Update app.py

app.py

@@ -49,10 +49,12 @@ def run_linear_regression(X, y, alpha_prior, beta_prior, sigma_prior):
 # User Input
 st.write("# Bayesian Linear Regression")
 
+st.latex(r'''Prior''')
 st.latex(r'''p(\alpha) = N(\mu_0, \Sigma_0), p(\beta) = N(\mu_1, \Sigma_1), p(\sigma) = N(\mu_2, \Sigma_2)''')
+st.latex(r'''Likelihood''')
 st.latex(r'''p(y | X, \beta,\alpha, \sigma) = N(X\beta + \alpha, \sigma)''')
-st.latex(r'''p(\beta | X, y, \tau) \propto p(y | X, \beta, \tau) p(\beta)''')
-st.latex(r'''p(\tau | X, y, \beta) \propto p(y | X, \beta, \tau) p(\tau)''')
+st.latex(r'''Posterior''')
+st.latex(r'''p(\alpha | X, y) \propto p(y | X, \beta, \sigma) p(\alpha), p(\beta | X, y) \propto p(y | X, \alpha, \sigma) p(\beta), p(\sigma | X, y) \propto p(y | X, \beta, \alpha) p(\sigma)''')
 
 alpha_prior_option = st.selectbox("Choose an option for alpha prior:", ["Normal", "Laplace", "Cauchy"])
 if alpha_prior_option == "Normal":