This vignettes demonstrates how to fit a Bayesian variable selection model using **varbvs** to identify genetic markers associated with Crohn’s disease risk. The data consist of 442,001 SNPs genotyped for 1,748 cases and 2,938 controls. Note that file `cd.RData`

cannot be made publicly available due to data sharing restrictions, so this vignette is for viewing only.

Begin by loading a couple packages into the R environment.

```
library(lattice)
library(varbvs)
```

Set the random number generator seed.

`set.seed(1)`

`load("cd.RData")`

Here we fit the fully-factorized variational approximation to the posterior distribution of the coefficients for a logistic regression model of a binary outcome (case-control status), with spike and slab priors on the coefficients.

```
r <- system.time(fit <- varbvs(X,NULL,y,family = "binomial",
logodds = seq(-6,-3,0.25),n0 = 0)
cat(sprintf("Model fitting took %0.2f minutes.\n",r["elapsed"]/60))
```

Compute “single-marker” posterior inclusion probabilities.

`pip <- c(varbvsindep(fit,X,NULL,y)$alpha %*% fit$w)`

```
save(list = c("fit","map","pip","r"),
file = "varbvs.demo.cd.RData")
```

`print(summary(fit,nv = 9))`

Show two “genome-wide scans”, one using the posterior inclusion probabilities (PIPs) computed in the joint analysis of all variables, and one using the PIPs that ignore correlations between the variables. The latter is meant to look like a typical genome-wide “Manhattan” plot used to summarize the results of a genome-wide association study. Variables with `PIP > 0.5`

are highlighted.

```
i <- which(fit$pip > 0.5)
var.labels <- paste0(round(map$pos[i]/1e6,digits = 2),"Mb")
print(plot(fit,groups = map$chr,vars = i,var.labels = var.labels,gap = 7500,
ylab = "posterior prob."),
split = c(1,1,1,2),more = TRUE)
print(plot(fit,groups = map$chr,score = log10(pip + 0.001),vars = i,
var.labels = var.labels,gap = 7500,ylab = "log10 posterior prob."),
split = c(1,2,1,2),more = FALSE)
```