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06-worked-example-x101.html
<!doctype html><html lang="zh-Hant"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width,initial-scale=1"><title>KP16 06 Worked Example X101</title>
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</head><body><div class="wrap"><div class="stage" id="stage"><canvas id="c" width="1600" height="900"></canvas><div id="math-layer"></div><div class="hint">互動：點擊 / 拖曳 • Click / Drag</div></div></div>
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/* ===== Page script ===== */
const P1=[0.8,0.3,0.7]; /* P(xj=1 | omega_1) */
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title('三維手算範例：觀察向量 x = (1, 0, 1)','Hand-Calculation Walkthrough for a 3-Feature Vector',6);
/* ---------- given parameters ---------- */
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txt('已知參數 Given parameters',90,202,19,P.ink,'left',800);
txt('ω₁: p₁=0.80 p₂=0.30 p₃=0.70',90,236,18,C1,'left',750);
txt('ω₂: q₁=0.40 q₂=0.60 q₃=0.50',90,266,18,C2,'left',750);
txt('點擊切換每一位的 0 / 1，觀察連乘分數與後驗機率即時變化',880,236,16,P.amber,'left',650);
txt('Click each bit to toggle 0/1 and watch S₁, S₂ and the posterior update live',880,264,13,P.muted,'left',550);
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/* ---------- per-term lookup table ---------- */
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txt('ω₁ 逐項查表',90,430,19,C1,'left',800);
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txt(`S₁ = ${P1.map((p,j)=>(X[j]===1?p:1-p).toFixed(2)).join(' × ')} = ${s1.toFixed(3)}`,90,725,19,C1,'left',850);
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txt('ω₂ 逐項查表',850,430,19,C2,'left',800);
let s2=1;
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txt(X[j]===1?`q${j+1} = ${Q1[j].toFixed(2)}`:`1 − q${j+1} = 1 − ${Q1[j].toFixed(2)} = ${val.toFixed(2)}`,1080,y+30,17,P.muted,'left',600);
txt(val.toFixed(2),1452,y+30,20,C2,'right',800);
}
txt(`S₂ = ${Q1.map((q,j)=>(X[j]===1?q:1-q).toFixed(2)).join(' × ')} = ${s2.toFixed(3)}`,850,725,19,C2,'left',850);
/* ---------- verdict ---------- */
const total=s1+s2, pr1=s1/total, pr2=s2/total, win=s1>=s2?1:2;
rr(60,790,1460,76,18,win===1?'#63b3ed18':'#ff7b7218',win===1?C1:C2,2.5);
txt(`S₁ = ${s1.toFixed(3)} ${s1>=s2?'>':'<'} S₂ = ${s2.toFixed(3)} ⟹ ω̂ = ω${win}`,90,820,22,win===1?C1:C2,'left',900);
txt(`後驗機率 P(ω${win}|x) ≈ ${(Math.max(pr1,pr2)*100).toFixed(1)}%`,1490,820,19,win===1?C1:C2,'right',800);
showF(['s1','s2']);
}
render();
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