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07-medical-network.html
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/* ===== Page script ===== */
/* ===== Shared helpers for KP18: DAG drawing, parent sets, CPT parameter counting ===== */
const C1='#63b3ed',C2='#ff7b72';
const NM=['x₁','x₂','x₃','x₄','x₅','x₆'];
const POS6=[[.10,.26],[.10,.76],[.38,.93],[.42,.50],[.70,.22],[.90,.60]]; /* normalised node positions */
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const SUPM={'0':'⁰','1':'¹','2':'²','3':'³','4':'⁴','5':'⁵','6':'⁶','7':'⁷','8':'⁸','9':'⁹','-':'⁻'};
const sup=n=>String(n).split('').map(c=>SUPM[c]||c).join('');
/* 07 — Medical diagnosis network: the arrows are expert knowledge; inference by exact enumeration (illustrative CPTs) */
const NN=['S','C','H','C₁','C₂','H₁','H₂'];
const POSM=[[.50,.10],[.24,.46],[.76,.46],[.10,.88],[.38,.88],[.62,.88],[.90,.88]];
const EM=[[1,2],[1,3],[2,4],[2,5],[3,6],[3,7]];
const CPT={S:.30,C:[.05,.20],H:[.10,.25],C1:[.08,.90],C2:[.10,.85],H1:[.07,.88],H2:[.12,.80]}; /* P(true | parent false/true) */
let evS=0,evC=0,evH=0; /* 0 unknown, 1 true/positive, 2 false/negative */
function post(){const acc=[0,0,0,0,0,0,0];let Z=0;
for(let m=0;m<128;m++){const v=[0,1,2,3,4,5,6].map(i=>(m>>i)&1);const [S,C,H,C1,C2,H1,H2]=v;
if(evS&&S!==(evS===1?1:0))continue;if(evC&&C1!==(evC===1?1:0))continue;if(evH&&H1!==(evH===1?1:0))continue;
const pr=(p,x)=>x?p:1-p;
const j=pr(CPT.S,S)*pr(CPT.C[S],C)*pr(CPT.H[S],H)*pr(CPT.C1[C],C1)*pr(CPT.C2[C],C2)*pr(CPT.H1[H],H1)*pr(CPT.H2[H],H2);
Z+=j;v.forEach((x,i)=>{if(x)acc[i]+=j})}
return acc.map(a=>a/Z)}
const nParamMed=1+2*6; /* S:1, and six binary nodes with one binary parent: 2 each */
function render(){
reset();title('領域實戰：醫療診斷網路與箭頭意義','Domain case: a medical diagnosis network',7);
const pp=post();
rr(60,170,860,680,24,P.panel,'#ffffff14',2);
txt('箭頭不是畫好看的：專家知識 + 統計學習',90,205,23,P.ink,'left',850);txt('Arrows encode causal knowledge; probabilities come from data',90,233,15,P.cyan,'left',650);
const box={x:110,y:270,w:760,h:330};
const pts=drawDAG(box,POSM,EM,{names:NN,r:30});
pts.forEach((p,i)=>{const col=pp[i]>.5?C2:P.cyan;txt('P = '+pp[i].toFixed(2),p[0],p[1]+50,15,col,'center',800)});
[['抽菸行為','根節點'],['肺癌','病理中介'],['心臟病','病理中介'],['X光/切片','臨床觀測'],['',''],['心電圖','臨床觀測'],['','']].forEach((d,i)=>{if(d[0])txt(d[0],pts[i][0],pts[i][1]-48,14,P.muted,'center',650)});
rr(90,632,800,200,18,'#4fd1c514',P.cyan,2);
txt('實務建立貝氏網路的兩步工法',114,660,19,P.cyan,'left',900);
wrap('① 結構學習：由醫學專家劃定 DAG 箭頭，或用資料演算法（如評分搜尋）找最優拓撲。',114,684,750,24,16,P.ink,650);
wrap('② 參數估計：結構固定後，用病歷大資料以最大概似（MLE）填滿各節點的條件機率表（CPT）。',114,742,750,24,16,P.ink,650);
txt(`參數量：本圖 ${nParamMed} 個，若七個二元變數完全相依需 2⁷ − 1 = 127 個`,114,806,16,P.amber,'left',800);
rr(950,170,590,680,24,P.panel,'#ffffff14',2);
txt('設定證據，看後驗機率如何傳播',976,205,21,P.ink,'left',850);txt('Exact enumeration over all 2⁷ states',976,232,14,P.cyan,'left',650);
const rowsE=[['抽菸 S',['未知','是','否'],v=>{evS=v},evS],['X光 C₁',['未知','陽性','陰性'],v=>{evC=v},evC],['心電圖 H₁',['未知','陽性','陰性'],v=>{evH=v},evH]];
rowsE.forEach((r,i)=>{const y=270+i*74;txt(r[0],976,y,18,P.ink,'left',800);r[1].forEach((l,j)=>btn(l,1090+j*140,y-22,130,44,()=>{r[2](j);render()},r[3]===j,[P.muted,C2,P.lime][j],16))});
[['肺癌 C',pp[1],C2],['心臟病 H',pp[2],P.amber],['抽菸 S',pp[0],P.violet]].forEach((b,i)=>{const y=530+i*62;txt('P('+b[0]+' = 真 | 證據)',976,y-4,16,P.ink,'left',700);
rr(976,y+8,520,24,8,'#ffffff12');rr(976,y+8,Math.max(3,520*b[1]),24,8,b[2]+'cc');(b[1]>.85?txt(b[1].toFixed(3),976+520*b[1]-10,y+20,17,'#04121b','right',900):txt(b[1].toFixed(3),976+Math.max(3,520*b[1])+8,y+20,17,b[2],'left',900))});
wrap('CPT 為示意數值（僅 P(C=真 | S=真) = 0.20 取自講義），用來示範推論；真實應用需由病歷資料估計。',976,730,530,22,14,P.muted,600);
showF([]);
}
render();
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