README.md

In Marie-PerrotDockes/sanssouci.hmm: Confindence bound on the FDP after post-selection under an HMM

This package provides confidences bounds on the false discovery proportion after a post selection, under a Hidden MArkov Model settings.

Introduction

In this scenario we observe a series of m mesures $X_1,\dots,X_m \in\R$ comming from a law depending on hiden states θ1, …, θm ∈ {0, 1}. In our settings θi = 0/1 for the absence / presence of a given signalat the position i of the series.

Our goal is to provide an confidences bounds at levels 1 − β of $$ FDP(S(X))= \sum_{i\in S(X)} \frac{(1-\theta_i)}{\|S(X)\|}, $$ for any $S\subseteq \Nm:=\1,\dots,m\$. This quantity is the number of position in S(X) where there is no signals, this will be call in the remaining of this vignette the number of false positive.

Install the package

devtools::install_github("Marie-PerrotDockes/sanssouci.hmm")

library(tidyverse)

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library(hmm.sanssouci)

A toy example

In this toy example we have m = 2000 simulations and we assume that the hypothesis are naturally ordered. For instance in a setting of test betwen two groups along the genome. We have statistics xi, for 1 ≤ i ≤ m, xi can be a statistics comparing the DNA copy number at position i. The law of x depend of the θ.

m <- 2000
theta <- sim_markov(m, Pi = c(0.8,0.2), A = matrix(c(0.95, 0.05, 0.2, 0.80), 2, 2, byrow = T))
x <- rep(0, m)
x[theta == 0] <- rnorm(sum(theta ==0))
x[theta == 1] <- rnorm(sum(theta ==1), 2, 1)

The package provides a function to calculate different bounds available (here with a risk alpha = 10%) in our article and a function ploting the main bounds proposed in the article.

Final <- sanssouci.hmm(x, al= 0.1, sel_function = Selection_delta) 

plot_IC(Final)

A toy simulation

One can also add simulation studies.

Test <- simu_delta( m = c(1000),
                    A = matrix(c(0.95, 0.05, 0.2, 0.80), 2, 2, byrow = T),
                    Pi = c(0.95, 0.05),
                    rho = c(0),
                    SNR = 2,
                    prob = c(0.5),
                    type_sim = c("HMM"),
                    n_boot = 20,
                    al = 0.2, s_dbnr = 10, b_act = 2, d = 1, seuil= 0.05,
                    min_size = 2, norm = TRUE, sd0 = 0.5, m0= 0,sd0_init = 0.5, m0_init= 0,
                    norm_init = TRUE, df= 2, num_seed= 1234, type_init="given", f0_known=TRUE,
                    approx = TRUE, delta = 0.9)

test_mf<- mise_en_forme(Test)
plot_IC(test_mf, sim = TRUE)

Marie-PerrotDockes/sanssouci.hmm documentation built on Oct. 26, 2023, 10:36 a.m.