diff --git a/birdman/default_models.py b/birdman/default_models.py
index 24000b4..b7452ec 100644
--- a/birdman/default_models.py
+++ b/birdman/default_models.py
@@ -127,17 +127,25 @@ class NegativeBinomialSingle(SingleFeatureModel):
 
         y_{ij} &\\sim \\textrm{NB}(\\mu_{ij},\\phi_j)
 
-        \\mu_{ij} &= n_i p_{ij}
-
-        \\textrm{alr}(p_i) &= x_i \\beta
+        \\log(\\mu_{ij}) &= \\log(\\textrm{Depth}_i) + x_i \\beta
 
     Priors:
 
     .. math::
 
-        \\beta_j &\\sim \\textrm{Normal}(0, B_p), B_p \\in \\mathbb{R}_{>0}
+        \\begin{cases}
+        \\beta_j \\sim \\textrm{Normal}(-5.5, B_p), & j = 0
 
-        \\frac{1}{\\phi_j} &\\sim \\textrm{Cauchy}(0, C_s), C_s \\in
+        \\beta_j \\sim \\textrm{Normal}(0, B_p), & j > 0
+        \\end{cases}
+
+    .. math::
+
+        B_p \\in \\mathbb{R}_{>0}
+
+    .. math::
+
+        \\frac{1}{\\phi_j} \\sim \\textrm{Cauchy}(0, C_s), C_s \\in
             \\mathbb{R}_{>0}
 
 
diff --git a/birdman/model_base.py b/birdman/model_base.py
index 44b7541..1f180bb 100644
--- a/birdman/model_base.py
+++ b/birdman/model_base.py
@@ -17,9 +17,6 @@ class BaseModel(ABC):
     :param table: Feature table (features x samples)
     :type table: biom.table.Table
 
-    :param metadata: Metadata for design matrix
-    :type metadata: pd.DataFrame
-
     :param model_path: Filepath to Stan model
     :type model_path: str
 
@@ -239,9 +236,6 @@ def to_inference_object(self) -> az.InferenceData:
 class SingleFeatureModel(BaseModel):
     """Fit a model for a single feature."""
     def __init__(self, table: biom.Table, feature_id: str, **kwargs):
-        if feature_id is None:
-            raise ValueError("Must provide feature ID!")
-
         super().__init__(table=table, **kwargs)
         self.feature_id = feature_id
         values = table.data(
diff --git a/birdman/templates/negative_binomial_single.stan b/birdman/templates/negative_binomial_single.stan
index f53ab27..7acec16 100644
--- a/birdman/templates/negative_binomial_single.stan
+++ b/birdman/templates/negative_binomial_single.stan
@@ -25,7 +25,8 @@ transformed parameters {
 model {
   // setting priors ...
   reciprocal_phi ~ cauchy(0., phi_s);
-  for (j in 1:p){
+  beta[1] ~ normal(-5.5, B_p);
+  for (j in 2:p){
     beta[j] ~ normal(0., B_p); // uninformed prior
   }
   // generating counts
diff --git a/docs/conf.py b/docs/conf.py
index f806850..0e6baf6 100644
--- a/docs/conf.py
+++ b/docs/conf.py
@@ -28,7 +28,8 @@
 # extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
 # ones.
 extensions = [
-    'sphinx.ext.autodoc'
+    'sphinx.ext.autodoc',
+    'sphinx.ext.mathjax'
 ]
 
 # Add any paths that contain templates here, relative to this directory.