examples

## Simulate mixture data:
mixt1 <- twoComp_mixt(n = 400, weight = 0.4,
                      comp.dist = list("norm", "norm"),
                      comp.param = list(list("mean" = -2, "sd" = 0.5),
                                        list("mean" = 0, "sd" = 1)))
data1 <- getmixtData(mixt1)
## Define the admixture models:
admixMod1 <- admix_model(knownComp_dist = mixt1$comp.dist[[2]],
                         knownComp_param = mixt1$comp.param[[2]])
## Estimation:
est <- admix_estim(samples = list(data1), admixMod = list(admixMod1),
                   est_method = 'PS')
## Determine the decontaminated version of the unknown density by inversion:
decontaminated_density(sample1 = data1, estim.p = est$estimated_mixing_weights[1],
                       admixMod = admixMod1)

####### Discrete support:
mixt1 <- twoComp_mixt(n = 5000, weight = 0.6,
                      comp.dist = list("pois", "pois"),
                      comp.param = list(list("lambda" = 3),
                                        list("lambda" = 2)))
mixt2 <- twoComp_mixt(n = 4000, weight = 0.8,
                      comp.dist = list("pois", "pois"),
                      comp.param = list(list("lambda" = 3),
                                        list("lambda" = 4)))
data1 <- getmixtData(mixt1)
data2 <- getmixtData(mixt2)
## Define the admixture models:
admixMod1 <- admix_model(knownComp_dist = mixt1$comp.dist[[2]],
                         knownComp_param = mixt1$comp.param[[2]])
admixMod2 <- admix_model(knownComp_dist = mixt2$comp.dist[[2]],
                         knownComp_param = mixt2$comp.param[[2]])
## Estimation:
est <- admix_estim(samples = list(data1, data2),
                   admixMod = list(admixMod1, admixMod2), est_method = 'IBM')
## Determine the decontaminated version of the unknown density by inversion:
decontaminated_density(sample1 = data1, estim.p = est$estimated_mixing_weights[1],
                       admixMod = admixMod1)

####### Finite discrete support:
mixt1 <- twoComp_mixt(n = 12000, weight = 0.6,
                      comp.dist = list("multinom", "multinom"),
                      comp.param = list(list("size" = 1, "prob" = c(0.3,0.4,0.3)),
                                        list("size" = 1, "prob" = c(0.6,0.3,0.1))))
mixt2 <- twoComp_mixt(n = 10000, weight = 0.8,
                      comp.dist = list("multinom", "multinom"),
                      comp.param = list(list("size" = 1, "prob" = c(0.3,0.4,0.3)),
                                        list("size" = 1, "prob" = c(0.2,0.6,0.2))))
data1 <- getmixtData(mixt1)
data2 <- getmixtData(mixt2)
## Define the admixture models:
admixMod1 <- admix_model(knownComp_dist = mixt1$comp.dist[[2]],
                         knownComp_param = mixt1$comp.param[[2]])
admixMod2 <- admix_model(knownComp_dist = mixt2$comp.dist[[2]],
                         knownComp_param = mixt2$comp.param[[2]])
## Estimation:
est <- admix_estim(samples = list(data1, data2),
                   admixMod = list(admixMod1, admixMod2), est_method = 'IBM')
## Determine the decontaminated version of the unknown density by inversion:
decontaminated_density(sample1 = data1, estim.p = est$estimated_mixing_weights[1],
                       admixMod = admixMod1)