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

knitr::opts_chunk$set(echo = TRUE)

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 $\theta_1,\dots,\theta_m\in{0,1}$. In our settings $\theta_i=0/1$ for the absence / presence of a given \og signal\fg at the position $i$ of the series.

Our goal is to provide an confidences bounds at levels $1 - \beta$ 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)
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 $x_i$, for $1 \leq i \leq m$, $x_i$ can be a statistics comparing the DNA copy number at position $i$. The law of $x$ depend of the $\theta$.

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.