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bayes.py

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+import gradio as gr
+import numpy as np
+import matplotlib.pyplot as plt
+import seaborn as sns
+import matplotlib.patches as patches
+from matplotlib.gridspec import GridSpec
+import matplotlib.colors as mcolors
+from matplotlib.ticker import PercentFormatter
+
+# Set up the styling for better readability
+plt.rcParams.update({
+    'font.family': 'sans-serif',
+    'font.sans-serif': ['Arial', 'Helvetica', 'DejaVu Sans'],
+    'font.size': 12,
+    'axes.titlesize': 16,
+    'axes.labelsize': 14,
+    'xtick.labelsize': 12,
+    'ytick.labelsize': 12,
+    'legend.fontsize': 12,
+    'figure.titlesize': 20
+})
+
+def create_bayes_visualization(prior_prob, sensitivity, specificity, population=1000):
+    """Create a clear, readable visualization of Bayes' theorem."""
+
+    # Calculate values based on Bayes theorem
+    true_positive = prior_prob * sensitivity * population
+    false_positive = (1 - prior_prob) * (1 - specificity) * population
+    true_negative = (1 - prior_prob) * specificity * population
+    false_negative = prior_prob * (1 - sensitivity) * population
+
+    # Calculate posterior probability (positive predictive value)
+    posterior_prob = true_positive / (true_positive + false_positive) if (true_positive + false_positive) > 0 else 0
+
+    # Create a large figure with a clean white background
+    fig = plt.figure(figsize=(16, 12), facecolor='white')
+    gs = GridSpec(3, 2, height_ratios=[1, 2, 1], width_ratios=[1, 1])
+
+    # Title for the entire visualization
+    fig.suptitle("Bayes' Theorem: Medical Test Visualization", fontsize=22, fontweight='bold', y=0.98)
+
+    # Add parameter information at the top
+    param_ax = fig.add_subplot(gs[0, :])
+    param_ax.axis('off')
+    param_text = (
+        f"Disease Prevalence: {prior_prob:.1%}  |  "
+        f"Test Sensitivity: {sensitivity:.1%}  |  "
+        f"Test Specificity: {specificity:.1%}"
+    )
+    param_ax.text(0.5, 0.5, param_text, ha='center', va='center', fontsize=16,
+                 bbox=dict(facecolor='#e6f2ff', edgecolor='#3399ff', boxstyle='round,pad=0.5'))
+
+    # 1. Population Distribution (Left)
+    pop_ax = fig.add_subplot(gs[1, 0])
+    pop_ax.set_title("Population Distribution", fontsize=18, pad=15)
+    pop_ax.axis('equal')
+    pop_ax.set_xlim(0, 100)
+    pop_ax.set_ylim(0, 100)
+
+    # Create a clean, modern look with a light grid
+    pop_ax.grid(False)
+    pop_ax.set_xticks([])
+    pop_ax.set_yticks([])
+    pop_ax.spines['top'].set_visible(False)
+    pop_ax.spines['right'].set_visible(False)
+    pop_ax.spines['bottom'].set_visible(False)
+    pop_ax.spines['left'].set_visible(False)
+
+    # Draw the population rectangle with a light border
+    pop_rect = patches.Rectangle((0, 0), 100, 100, linewidth=2, edgecolor='#666666', facecolor='#f0f0f0', alpha=0.3)
+    pop_ax.add_patch(pop_rect)
+
+    # Draw the disease prevalence with a distinct color
+    disease_width = prior_prob * 100
+    disease_rect = patches.Rectangle((0, 0), disease_width, 100, linewidth=1,
+                                    edgecolor='#cc0000', facecolor='#ff9999', alpha=0.7)
+    pop_ax.add_patch(disease_rect)
+
+    # Add clear labels with contrasting backgrounds
+    pop_ax.text(disease_width/2, 50, f"Have disease\n{int(prior_prob*population)} people\n({prior_prob:.1%})",
+               ha='center', va='center', fontsize=14, fontweight='bold',
+               bbox=dict(facecolor='white', alpha=0.8, edgecolor='#cc0000', boxstyle='round,pad=0.3'))
+
+    pop_ax.text(disease_width + (100-disease_width)/2, 50,
+               f"Don't have disease\n{int((1-prior_prob)*population)} people\n({1-prior_prob:.1%})",
+               ha='center', va='center', fontsize=14, fontweight='bold',
+               bbox=dict(facecolor='white', alpha=0.8, edgecolor='#666666', boxstyle='round,pad=0.3'))
+
+    # Add a dividing line
+    pop_ax.axvline(x=disease_width, color='#666666', linestyle='--', linewidth=2, alpha=0.7)
+
+    # 2. Test Results (Right)
+    test_ax = fig.add_subplot(gs[1, 1])
+    test_ax.set_title("Test Results", fontsize=18, pad=15)
+    test_ax.axis('equal')
+    test_ax.set_xlim(0, 100)
+    test_ax.set_ylim(0, 100)
+
+    # Clean styling
+    test_ax.grid(False)
+    test_ax.set_xticks([])
+    test_ax.set_yticks([])
+    test_ax.spines['top'].set_visible(False)
+    test_ax.spines['right'].set_visible(False)
+    test_ax.spines['bottom'].set_visible(False)
+    test_ax.spines['left'].set_visible(False)
+
+    # Draw the test results rectangle
+    test_rect = patches.Rectangle((0, 0), 100, 100, linewidth=2, edgecolor='#666666', facecolor='#f0f0f0', alpha=0.3)
+    test_ax.add_patch(test_rect)
+
+    # Calculate proportions for visualization
+    tp_width = (prior_prob * sensitivity) * 100
+    fp_width = ((1 - prior_prob) * (1 - specificity)) * 100
+    fn_width = (prior_prob * (1 - sensitivity)) * 100
+    tn_width = ((1 - prior_prob) * specificity) * 100
+
+    # Use a clear, distinct color palette
+    tp_rect = patches.Rectangle((0, 0), tp_width, 100, linewidth=1,
+                               edgecolor='#990000', facecolor='#ff5555', alpha=0.8)
+    test_ax.add_patch(tp_rect)
+
+    fp_rect = patches.Rectangle((tp_width, 0), fp_width, 100, linewidth=1,
+                               edgecolor='#994400', facecolor='#ffaa77', alpha=0.8)
+    test_ax.add_patch(fp_rect)
+
+    fn_rect = patches.Rectangle((tp_width + fp_width, 0), fn_width, 100, linewidth=1,
+                               edgecolor='#004499', facecolor='#77aaff', alpha=0.8)
+    test_ax.add_patch(fn_rect)
+
+    tn_rect = patches.Rectangle((tp_width + fp_width + fn_width, 0), tn_width, 100, linewidth=1,
+                               edgecolor='#000066', facecolor='#5588ff', alpha=0.8)
+    test_ax.add_patch(tn_rect)
+
+    # Add dividing lines
+    test_ax.axvline(x=tp_width + fp_width, color='#666666', linestyle='--', linewidth=2, alpha=0.7)
+    test_ax.axvline(x=tp_width, color='#666666', linestyle=':', linewidth=1.5, alpha=0.7)
+    test_ax.axvline(x=tp_width + fp_width + fn_width, color='#666666', linestyle=':', linewidth=1.5, alpha=0.7)
+
+    # Improved label placement to avoid overlap
+    # Use vertical positioning to separate labels
+
+    # True Positives - top position
+    test_ax.text(tp_width/2, 75, f"True Positives\n{int(true_positive)} people",
+                ha='center', va='center', fontsize=14, fontweight='bold',
+                bbox=dict(facecolor='white', alpha=0.9, edgecolor='#990000', boxstyle='round,pad=0.3'))
+
+    # False Positives - bottom position if narrow, otherwise center
+    if fp_width < 10:  # If the section is narrow
+        fp_y_pos = 25 if tp_width > 10 else 50  # Adjust based on TP width
+        test_ax.text(tp_width + fp_width/2, fp_y_pos, f"False\nPositives\n{int(false_positive)}",
+                    ha='center', va='center', fontsize=12, fontweight='bold',
+                    bbox=dict(facecolor='white', alpha=0.9, edgecolor='#994400', boxstyle='round,pad=0.3'))
+    else:
+        test_ax.text(tp_width + fp_width/2, 50, f"False Positives\n{int(false_positive)} people",
+                    ha='center', va='center', fontsize=14, fontweight='bold',
+                    bbox=dict(facecolor='white', alpha=0.9, edgecolor='#994400', boxstyle='round,pad=0.3'))
+
+    # False Negatives - top position if narrow, otherwise center
+    if fn_width < 10:  # If the section is narrow
+        fn_y_pos = 75 if tn_width > 10 else 50  # Adjust based on TN width
+        test_ax.text(tp_width + fp_width + fn_width/2, fn_y_pos, f"False\nNegatives\n{int(false_negative)}",
+                    ha='center', va='center', fontsize=12, fontweight='bold',
+                    bbox=dict(facecolor='white', alpha=0.9, edgecolor='#004499', boxstyle='round,pad=0.3'))
+    else:
+        test_ax.text(tp_width + fp_width + fn_width/2, 50, f"False Negatives\n{int(false_negative)} people",
+                    ha='center', va='center', fontsize=14, fontweight='bold',
+                    bbox=dict(facecolor='white', alpha=0.9, edgecolor='#004499', boxstyle='round,pad=0.3'))
+
+    # True Negatives - bottom position
+    test_ax.text(tp_width + fp_width + fn_width + tn_width/2, 25, f"True Negatives\n{int(true_negative)} people",
+                ha='center', va='center', fontsize=14, fontweight='bold',
+                bbox=dict(facecolor='white', alpha=0.9, edgecolor='#000066', boxstyle='round,pad=0.3'))
+
+    # Add test positive/negative regions with clear separation and improved positioning
+    test_positive = true_positive + false_positive
+    test_negative = false_negative + true_negative
+
+    # Create a separate area below the main visualization for test result summaries
+    test_ax.add_patch(patches.Rectangle((0, -20), tp_width + fp_width, 15,
+                                       facecolor='#ffeeee', alpha=0.7, edgecolor='#cc0000'))
+    test_ax.add_patch(patches.Rectangle((tp_width + fp_width, -20), fn_width + tn_width, 15,
+                                       facecolor='#eeeeff', alpha=0.7, edgecolor='#0044cc'))
+
+    # Add clear labels for test positive/negative
+    test_ax.text(tp_width/2 + fp_width/2, -12.5,
+                f"Test Positive: {int(test_positive)} people ({test_positive/population:.1%})",
+                ha='center', va='center', fontsize=14, fontweight='bold', color='#990000')
+
+    test_ax.text(tp_width + fp_width + fn_width/2 + tn_width/2, -12.5,
+                f"Test Negative: {int(test_negative)} people ({test_negative/population:.1%})",
+                ha='center', va='center', fontsize=14, fontweight='bold', color='#000066')
+
+    # 3. Formula and Conclusion (Bottom)
+    formula_ax = fig.add_subplot(gs[2, :])
+    formula_ax.axis('off')
+
+    # Create a box for the formula
+    formula_box = patches.FancyBboxPatch((0.1, 0.4), 0.8, 0.5, boxstyle=patches.BoxStyle("Round", pad=0.6),
+                                        facecolor='#f5f5f5', edgecolor='#3399ff', linewidth=2, alpha=0.7,
+                                        transform=formula_ax.transAxes)
+    formula_ax.add_patch(formula_box)
+
+    # Add Bayes formula with clear formatting
+    formula_title = "Bayes' Theorem Applied to Medical Testing:"
+    formula_ax.text(0.5, 0.8, formula_title, ha='center', va='center', fontsize=16, fontweight='bold',
+                   transform=formula_ax.transAxes)
+
+    formula = r"$P(Disease|Positive) = \frac{P(Positive|Disease) \times P(Disease)}{P(Positive)}$"
+    formula_ax.text(0.5, 0.65, formula, ha='center', va='center', fontsize=16,
+                   transform=formula_ax.transAxes)
+
+    formula_explained = "Posterior Probability = Sensitivity × Prior Probability / Probability of Positive Test"
+    formula_ax.text(0.5, 0.5, formula_explained, ha='center', va='center', fontsize=14, color='#555555',
+                   transform=formula_ax.transAxes)
+
+    # Add the calculation with the actual values
+    test_positive_prob = test_positive/population
+    calculation = f"= {sensitivity:.1%} × {prior_prob:.1%} / {test_positive_prob:.1%} = {posterior_prob:.1%}"
+    formula_ax.text(0.5, 0.35, calculation, ha='center', va='center', fontsize=16,
+                   transform=formula_ax.transAxes)
+
+    # Create a highlighted conclusion box
+    conclusion_box = patches.FancyBboxPatch((0.15, 0.05), 0.7, 0.2, boxstyle=patches.BoxStyle("Round", pad=0.6),
+                                          facecolor='#ffffcc', edgecolor='#ffcc00', linewidth=2,
+                                          transform=formula_ax.transAxes)
+    formula_ax.add_patch(conclusion_box)
+
+    # Add the conclusion with emphasis
+    conclusion = f"If someone tests positive, they have a {posterior_prob:.1%} chance of having the disease"
+    formula_ax.text(0.5, 0.15, conclusion, ha='center', va='center', fontsize=18, fontweight='bold',
+                   transform=formula_ax.transAxes)
+
+    plt.tight_layout()
+    plt.subplots_adjust(top=0.92, hspace=0.1, wspace=0.1)
+
+    return fig
+
+def explain_bayes(prior_prob, sensitivity, specificity):
+    """Generate the Bayes' theorem explanation and visualization."""
+    population = 1000
+
+    # Calculate values based on Bayes theorem
+    true_positive = prior_prob * sensitivity * population
+    false_positive = (1 - prior_prob) * (1 - specificity) * population
+    true_negative = (1 - prior_prob) * specificity * population
+    false_negative = prior_prob * (1 - sensitivity) * population
+
+    # Calculate posterior probability (positive predictive value)
+    test_positive = true_positive + false_positive
+    test_positive_prob = test_positive / population
+    posterior_prob = true_positive / test_positive if test_positive > 0 else 0
+
+    # Create the visualization
+    fig = create_bayes_visualization(prior_prob, sensitivity, specificity, population)
+
+    # Generate explanation text with clearer explanations of the percentages
+    explanation = f"""
+### Medical Test Example Explained Step-by-Step
+
+Imagine a medical test for a disease that affects {prior_prob:.1%} of the population (prior probability).
+
+**What the percentages mean:**
+
+1. **Disease Prevalence ({prior_prob:.1%})**:
+   - This means that out of every 100 people, about {int(prior_prob*100)} people have the disease
+   - In our population of 1,000 people, {int(prior_prob*population)} people have the disease and {int((1-prior_prob)*population)} people don't
+
+2. **Test Sensitivity ({sensitivity:.1%})**:
+   - This means the test correctly identifies {sensitivity:.1%} of people who actually have the disease
+   - Out of the {int(prior_prob*population)} people with the disease:
+     * {int(true_positive)} people test positive (true positives) = {int(prior_prob*population)} × {sensitivity:.1%}
+     * {int(false_negative)} people test negative (false negatives) = {int(prior_prob*population)} × {(1-sensitivity):.1%}
+
+3. **Test Specificity ({specificity:.1%})**:
+   - This means the test correctly identifies {specificity:.1%} of people who don't have the disease
+   - Out of the {int((1-prior_prob)*population)} people without the disease:
+     * {int(true_negative)} people test negative (true negatives) = {int((1-prior_prob)*population)} × {specificity:.1%}
+     * {int(false_positive)} people test positive (false positives) = {int((1-prior_prob)*population)} × {(1-specificity):.1%}
+
+4. **Probability of Positive Test ({test_positive_prob:.1%})**:
+   - This is the total percentage of people who test positive, regardless of whether they have the disease
+   - It's calculated by adding:
+     * True positives: {int(true_positive)} people = {prior_prob:.1%} × {sensitivity:.1%} × 1,000
+     * False positives: {int(false_positive)} people = {(1-prior_prob):.1%} × {(1-specificity):.1%} × 1,000
+   - Total positive tests: {int(test_positive)} people out of 1,000 = {test_positive_prob:.1%} of the population
+
+**How the formula works:**
+
+Bayes' theorem calculates the probability that someone actually has the disease if they test positive:
+
+P(Disease|Positive) = P(Positive|Disease) × P(Disease) / P(Positive)
+
+Breaking this down with our numbers:
+- P(Positive|Disease) = Sensitivity = {sensitivity:.1%}
+- P(Disease) = Prior Probability = {prior_prob:.1%}
+- P(Positive) = Probability of a positive test = {test_positive_prob:.1%}
+
+Putting these into the formula:
+- Posterior Probability = {sensitivity:.1%} × {prior_prob:.1%} ÷ {test_positive_prob:.1%}
+- = {sensitivity * prior_prob:.1%} ÷ {test_positive_prob:.1%}
+- = {posterior_prob:.1%}
+
+**The key insight:** If someone tests positive, they have a {posterior_prob:.1%} chance of having the disease, not {sensitivity:.1%} as many people might think!
+
+This is often surprising because:
+1. Even a good test ({sensitivity:.1%} accurate) can give misleading results when a disease is rare
+2. Most positive results might actually be false alarms when testing for rare conditions
+3. The more common a disease is, the more likely a positive test is to be correct
+"""
+
+    return fig, explanation
+
+# Create the Gradio interface
+with gr.Blocks(title="Bayes' Theorem Visualizer") as demo:
+    gr.Markdown("# Bayes' Theorem Visualizer")
+    gr.Markdown("""
+    Bayes' theorem helps us update our beliefs based on new evidence. This interactive tool visualizes how prior probability,
+    sensitivity, and specificity affect the posterior probability in a medical testing scenario.
+
+    Adjust the sliders below and see how the results change in real-time!
+    """)
+
+    with gr.Column():
+        with gr.Group():
+            gr.Markdown("### Adjust Parameters")
+
+            prior_prob = gr.Slider(
+                minimum=0.01, maximum=0.5, value=0.1, step=0.01,
+                label="Disease Prevalence (Prior Probability)",
+                info="What percentage of the population has the disease?"
+            )
+
+            sensitivity = gr.Slider(
+                minimum=0.5, maximum=1.0, value=0.9, step=0.01,
+                label="Test Sensitivity (True Positive Rate)",
+                info="How good is the test at detecting people who have the disease?"
+            )
+
+            specificity = gr.Slider(
+                minimum=0.5, maximum=1.0, value=0.9, step=0.01,
+                label="Test Specificity (True Negative Rate)",
+                info="How good is the test at correctly identifying people who don't have the disease?"
+            )
+
+        output_plot = gr.Plot(label="Visualization")
+        output_text = gr.Markdown(label="Explanation")
+
+        with gr.Accordion("Key Terms", open=False):
+            gr.Markdown("""
+            - **Prior Probability (Prevalence)**: The initial probability of having a disease before testing
+            - **Sensitivity**: The ability to correctly identify those with the disease (true positive rate)
+            - **Specificity**: The ability to correctly identify those without the disease (true negative rate)
+            - **Posterior Probability**: The updated probability of having the disease after a positive test
+            - **True Positive**: Correctly identified as having the disease
+            - **False Positive**: Incorrectly identified as having the disease (also called a "Type I error")
+            - **True Negative**: Correctly identified as not having the disease
+            - **False Negative**: Incorrectly identified as not having the disease (also called a "Type II error")
+            """)
+
+    # Update when any parameter changes
+    for param in [prior_prob, sensitivity, specificity]:
+        param.change(
+            explain_bayes,
+            inputs=[prior_prob, sensitivity, specificity],
+            outputs=[output_plot, output_text]
+        )
+
+    # Add examples
+    gr.Examples(
+        examples=[
+            [0.01, 0.99, 0.99],  # Rare disease, excellent test
+            [0.1, 0.9, 0.9],     # Common scenario
+            [0.3, 0.8, 0.7],     # More common disease, less accurate test
+            [0.5, 0.7, 0.95]     # Very common disease, asymmetric test accuracy
+        ],
+        inputs=[prior_prob, sensitivity, specificity],
+        outputs=[output_plot, output_text],
+        fn=explain_bayes,
+        label="Try These Examples"
+    )
+
+    # Initialize the visualization
+    demo.load(
+        explain_bayes,
+        inputs=[prior_prob, sensitivity, specificity],
+        outputs=[output_plot, output_text]
+    )
+
+# Launch the app
+if __name__ == "__main__":
+    demo.launch()

requirements.txt

@@ -0,0 +1,4 @@
+gradio>=4.0.0
+matplotlib>=3.5.0
+numpy>=1.20.0
+seaborn>=0.11.0