diff --git a/DESCRIPTION b/DESCRIPTION
index 3f1539d..cd27a32 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,7 +1,7 @@
 Type: Package
 Package: CASE
 Title: Cell-type-specific And Shared EQTL fine-mapping
-Version: 0.2.0
+Version: 0.2.1
 Authors@R: c(
     person("Chen", "Lin", , "c.lin@yale.edu", role = c("aut", "cre"),
            comment = c(ORCID = "0000-0001-9821-2578")),
@@ -16,7 +16,10 @@ Imports:
     magrittr,
     MASS,
     mvtnorm,
-    stats
+    stats,
+    CorBin,
+    mvsusieR,
+    susieR
 Encoding: UTF-8
 RoxygenNote: 7.3.1
 Suggests: 
diff --git a/NAMESPACE b/NAMESPACE
index a56bd87..e44aa47 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -4,14 +4,21 @@ export(CASE)
 export(CASE_test)
 export(CASE_train)
 export(get_credible_sets)
+importFrom(CorBin,cBern)
 importFrom(MASS,ginv)
 importFrom(magrittr,"%>%")
+importFrom(mvsusieR,create_mixture_prior)
+importFrom(mvsusieR,mvsusie_rss)
 importFrom(mvtnorm,rmvnorm)
+importFrom(stats,cor)
 importFrom(stats,cov2cor)
+importFrom(stats,lm)
 importFrom(stats,p.adjust)
 importFrom(stats,pnorm)
 importFrom(stats,qchisq)
 importFrom(stats,qnorm)
 importFrom(stats,quantile)
 importFrom(stats,rmultinom)
+importFrom(stats,rnorm)
 importFrom(stats,sd)
+importFrom(susieR,susie_rss)
diff --git a/R/CASE.R b/R/CASE.R
index 12e1ea4..e0e8d46 100644
--- a/R/CASE.R
+++ b/R/CASE.R
@@ -1,4 +1,4 @@
-#' @title CASE Model
+#' @title CASE
 #' 
 #' @description Perform Multi-trait Fine-mapping
 #' @author Chen Lin, Hongyu Zhao
@@ -77,10 +77,10 @@ CASE <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, V = NULL, cs = TRUE,
     hatS = hatBS$hatS
     
     # V = estimate_null_correlation_simple(mash_set_data(do.call(rbind, raw.data$hatB), do.call(rbind, raw.data$hatS)))
+
+    m1 <- CASE_train(hatB = hatB, hatS = hatS, V = V, R = R, N = N, Z = NULL, ...)
     
-    m1 <- CASE_train(hatB = hatB, hatS = hatS, V = V, R = R, N = N, Z = NULL, list(...))
-    
-    res <- CASE_test(hatB = hatB, hatS = hatS, R = R, N = N, CASE_training = m1, Z = NULL, list(...))
+    res <- CASE_test(hatB = hatB, hatS = hatS, R = R, N = N, CASE_training = m1, Z = NULL, ...)
     t2 = Sys.time()
     res$time = difftime(t2, t1, units = "secs")
     if (cs){
diff --git a/R/CASE_models.R b/R/CASE_models.R
index 4ae60d9..637b543 100644
--- a/R/CASE_models.R
+++ b/R/CASE_models.R
@@ -21,6 +21,8 @@
 CASE_train <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, V = NULL, ...){
   args = list(...)
   
+  cat("Start Prior fitting.", "\n")
+  
   if (is.null(Z)){
     Z = hatB / hatS
   }
@@ -64,8 +66,6 @@ CASE_train <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, V = NULL, ...){
     pi = args$pi.init
     U = args$U.orig
   } else{
-    #print(hatB)
-    #print(hatS)
     init = Initialize_pi_U(hatB, hatS, C, M = nrow(R))
     pi = init$pi
     U = init$U
@@ -89,7 +89,7 @@ CASE_train <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, V = NULL, ...){
   pi.in = M1 / M0
   M <- nrow(R)
   if (M1 == 0){
-    cat("No marginally significant variants.")
+    cat("No marginally significant variants in the inputs.", "\n")
     return(list(pi = 1, U = list(matrix(0, C, C)), V = V, n.iter = 0))
   }
   
@@ -97,7 +97,8 @@ CASE_train <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, V = NULL, ...){
   g <- list()
   patterns.old = names(U)
   repeated_pattern = 0
-  
+  alpha = ifelse("alpha" %in% names(args), args$alpha, 0.05)
+
   # MCEM steps
   for (kk in 1:n.iter){
     # cat("\n iter:", kk, " ")
@@ -114,7 +115,7 @@ CASE_train <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, V = NULL, ...){
     while (nsim < MC.sim[kk]){
       BB[, , nsim + 1] = gBupdate(B = BB[, , nsim], hatB = hatB,
                     R = R, pi = pi, h = args$h,
-                    TT = gBc$TT, TT_det = gBc$TT_det, mu1 = gBc$mu1, Sigma1 = gBc$Sigma1, alpha = args$alpha)
+                    TT = gBc$TT, TT_det = gBc$TT_det, mu1 = gBc$mu1, Sigma1 = gBc$Sigma1, alpha = alpha)
       
       nsim  = nsim + 1
       gg[, nsim] = ifelse(as.matrix(BB[, , nsim]) != 0, 1, 0) %>% apply(1, paste, collapse = "")
@@ -134,7 +135,7 @@ CASE_train <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, V = NULL, ...){
     L = length(patterns)
     
     if (L <= 1){
-      cat("Estimated no eQTL effects in the CASE prior fitting step.")
+      cat("Estimates no eQTL effects in the CASE prior fitting step.", "\n")
       return(list(pi = pi, U = U, V = V, n.iter = kk, pi.in = pi.in, M1 = M1))
     }
     
@@ -205,13 +206,12 @@ CASE_train <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, V = NULL, ...){
       ll = which(pi < 1e-2 / M * pi.in)
     }
     if (length(ll) > 0){
-      # cat("pi delete", ll, "\n")
       U = U[-ll]
       pi = pi[-ll]
     }
     
     if (length(pi) <= 1){
-      cat("Estimated no eQTL effects in the CASE prior fitting step.")
+      cat("Estimated no eQTL effects in the CASE prior fitting step.", "\n")
       return(list(pi = pi, U = U, V = V, n.iter = kk, pi.in = pi.in, M1 = M1))
     }
     
@@ -222,7 +222,7 @@ CASE_train <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, V = NULL, ...){
     ll = integer(0)
     dd = 0
     for (l in 1:(L-1)){
-      ind = which(diag(U[[l]]) <= qchisq(0.95, 1) * diag(V))
+      ind = which(diag(U[[l]]) <= qchisq(1 - alpha, 1) * diag(V))
       U[[l]][ind, ] = 0
       U[[l]][, ind] = 0
       lp = 0
@@ -240,19 +240,16 @@ CASE_train <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, V = NULL, ...){
     }
     
     if (length(ll) > 0){
-      # cat("U delete", ll, "\n")
       U = U[-ll]
       pi = pi[-ll]
     }
     
     L = length(U)
     if (L <= 1){
-      cat("Estimated no eQTL effects in the CASE prior fitting step.")
+      cat("Estimated no eQTL effects in the CASE prior fitting step.", "\n")
       return(list(pi = pi, U = U, V = V, n.iter = kk, pi.in = pi.in, M1 = M1))
     }
     
-    # cat("\n", names(pi), "\n")
-    # print(pi)
     if (setequal(patterns.old, names(pi))){
       repeated_pattern = repeated_pattern + 1
     } else{
@@ -295,8 +292,8 @@ CASE_test <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, CASE_training, .
   # Here V is V adjusted for sample sizes
   #### Testing ####
   args = list(...)
-  cat("Start Posterior Analysis.")
-  
+  cat("Start Posterior Analysis.", "\n")
+
   U = CASE_training$U
   V = CASE_training$V
   pi = CASE_training$pi
@@ -371,7 +368,7 @@ CASE_test <- function(Z = NULL, R, hatB = NULL, hatS = NULL, N, CASE_training, .
 #' @importFrom magrittr %>%
 #' @export
 get_credible_sets <- function(pvalues, R, cor.min = 0.5, pip = 0.95, ruled_out = 1e-4){
-  cat("Start getting credible sets.")
+  cat("Start getting credible sets.", "\n")
   
   pvalues = as.matrix(pvalues)
   C = ncol(pvalues)
diff --git a/R/CASE_uitility.R b/R/CASE_uitility.R
index 05fbf95..304a687 100644
--- a/R/CASE_uitility.R
+++ b/R/CASE_uitility.R
@@ -233,7 +233,7 @@ Initialize_pi_U <- function(hatB, hatS, C, M, sig_threshold = 0.1){
   
   U = list()
   for (l in patterns){
-    U[[l]] = matrix(.1, C, C)
+    U[[l]] = matrix(.2, C, C)
     diag(U[[l]]) = 1
     idx = which(as.numeric(strsplit(l, "")[[1]]) == 0)
     U[[l]][idx, ] = 0
diff --git a/R/Example.R b/R/Example.R
new file mode 100644
index 0000000..29086cb
--- /dev/null
+++ b/R/Example.R
@@ -0,0 +1,52 @@
+#' @importFrom mvsusieR mvsusie_rss create_mixture_prior 
+#' @importFrom susieR susie_rss
+#' @importFrom CorBin cBern
+#' @importFrom stats cor lm rnorm
+generate_example_data <- function(){
+  set.seed(1130)
+  N = 500
+  M = 1000
+  C = 3
+  
+  X = cbind(cBern(N, rep(0.3, M/4), rho = 0.95, type = "DCP"),
+            cBern(N, rep(0.3, M/2), rho = 0.85, type = "DCP"),
+            cBern(N, rep(0.3, M/4), rho = 0.98, type = "DCP"))
+  
+  B = matrix(0, M, C)
+  idx1 = 10
+  idx2 = 950
+  B[idx1, ] = c(sqrt(0.3), sqrt(0.2), sqrt(0.1))
+  B[idx2, ] = c(sqrt(0.2), sqrt(0.2), 0)
+  e = matrix(rnorm(N * C), N, C)
+  Y = X %*% B + e
+  
+  
+  ### heritability
+  # apply(X %*% B, 2, var) / apply(Y, 2, var)
+  
+  R = cor(X)
+  
+  Z = matrix(0, M, C)
+  for (i in 1:M){
+    m1 = summary(lm(Y ~ X[, i]))
+    Z[i, ] = sapply(m1, function(x) x$coefficients[2, 3])
+  }
+  Z[c(idx1, idx2), ]
+  B[c(idx1, idx2), ]
+  
+  fit <- CASE(Z = Z, R = R, N = rep(N, C))
+  # fit$sets
+  
+  f1 = susie_rss(z = Z[, 1], R = R, n = N)
+  # f1$sets
+  
+  prior <- create_mixture_prior(R = C)
+  f2 = mvsusie_rss(Z = Z, R = R, N = N, prior_variance = prior)
+  # f2$sets
+  # f2$single_effect_lfsr
+  
+  # mvsusie_plot(f2)
+}
+
+
+
diff --git a/man/CASE.Rd b/man/CASE.Rd
index e24ecea..3959d18 100644
--- a/man/CASE.Rd
+++ b/man/CASE.Rd
@@ -2,7 +2,7 @@
 % Please edit documentation in R/CASE.R
 \name{CASE}
 \alias{CASE}
-\title{CASE Model}
+\title{CASE}
 \usage{
 CASE(Z = NULL, R, hatB = NULL, hatS = NULL, N, V = NULL, cs = TRUE, ...)
 }