diff --git a/LICENSE b/LICENSE
index 37a50ff..32027c8 100644
--- a/LICENSE
+++ b/LICENSE
@@ -1,3 +1,2 @@
 YEAR: 2025
-COPYRIGHT HOLDER: Xuewei Cao, Haochen Sun, Ru Feng, Daniel Nachun, Kushal Dey, Gao Wang
-ORGANIZATION: StatFunGen Lab, Columbia University
\ No newline at end of file
+COPYRIGHT HOLDER: Xuewei Cao, Haochen Sun, Ru Feng, Daniel Nachun, Kushal Dey, Gao Wang
\ No newline at end of file
diff --git a/R/colocboost_inference.R b/R/colocboost_inference.R
index 567d43d..bc709b5 100644
--- a/R/colocboost_inference.R
+++ b/R/colocboost_inference.R
@@ -537,7 +537,12 @@ get_cos_evidence <- function(cb_obj, coloc_out, data_info) {
 
   get_npuc <- function(npc_outcome) {
     max_idx <- which.max(npc_outcome)
-    npc_outcome[max_idx] * prod(1 - npc_outcome[-max_idx])
+    npc_max <- npc_outcome[max_idx]
+    if (npc_max == 0) {
+      return(0)
+    } else {
+      return(npc_outcome[max_idx] * prod(1 - npc_outcome[-max_idx]))
+    }
   }
 
   avWeight <- coloc_out$avWeight
diff --git a/vignettes/FineBoost_Special_Case.Rmd b/vignettes/FineBoost_Special_Case.Rmd
index af081be..547d136 100644
--- a/vignettes/FineBoost_Special_Case.Rmd
+++ b/vignettes/FineBoost_Special_Case.Rmd
@@ -16,8 +16,9 @@ knitr::opts_chunk$set(
 ```
 
 
-This vignette demonstrates how to perform single-trait fine-mapping analysis using FineBoost, a specialized single-trait version of ColocBoost, with both individual-level data and summary statistics. Specifically focusing on the 2nd trait with 2 causal variants (644 and 2289) from the `Ind_5traits` and `Sumstat_5traits` datasets included in the package.
-
+This vignette demonstrates how to perform single-trait fine-mapping analysis using FineBoost, a specialized single-trait version of ColocBoost, 
+with both individual-level data and summary statistics. Specifically focusing on the 2nd trait with 2 causal variants (194 and 589) from the 
+`Ind_5traits` and `Sumstat_5traits` datasets included in the package.
 
 ```{r setup}
 library(colocboost)
@@ -65,4 +66,10 @@ This approach is less computationally intensive but assumes that only one varian
 # Load example data
 res <- colocboost(sumstat = sumstat)
 colocboost_plot(res)
-```
\ No newline at end of file
+```
+
+
+**Note**: Weak learners SEL in FineBoost may capture noise as putative signals, potentially introducing false positives to our findings. 
+To identify and filter spurious signals, we discard fine-tunned the threshold of $\Delta L_l$ using extensive simulations to balance sensitivity and specificity.
+This threshold is set to 0.025 by default for ColocBoost when detect the colocalization, but we suggested a less conservative threshold of 0.015 for FineBoost
+when performing single-trait fine-mapping analysis (`check_null_max = 0.015` as we suggested).
\ No newline at end of file
diff --git a/vignettes/LD_Free_Colocalization.Rmd b/vignettes/LD_Free_Colocalization.Rmd
index 6011eee..7ed10b9 100644
--- a/vignettes/LD_Free_Colocalization.Rmd
+++ b/vignettes/LD_Free_Colocalization.Rmd
@@ -45,8 +45,8 @@ ColocBoost provides diagnostic warnings for assessing the consistency of the sum
 
 - Estimated residual variance of the model is negative or greater than phenotypic variance (`rtr < 0` or `rtr > var_y`; 
 see details in Supplementary Note S3.5.2). 
-- Change in trait-specific profile log-likelihood according to a CoS is negative (see details in Supplementary Note S3.5.3).
 - The trait-specific gradient boosting model fails to converge.
+- Change in trait-specific profile log-likelihood according to a CoS is negative (see details in Supplementary Note S3.5.3).
 
 
 ### Example of including LD mismatch
@@ -79,11 +79,30 @@ However, the results may be less reliable due to the mismatch, and the computati
 
 ```{r LD-mismatch-runcode}
 res <- colocboost(sumstat = sumstat, LD = LD)
+res$cos_details$cos$cos_index
 ```
 
 These warnings serve as diagnostic tools to alert users about potential inconsistencies in the input data.
 
 
+```{r LD-mismatch-mpc_0}
+res$cos_details$cos_outcomes_npc
+```
+
+**Note**: In the above example, the normalized probability of trait 2 is 0, indicating that colocalization with trait 2 may be less reliable due to the LD mismatch. 
+This is a warning, not an error, and the colocalization analysis will still proceed. Therefore, in this case, we suggest treating the colocalization of trait 2 with caution.
+
+Potential solutions include:
+
+- Using a more accurate LD matrix for trait 2.
+- Excluding trait 2 from the analysis or colocalization results.
+- Using the LD-mismatch or LD-free approach for colocalization analysis (below).
+- Check the visualization of colocalization results including trait 2 using `colocboost_plot(res)`. Remove the potential spurious signals when LD mismatch is detected using 
+  - `get_robust_colocalization(res, cos_npc_cutoff = 0.5, npc_outcome_cutoff = 0.2)` to exclude the trait 2 in the above example if the signals are not reasonable.
+  - `get_robust_colocalization(res, pvalue_cutoff = 1e-5, cos_npc_cutoff = 0, npc_outcome_cutoff = 0)` to include all colocalized traits with the larger marginal evidence, 
+  but the mismatch is detected.
+
+
 # 2. LD-free and LD-mismatch colocalization analysis
 
 When there is substantial discordance between the LD matrix and summary statistics,