2a:null 2b:["$","title",null,{"children":"Conditioning | Pierre PC | Observable"}] 30:T802,experiment = { const experiment = { values: [[false,false]], n: 1, m: 1, precision: 1 }; experiment.update = function (n,m) { this.n = n; this.m = m; let values = Array.from({length: n}, function() { return Array.from({length: m}, () => probabilities.randomOutcome()) }); this.values = values; this.precision = Math.pow(10,Math.floor(Math.log10(n*m))); return values }; experiment.stats = function () { let array = [0,0,0,0]; this.values.forEach((l,i) => l.forEach(function (outcome,j) { array[outcome.value] += 1 })); return array }; experiment.description = function () { const practArray = experiment.stats(); const theoArray = probabilities.values; let theoCond = theoArray[0]; let theoA = theoArray[0]; let theoB = theoArray[0]; let practCond = practArray[0]; let practA = practArray[0]; let practB = practArray[0]; theoA += conditioning.onB() ? 0 : theoArray[1]; theoB += conditioning.onA() ? 0 : theoArray[2]; theoCond += conditioning.cases( 0, theoArray[1], theoArray[2], 0 ); practA += conditioning.onB() ? 0 : practArray[1]; practB += conditioning.onA() ? 0 : practArray[2]; practCond += conditioning.cases( 0, practArray[1], practArray[2], 0 ); if (conditioning.mask.value === 3) { theoCond = 1; practCond = practArray.reduce((a,b) => a+b, 0) } const f = (x) => Math.round(this.precision*x)/this.precision; this.theo = `Theoretical probabilities: ℙ(A${conditioning.text()})≃${f(theoA/theoCond)} ℙ(B${conditioning.text()})≃${f(theoB/theoCond)}.`; this.pract = `Observed probabilities: ℙ(A${conditioning.text()})≃${f(practA/practCond)} ℙ(B${conditioning.text()})≃${f(practB/practCond)}.`; return `${this.theo}

${this.pract}` }; return experiment }31:T66e,drawExperiment = function (exp,ctx,sizex,sizey) { const dx = 0.5*sizex / exp.n; const dy = 0.5*sizey / exp.m; const radius = Math.min(0.6*dx,0.7*dy); const textSize = Math.floor(radius); const centers = Array.from({length: exp.n}, function (a,i) { return Array.from({length: exp.m}, (b,j) => [dx+2*i*dx, dy+2*j*dy]) }); ctx.clearRect(0,0,sizex,sizey); ctx.globalAlpha = 0.7; ctx.textAlign = "center"; ctx.textBaseline = "middle"; ctx.font = `${textSize}px Arial`; centers.forEach((l,i) => l.forEach(function (center,j) { ctx.beginPath(); ctx.moveTo(center[0] + 0.5*radius, center[1]); ctx.arc(center[0]-0.5*radius, center[1], radius, 0, 2 * Math.PI); ctx.stroke(); if (exp.values[i][j].AOccurs()) { ctx.fillStyle = "#ff6080"; ctx.fill() } ctx.beginPath(); ctx.moveTo(center[0] + 1.5*radius, center[1]); ctx.arc(center[0]+0.5*radius, center[1], radius, 0, 2 * Math.PI); ctx.stroke(); if (exp.values[i][j].BOccurs()) { ctx.fillStyle = "#6080ff"; ctx.fill() } ctx.fillStyle = "black"; if (exp.values[i][j].AOccurs()) { ctx.fillText("A",center[0]-0.5*radius,center[1]) } if (exp.values[i][j].BOccurs()) { ctx.fillText("B",center[0]+0.5*radius,center[1]) } ctx.fillStyle = "white"; if (!exp.values[i][j].AOccurs() & conditioning.onA()) { ctx.rect(center[0]-dx,center[1]-dy,2*dx,2*dy); ctx.fill() } else if (!exp.values[i][j].BOccurs() & conditioning.onB()) { ctx.rect(center[0]-dx,center[1]-dy,2*dx,2*dy); ctx.fill() } })); }32:[] 2e:{"id":"8214f2839749327f","slug":"conditioning","title":"Conditioning","thumbnail":"0a2cf9c0b6049fe2736fff9cde782f2231cf390a5b58c78b6fa7cffbe23d08ff","access_level":"public","create_time":"$D2020-01-21T22:17:21.463Z","update_time":"$D2025-03-14T15:50:06.031Z","view_time":null,"first_public_time":"$D2020-01-22T06:34:56.705Z","fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"e63037398666117f","login":"pierrepc","name":"Pierre PC","avatar_url":"https://avatars-next.observableusercontent.com/22250a38885985472d38da2a64469ebd2a0f1b7ba0e6869a5ccb10ce8ca7aa66","tier":"starter_2024"},"version":1067,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"e1fb4a1ab7bf50c7","login":"pierrepc","name":"Pierre PC","avatar_url":"https://avatars-next.observableusercontent.com/22250a38885985472d38da2a64469ebd2a0f1b7ba0e6869a5ccb10ce8ca7aa66","tier":null}],"members":[{"type":"individual","id":"e1fb4a1ab7bf50c7","login":"pierrepc","name":"Pierre PC","avatar_url":"https://avatars-next.observableusercontent.com/22250a38885985472d38da2a64469ebd2a0f1b7ba0e6869a5ccb10ce8ca7aa66","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":{"id":"ac21ca0b7e8ed20d","slug":"probability-course","title":"Probability course","owner":{"id":"e63037398666117f","login":"pierrepc","name":"Pierre PC"}},"type":"notebook","body":{"title":"Conditioning","cells":[{"id":0,"value":"md`# Conditioning\n\nWe are interested in two events A and B. The probability of them happening can be chosen below, including the probability that they happen simultaneously. We can then sample a few realisations and condition on the desired results, to see the conditional probability in action.`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":6,"value":"element = {\n const elmt =\n html`

ℙ(A) =
\n ℙ(B) =
\n ℙ(A∩B) =
\n \n Warning: these probabilities are not compatible; the simulations will be nonsensical.\n \n

`;\n elmt.addEventListener(\"input\", function () {\n master.element = elmt;\n master.reload(\"hard\");\n elmt.getElementsByTagName(\"span\")[0].style.display = (master.healthy ? \"none\" : \"inline\")\n });\n elmt.dispatchEvent(new CustomEvent(\"input\"));\n return elmt\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":520,"value":"checkBoxes = {\n const form = html`Conditioning on A B`;\n const inputs = form.getElementsByTagName(`input`);\n \n form.addEventListener(\"change\", () => form.dispatchEvent(new CustomEvent(\"input\")));\n form.addEventListener(\"input\", () => {master.inputs = inputs, master.reload(\"soft\")});\n \n master.inputs = inputs;\n \n return form\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":46,"value":"{ const button = html``;\n button.addEventListener(\"click\", (e) => master.reload(\"hard\"));\n return button\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":180,"value":"img = {\n const canvas = document.createElement('canvas');\n const context = canvas.getContext('2d');\n canvas.width = width;\n canvas.height = height;\n \n master.image = canvas;\n \n canvas.update = function (option) {\n if (option != \"soft\") {\n experiment.update(...grid)\n }\n drawExperiment(experiment,context,width,height)\n };\n \n canvas.update();\n \n return canvas\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":553,"value":"description = {\n const descr = html`

`;\n \n descr.set = function (s) {\n descr.innerHTML = s\n };\n \n return descr\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":548,"value":"md`### *Don't bother reading below this point*\n(Unless you like to read code...)`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":479,"value":"conditioning = {\n const conditioning = { mask: new Outcome(true,false) };\n \n conditioning.update = function (inputs) {\n this.mask.setBooleans(inputs[0].checked, inputs[1].checked);\n \n return this.mask\n };\n \n conditioning.text = function () {\n return this.mask.cases(\"|A∩B\",\"|A\",\"|B\",\"\")\n };\n \n conditioning.onA = function () {\n return this.mask.AOccurs()\n };\n conditioning.onB = function () {\n return this.mask.BOccurs()\n };\n \n conditioning.cases = function (x1,x2,x3,x4) {\n return this.mask.cases(x1,x2,x3,x4)\n };\n \n return conditioning\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":237,"value":"$30","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":861,"value":"$31","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":8,"value":"probabilities = {\n const probabilities = { values: [0.25,0.25,0.25,0.25] };\n \n probabilities.update = function (elmt) {\n let p = elmt.getElementsByTagName(`input`);\n p = Object.values(p).map(e => parseFloat(e.value));\n p = [p[2], p[0] - p[2], p[1] - p[2], 1 - p[0] - p[1] + p[2]];\n this.values = p;\n this.healthy = (p[1] >= 0 && p[2] >= 0 && p[3] >= 0);\n return this.healthy\n };\n \n probabilities.outcomeFromRandom = function (rand) {\n const self = this;\n let level = 1;\n let s = 3;\n self.values.forEach(function (p,i) {\n if (rand < level) {\n s = i\n }\n level -= p\n });\n return new Outcome(s)\n };\n \n probabilities.randomOutcome = function () {\n return this.outcomeFromRandom(Math.random())\n };\n \n return probabilities\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":872,"value":"Outcome = function (value) {\n this.value = (value === undefined) ? 0 : value;\n \n this.setId = (i) => { this.value = i };\n this.setBooleans = function (A,B) {\n this.value = 3;\n this.value -= A ? 2 : 0;\n this.value -= B ? 1 : 0\n };\n \n this.booleans = function () {\n const array = [[true,true], [true,false], [false,true], [false,false]];\n return array[this.value]\n };\n \n this.cases = function (x1,x2,x3,x4) {\n const array = [x1, x2, x3, x4];\n return array[this.value]\n };\n \n this.AOccurs = () => this.cases(true,true,false,false);\n this.BOccurs = () => this.cases(true, false, true, false);\n \n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":506,"value":"master = {\n const master = {};\n master.healthy = true;\n \n master.reload = function (option) {\n conditioning.update(this.inputs);\n this.healthy = probabilities.update(this.element);\n this.image.update(option);\n description.set(experiment.description())\n };\n \n return master\n }","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":181,"value":"height = 600","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"},{"id":1030,"value":"grid = [10, 10]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined"}],"files":"$W32","stdlib":"1","titling":"auto"}} 2f:"$2e:body"