55 lines
3.7 KiB
XML
55 lines
3.7 KiB
XML
<svg width="700" height="300" xmlns="http://www.w3.org/2000/svg">
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<text x="350" y="22" fill="#333" font-size="14" font-weight="bold" text-anchor="middle">MLE vs MAP Estimation</text>
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<!-- Left: MLE -->
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<text x="175" y="50" fill="#3498db" font-size="12" font-weight="bold" text-anchor="middle">MLE: maximise likelihood</text>
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<!-- Axes -->
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<line x1="40" y1="220" x2="310" y2="220" stroke="#333" stroke-width="1.2"/>
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<line x1="40" y1="220" x2="40" y2="55" stroke="#333" stroke-width="1.2"/>
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<text x="175" y="245" fill="#666" font-size="10" text-anchor="middle">parameter θ</text>
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<text x="20" y="140" fill="#666" font-size="10" text-anchor="middle" transform="rotate(-90,20,140)">value</text>
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<!-- Likelihood curve -->
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<path d="M 55,218 C 80,215 100,200 120,170 C 140,130 160,85 185,70 C 200,65 210,68 225,85 C 245,115 265,170 285,210 C 295,216 300,218 305,219" fill="none" stroke="#3498db" stroke-width="2.5"/>
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<path d="M 55,218 C 80,215 100,200 120,170 C 140,130 160,85 185,70 C 200,65 210,68 225,85 C 245,115 265,170 285,210 C 295,216 300,218 305,219 L 305,220 L 55,220 Z" fill="#3498db" opacity="0.1"/>
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<!-- MLE peak marker -->
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<line x1="190" y1="68" x2="190" y2="220" stroke="#3498db" stroke-width="1.5" stroke-dasharray="4,3"/>
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<circle cx="190" cy="68" r="5" fill="#3498db"/>
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<text x="190" y="232" fill="#3498db" font-size="10" text-anchor="middle">θ_MLE</text>
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<text x="120" y="120" fill="#3498db" font-size="10">L(θ|data)</text>
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<!-- Divider -->
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<line x1="350" y1="40" x2="350" y2="260" stroke="#ccc" stroke-width="1" stroke-dasharray="4,4"/>
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<!-- Right: MAP -->
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<text x="525" y="50" fill="#e74c3c" font-size="12" font-weight="bold" text-anchor="middle">MAP: likelihood × prior</text>
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<!-- Axes -->
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<line x1="380" y1="220" x2="660" y2="220" stroke="#333" stroke-width="1.2"/>
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<line x1="380" y1="220" x2="380" y2="55" stroke="#333" stroke-width="1.2"/>
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<text x="520" y="245" fill="#666" font-size="10" text-anchor="middle">parameter θ</text>
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<!-- Likelihood (same shape, lighter) -->
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<path d="M 395,218 C 420,215 440,200 460,170 C 480,130 500,85 525,70 C 540,65 550,68 565,85 C 585,115 605,170 625,210 C 635,216 640,218 645,219" fill="none" stroke="#3498db" stroke-width="1.5" opacity="0.4"/>
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<text x="470" y="120" fill="#3498db" font-size="9" opacity="0.6">likelihood</text>
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<!-- Prior (shifted left) -->
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<path d="M 395,218 C 410,210 420,185 435,145 C 445,115 455,90 470,80 C 480,76 490,80 500,95 C 515,120 530,160 545,190 C 560,210 570,216 580,218" fill="none" stroke="#27ae60" stroke-width="1.5" stroke-dasharray="5,3"/>
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<text x="440" y="95" fill="#27ae60" font-size="9">prior</text>
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<!-- Posterior (product, shifted) -->
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<path d="M 410,218 C 425,215 440,200 455,175 C 470,145 480,110 495,88 C 505,80 510,78 515,80 C 525,85 535,100 545,125 C 560,165 575,200 595,215 C 600,217 605,218 610,219" fill="none" stroke="#e74c3c" stroke-width="2.5"/>
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<path d="M 410,218 C 425,215 440,200 455,175 C 470,145 480,110 495,88 C 505,80 510,78 515,80 C 525,85 535,100 545,125 C 560,165 575,200 595,215 C 600,217 605,218 610,219 L 610,220 L 410,220 Z" fill="#e74c3c" opacity="0.1"/>
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<!-- MAP peak marker -->
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<line x1="512" y1="78" x2="512" y2="220" stroke="#e74c3c" stroke-width="1.5" stroke-dasharray="4,3"/>
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<circle cx="512" cy="78" r="5" fill="#e74c3c"/>
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<text x="512" y="232" fill="#e74c3c" font-size="10" text-anchor="middle">θ_MAP</text>
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<text x="555" y="105" fill="#e74c3c" font-size="9">posterior</text>
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<!-- Bottom note -->
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<text x="350" y="275" fill="#666" font-size="11" text-anchor="middle">The prior pulls the MAP estimate away from the MLE toward the prior's peak.</text>
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<text x="350" y="292" fill="#666" font-size="11" text-anchor="middle">With more data, the likelihood dominates and MAP converges to MLE.</text>
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</svg> |
