Update app.py

app.py

@@ -43,6 +43,34 @@ This application analyzes asset price data using Wasserstein distances to detect
 Wasserstein distances, derived from persistence diagrams in Topological Data Analysis (TDA), help identify significant shifts in asset price behaviors for both stocks and cryptocurrencies.
 """)
 
+with st.expander("Wasserstein Distance Methodology", expanded=False):
+    # Explanation of the Wasserstein Distance method
+    st.subheader("Wasserstein Distance Methodology")
+    st.write("""
+    The Wasserstein distance is a measure from optimal transport theory, used here to compare distributions of log returns in different time windows.
+    A high Wasserstein distance indicates a significant change in the price dynamics, which might suggest a market event or shift in investor sentiment.
+    """)
+    
+    st.latex(r'''
+    W(P, Q) = \inf_{\gamma \in \Pi(P, Q)} \mathbb{E}_{(x,y) \sim \gamma} [d(x, y)]
+    ''')
+    
+    st.write("""
+    - Where \( W(P, Q) \) is the Wasserstein distance between distributions \( P \) and \( Q \).
+    - \( d(x, y) \) is the distance between points \( x \) and \( y \).
+    - \( \gamma \) is a joint distribution with marginals \( P \) and \( Q \).
+    """)
+    
+    # Interpretation of results
+    st.subheader("Interpretation of Results")
+    st.write("""
+    **Wasserstein Distance Analysis:**
+    The Wasserstein distance quantifies changes in the log returns of asset prices over time.
+    A high distance indicates a significant shift in price dynamics, potentially due to a market event or a change in investor behavior.
+    """)
+
+st.write(f"Threshold: {threshold}")
+
 # Sidebar for "How to Use" instructions inside an expander, closed by default
 with st.sidebar.expander("How to Use", expanded=False):
     st.write("""
@@ -98,33 +126,6 @@ if st.sidebar.button('Run Analysis'):
     fig.update_layout(title='Wasserstein Distances Over Time', xaxis_title='Date', yaxis_title='Wasserstein Distance')
     st.plotly_chart(fig, use_container_width=True)
 
-    # Explanation of the Wasserstein Distance method
-    st.subheader("Wasserstein Distance Methodology")
-    st.write("""
-    The Wasserstein distance is a measure from optimal transport theory, used here to compare distributions of log returns in different time windows.
-    A high Wasserstein distance indicates a significant change in the price dynamics, which might suggest a market event or shift in investor sentiment.
-    """)
-
-    st.latex(r'''
-    W(P, Q) = \inf_{\gamma \in \Pi(P, Q)} \mathbb{E}_{(x,y) \sim \gamma} [d(x, y)]
-    ''')
-    
-    st.write("""
-    - Where \( W(P, Q) \) is the Wasserstein distance between distributions \( P \) and \( Q \).
-    - \( d(x, y) \) is the distance between points \( x \) and \( y \).
-    - \( \gamma \) is a joint distribution with marginals \( P \) and \( Q \).
-    """)
-
-    # Interpretation of results
-    st.subheader("Interpretation of Results")
-    st.write("""
-    **Wasserstein Distance Analysis:**
-    The Wasserstein distance quantifies changes in the log returns of asset prices over time.
-    A high distance indicates a significant shift in price dynamics, potentially due to a market event or a change in investor behavior.
-    """)
-
-    st.write(f"Threshold: {threshold}")
-
     st.write("""
     **Plot Interpretation:**
     - The first plot shows the asset price over time with alerts marked in red.