From f241fca5cb1272378ec9b953fe7d58f71b37e882 Mon Sep 17 00:00:00 2001
From: John Yannotty <40618811+jcyannotty@users.noreply.github.com>
Date: Tue, 24 Oct 2023 00:25:38 -0400
Subject: [PATCH] Fix bold symbol for tilde{x} and tilde{y}

---
 joss_paper/paper.md | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/joss_paper/paper.md b/joss_paper/paper.md
index 207beaaa..2a6c9fa5 100644
--- a/joss_paper/paper.md
+++ b/joss_paper/paper.md
@@ -73,8 +73,8 @@ vector of input parameters $\boldsymbol x$, $f_k(\boldsymbol x)$ is the mean
 prediction under the $k^\mathrm{th}$ model $\mathcal{M}_k$, and
 $w_k(\boldsymbol x)$ is the corresponding weight function. The
 *density-mixing* approach estimates the underlying predictive density by
-$$p(\tilde{\boldsymbol Y} \mid \tilde{\boldsymbol x}) = \sum_{k = 1}^K w_k(\boldsymbol x)\;p(\tilde{\boldsymbol Y} \mid \boldsymbol \tilde{x},\boldsymbol Y, \mathcal{M}_k),$$
-where $p(\tilde{\boldsymbol Y} \mid \boldsymbol \tilde{x}, \boldsymbol Y, \mathcal{M}_k)$ represents
+$$p(\boldsymbol{\tilde{Y}} \mid \boldsymbol{\tilde{x}}) = \sum_{k = 1}^K w_k(\boldsymbol{\tilde{x}})\;p(\tilde{\boldsymbol Y} \mid \boldsymbol{\tilde{x}},\boldsymbol{Y}, \mathcal{M}_k),$$
+where $p(\tilde{\boldsymbol Y} \mid \boldsymbol{\tilde{x}}, \boldsymbol Y, \mathcal{M}_k)$ represents
 the predictive density of a future observation $\tilde{\boldsymbol Y}$ with
 respect to the $k^\mathrm{th}$ model $\mathcal{M}_k$. In either BMM
 setup, a key challenge is defining $w_k(\boldsymbol x)$---the functional