diff --git a/icom/encoder.py b/icom/encoder.py
new file mode 100644
index 0000000..9b6336b
--- /dev/null
+++ b/icom/encoder.py
@@ -0,0 +1,23 @@
+import numpy as np
+
+
+# encode a message using poisson rate coding
+def encode_message(symbol: str,
+                   signal_rate: float,
+                   noise_rate: float,
+                   duration: int, # in seconds
+                   **kwargs):
+  codebook = kwargs.get("codebook",None)
+
+  if codebook is None: raise TypeError("Invalid code book.")
+
+  #TODO
+  spikes = np.random.poisson(lam=signal_rate, size=duration)
+  spikes = [np.sum(spikes[1:i]) for i in range(len(spikes))]
+
+  print(np.mean(spikes))
+
+  # add leak spikes
+  return spikes
+
+encode_message("1", 5, .3, 10, codebook=[])

diff --git a/icom/encoder.py b/icom/encoder.py
new file mode 100644
index 0000000..9b6336b
--- /dev/null
+++ b/icom/encoder.py
@@ -0,0 +1,23 @@
+import numpy as np
+
+
+# encode a message using poisson rate coding
+def encode_message(symbol: str,
+                   signal_rate: float,
+                   noise_rate: float,
+                   duration: int, # in seconds
+                   **kwargs):
+  codebook = kwargs.get("codebook",None)
+
+  if codebook is None: raise TypeError("Invalid code book.")
+
+  #TODO
+  spikes = np.random.poisson(lam=signal_rate, size=duration)
+  spikes = [np.sum(spikes[1:i]) for i in range(len(spikes))]
+
+  print(np.mean(spikes))
+
+  # add leak spikes
+  return spikes
+
+encode_message("1", 5, .3, 10, codebook=[])
diff --git a/py/poisson_generator.py b/py/poisson_generator.py
index cbba848..3feab60 100644
--- a/py/poisson_generator.py
+++ b/py/poisson_generator.py
@@ -30,7 +30,7 @@
 
 
 #2 (points)
-poi = np.random.poisson(5,size=100)
+poi = np.random.poisson(lam=5,size=100)
 print(f"avergae is {np.average(poi)}")
 
 #poi = [i-j for i,j in zip(poi[:-1],poi[1:])]

diff --git a/icom/encoder.py b/icom/encoder.py
new file mode 100644
index 0000000..9b6336b
--- /dev/null
+++ b/icom/encoder.py
@@ -0,0 +1,23 @@
+import numpy as np
+
+
+# encode a message using poisson rate coding
+def encode_message(symbol: str,
+                   signal_rate: float,
+                   noise_rate: float,
+                   duration: int, # in seconds
+                   **kwargs):
+  codebook = kwargs.get("codebook",None)
+
+  if codebook is None: raise TypeError("Invalid code book.")
+
+  #TODO
+  spikes = np.random.poisson(lam=signal_rate, size=duration)
+  spikes = [np.sum(spikes[1:i]) for i in range(len(spikes))]
+
+  print(np.mean(spikes))
+
+  # add leak spikes
+  return spikes
+
+encode_message("1", 5, .3, 10, codebook=[])
diff --git a/py/poisson_generator.py b/py/poisson_generator.py
index cbba848..3feab60 100644
--- a/py/poisson_generator.py
+++ b/py/poisson_generator.py
@@ -30,7 +30,7 @@
 
 
 #2 (points)
-poi = np.random.poisson(5,size=100)
+poi = np.random.poisson(lam=5,size=100)
 print(f"avergae is {np.average(poi)}")
 
 #poi = [i-j for i,j in zip(poi[:-1],poi[1:])]
diff --git a/py/stan.py b/py/stan.py
index 738f7fc..f4ce9ae 100644
--- a/py/stan.py
+++ b/py/stan.py
@@ -5,7 +5,7 @@
 #%% cell 1. inference using Stan
 
 
-# PyStan
+# PyStan dependendency
 import pystan
 
 # visualization
@@ -24,8 +24,7 @@
 sns.set()
 np.random.seed(101)
 
-# initialize Stan model code
-
+# initialize Stan model code (basic conjigate case)
 model = """
   data {
     int<lower=0> N;
@@ -141,9 +140,9 @@
 plt.axhline(np.mean(alpha), linestyle='--', lw=1, color='lightblue')
 
 # CI lines
-low_conf, high_conf = np.percentile(alpha, 5), np.percentile(alpha, 95)
+low_conf, high_conf = np.percentile(alpha, 2.5), np.percentile(alpha, 97.5)
 plt.axhline(low_conf, linestyle = '--', lw=1, color='darkblue')
-plt.axhline(high_conf, linestyle = '--', lw=1, color='darkblue', label='90% CI')
+plt.axhline(high_conf, linestyle = '--', lw=1, color='darkblue', label='95% CI')
 
 plt.title("Diagnostic trace for alpha")
 plt.ylabel("alpha")
@@ -167,3 +166,46 @@
 
 plt.title("Posterior distribution of alpha")
 plt.show()
+
+
+#%% [markdown]
+# The following code illustrates a bayesian model with conjugate case for beta distribution.
+#
+# Prior: uniform, likelihood: binomial, posterior: beta
+
+import pystan
+import numpy as np
+
+# 0. define grand truth and random data
+#--------------------------------------
+grand_truth = 0.5
+# sample data = {k/n=5/10,6/10}
+
+# 1. define and compile model
+#--------------------------------------
+model_code = """
+  data {
+    int<lower=0> cnt;
+    vector[cnt] k;
+    vector[cnt] n;
+    //int k; // number of success
+    //int n; // number of trials
+  }
+  parameters {
+    real theta;
+
+  }
+  model {
+    theta ~ uniform(0,1); // or beta(1,1) which is also a uniform prior
+    k ~ beta(theta, n);
+  }
+"""
+model = pystan.StanModel(model_code = model_code)
+
+# 2. train model
+#--------------------------------------
+# number of chains = 2, thin=1, 20000, refresh=100
+
+# 3. diagnose convergence
+#--------------------------------------
+# 3.1 draw dynamic trace
\ No newline at end of file