# Manuscript results¶

Selective inference for a toy example
Here we investigate "selective inference" in the toy example of Wang et al (2018). We show that the approach will sometimes select the wrong variables -- which is inevitable in cases where variables are perfectly correlated -- and then assign them highly significant $p$ values. This is because even though the wrong variables are selected, their coefficients within the wrong model can be estimated precisely.

A pedagogical example of fine-mapping problem
Here we demonstrate with simulated data a setting of fine-mapping problem where it is clearly problematic to run forward stagewise selection, but SuSiE's Iterative Bayesian Stepwise Selection procedure can correctly identify the causal signals and compute posterior inclusion probability (posterior mean from a variational approximation to the posterior distribution). We also compared SuSiE results with other Bayesian sparse regression approach, and demonstrate that SuSiE is robust to prior choice and provide information more relevant to fine-mapping applications that other methods do not provide.

Numerical Comparisons
This page contains information to reproduce the numerical comparisons in SuSiE manuscript.

Experiment with variables of given high correlation structure
This notebook is meant to address to a shared concern from two referees. The motivating example in the manuscript was designed to be a simple toy for illustrating the novel type of inference SuSiE offers. Here are some slightly more complicated examples, based on the motivating example, but with variables in high (rather than perfect) correlations with each other.

A demonstration of SuSiE's motivations
This document explains with toy example illustration the unique type of inference SuSiE is interested in. For a more complicated where variables are in high but not perfect correlation please see this notebook.

Application to change point detection problem
Although we developed SuSiE primarily with the goal of performing variable selection in highly sparse settings -- and, in particular, for genetic fine-mapping -- the approach also has considerable potential for application to other large-scale regression problems. Here we briefly illustrate this potential by applying it to a non-parametric regression problem that at first sight seems to be ill-suited to our approach.

Splicing QTL analysis: application to Li et al 2016
In Li et al 2016 the authors systematically analyzed genetic effects (SNPs) on various molecular phenotypes of gene regulation, from the chromatin state through protein function.

Individual-level genotype-expression data preprocessing for association analysis
This pipeline aims to extract individual-level genotype-expression data in preparation for cis-eQTL fine-mapping. It was written by Jiarun Chen (Tsinghua U.) advised by Gao Wang.

© 2017-2018 authored by Gao Wang at Stephens Lab, The University of Chicago