2f:T5d9,// not used anymore function plotPdf(data, {w = width, h = height} = {}) { const svg = d3.create("svg") .attr("viewBox", [0, 0, w, h]) .attr("width", w) .attr("height", h); const x = svg.x = d3.scaleLinear() .domain([0, 1]) .range([margin.left, w - margin.right]); const y = svg.y = d3.scaleLinear() .domain([0, d3.max(data, d => d.y) * 1.05]).nice() .range([h - margin.bottom, margin.top]); svg.append("g") .attr("transform", `translate(0,${h - margin.bottom})`) .call(d3.axisBottom(x)) .append("text") .text("Success probability") .style("text-anchor", "middle") .attr("x", w/2) .attr("y", margin.bottom) .attr("dy", "-0.5em") .attr("fill", "currentColor"); svg.append("g") .attr("transform", `translate(${margin.left},0)`) .call(d3.axisLeft(y).ticks(h / (2 * em)).tickSizeOuter(0)) .append("text") .text("Probability density") .style("text-anchor", "middle") .call(attrs, { id: "yLabel", fill: "currentColor", x: -h / 2, y: 0, transform: "rotate(-90)", dy: "-3em", }) const line = d3.line() .x(d => x(d.x)) .y(d => y(d.y)); svg.append("path") .datum(data) .call(attrs, { fill: "none", stroke: "steelblue", "stroke-width": 1.5, "stroke-linejoin": "round", "stroke-linecap": "round", d: line, }); return svg; }30:T7c8,calcHdi = (xs, ys, hdi_prob) => { // create array of histogram bins. index of bin is the index of the smaller x. var arr = new Array(xs.length - 1); for (let i = 0; i < arr.length; i++) { arr[i] = {y: (ys[i+1] + ys[i]) / 2, dx: (xs[i+1] - xs[i]), idx: i}; } // sort the array by the height of each bin arr.sort((a, b) => d3.descending(a.y, b.y)); // collect bin indexes of the highest density hdi_prob% // TODO use d3.Adder for more precision var cumsum = 0.0; var idxs = new Array(); var last_dy; for (let d of arr) { cumsum += d.dx * d.y; idxs.push(d.idx); if (cumsum > hdi_prob && d.y !== last_dy) break; last_dy = d.y; } // sort these bin indexes idxs.sort(d3.ascending); // collect array of highest density intervals. var first_idx = idxs[0]; var last_idx = idxs[0] - 1; // good default to not start a new interval straight away var intervals = new Array(); function smoothed_interval(first_idx, last_idx) { // takes either the middle of this bin or // the range begin (resp. end) if it's the first (resp. last) bin var begin, end; if (first_idx === 0) { begin = xs[0]; } else { // the middle of this bin begin = (xs[first_idx] + xs[first_idx + 1]) / 2; } if (last_idx === xs.length - 2) { end = xs[last_idx + 1]; } else { // the middle of this bin end = (xs[last_idx] + xs[last_idx + 1]) / 2; } return [begin, end]; } // add a new interval where neighboring indexes are non-consecutive for (let i of idxs) { if (i === last_idx + 1) { // bin adjoins the previous one last_idx = i; } else { // create a new interval from the previous ones intervals.push(smoothed_interval(first_idx, last_idx)); // start a new interval first_idx = last_idx = i; } } // the last interval certainly wasn't pushed intervals.push(smoothed_interval(first_idx, last_idx)); return intervals; }31:[] 2d:{"title":"Easy compare: Simple binomial outcome analyzer","cells":[{"id":0,"value":"md`# Easy compare: Simple binomial outcome analyzer`","pinned":false,"hidden":false,"mode":"ojs"},{"id":773,"value":"md`\n_Have you ever wondered how likely your results are to happen again? This tool helps you understand the chances of success in simple terms, using your own data and a bit of smart statistics._\n\n## Calculator\n\n### 1. Setting the scene\n\nWhat’s your initial guess about the _${success_term.toLowerCase()}_? Use the sliders to set your starting expectations. Think of it as your gut feeling before seeing new results. The default setting means that initially you are clueless about the result.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":69,"value":"viewof alpha_0 = Inputs.range([0.1, 10], {value: 1, label: \"Optimism setting:\", step: 0.1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":70,"value":"viewof beta_0 = Inputs.range([0.1, 10], {value: 1, label: 'Pessimism setting:', step: 0.1})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1077,"value":"{\n const priorData = xs\n .map(x => ({x: x, y: jStat.beta.pdf(x, alpha_0, beta_0)}))\n .filter(d => Number.isFinite(d.y) && !Number.isNaN(d.y));\n const plot = Plot.plot({\n width: 20*em,\n height: 10*em,\n marginTop: 10,\n x: {label: success_term, labelAnchor: \"center\", ticks: 11, grid: true, labelArrow: false},\n y: {zero: true, label: \"Prior probability\", labelAnchor: \"center\", ticks: 5, grid: true},\n marks: [\n Plot.ruleX([0], {y1: d3.max(priorData, d => d.y) * 1.1, stroke: null}),\n Plot.ruleY([0]),\n Plot.line(priorData, {x: \"x\", y: \"y\", stroke: \"steelblue\"})\n ]\n });\n \n return md`These settings can be visualized as follows. The higher the graph is on the right, the more likely you consider optimistic results.\n\n ${plot}`;\n}\n ","pinned":false,"hidden":false,"mode":"ojs"},{"id":908,"value":"md`### 2. Observations\n\nTell us about your recent experiments. How many times did you try and how many times did it work?\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":133,"value":"viewof n = NumberText({\n label: 'Total experiments: ',\n value: 10,\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":194,"value":"viewof k = Inputs.range([0, n], {\n value: this?.value ?? Math.round(n / 2),\n label: 'Successful experiments:',\n step: 1\n});","pinned":false,"hidden":false,"mode":"ojs"},{"id":739,"value":"{\n const scaledN = Math.min(20, n);\n var scaledK = Math.round(k * scaledN / n);\n if (scaledK === 0 && k > 0) {\n scaledK = 1;\n }\n const icons = d3.shuffler(d3.randomLcg(42))(Array(scaledN).fill('🙂', 0, scaledK).fill('❌', scaledK, scaledN)).join(' ');\n return html`${icons}`\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":913,"value":"md`### 3. Fine-tuning your analysis\n\n#### Confidence\n\nChoose how sure you want to be about these predictions. Remember, being very sure might mean less precise results.\n`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1628,"value":"viewof hdi_enabled = Inputs.toggle({label: \"Enabled:\", value: true})","pinned":false,"hidden":false,"mode":"ojs"},{"id":343,"value":"viewof hdi_prob = Inputs.range([0.01, 1], {value: 0.9, step: 0.01, label: 'HDI probability:'})","pinned":false,"hidden":false,"mode":"ojs"},{"id":916,"value":"{\n const gcd_ = gcd(100 - hdi_percent, 100);\n const nearest_nice_denominator = nice_denominators.find(x => x <= gcd_ && gcd_ % x == 0);\n \n return md`This means ${(100 - hdi_percent) / nearest_nice_denominator} in ${100 / nearest_nice_denominator} similar predictions will be incorrect.`\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1554,"value":"#### Comparison with a fixed probability","pinned":false,"hidden":false,"mode":"md"},{"id":1565,"value":"viewof comparison_enabled = Inputs.toggle({label: \"Enabled:\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1609,"value":"viewof comparison_value = Inputs.range([0.0, 1.0], {value: 0.5, step: 0.01, default: 0.7, label: 'Comparison value:'})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1607,"value":"#### Comparison with another observation","pinned":false,"hidden":false,"mode":"md"},{"id":1608,"value":"viewof second_enabled = Inputs.toggle({label: \"Enabled:\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1611,"value":"viewof second_n = NumberText({\n label: 'Second total: ',\n value: this?.value ?? n,\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1612,"value":"viewof second_k = Inputs.range([0, second_n], {\n value: this?.value ?? Math.round(second_n / 2),\n label: 'Second successes:',\n step: 1\n});","pinned":false,"hidden":false,"mode":"ojs"},{"id":648,"value":"md`## Results`","pinned":false,"hidden":false,"mode":"ojs"},{"id":768,"value":"hdi_enabled ? md`The ${success_term.toLowerCase()} is very likely between ${hdis.length > 1 ? 'either' : ''} ${\n hdis.map(([x0, x1]) => {\n const numDigits = Math.max(2, 2-Math.ceil(Math.log10(x1-x0)));\n return `${x0.toFixed(numDigits)} and ${x1.toFixed(numDigits)}`}).join(', or ')\n} (marked with ${\n svg``\n}).` : md``","pinned":false,"hidden":false,"mode":"ojs"},{"id":1235,"value":"{\n var marks = [Plot.ruleY([0], {stroke: \"#666\"})]\n if (hdi_enabled) {\n marks.push(\n Plot.areaY(posteriorProbs, {\n x: \"x\",\n y0: 0,\n y1: d => hdis.some(hdi => hdi[0] <= d.x && d.x <= hdi[1]) ? d.y : NaN,\n fill: \"red\",\n fillOpacity: 0.3\n })\n )\n }\n marks.push(\n Plot.line(posteriorProbs, {x: \"x\", y: \"y\", stroke: \"steelblue\"})\n );\n if (comparison_enabled) {\n marks.push(\n Plot.ruleX([comparison_value], {stroke: \"darkorchid\"})\n )\n }\n if (second_enabled) {\n marks.push(\n Plot.line(second_posteriorProbs, {x: \"x\", y: \"y\", stroke: \"green\"})\n )\n }\n\n return Plot.plot({\n width: width,\n x: {\n grid: true,\n label: success_term,\n labelAnchor: \"center\",\n labelArrow: false\n },\n y: {\n grid: true,\n zero: true,\n label: \"Probability density\",\n labelAnchor: \"center\",\n },\n marks: marks\n })\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1573,"value":"comparison_enabled ? md`The success rate is ${(posterior_cdf(comparison_value) * 100).toFixed(0)}% likely to be below ${comparison_value} and ${(100 - posterior_cdf(comparison_value) * 100).toFixed(0)}% likely to be greater than that.` : md``","pinned":false,"hidden":false,"mode":"ojs"},{"id":1687,"value":"second_enabled ? md`The first ${success_term.toLowerCase()} (${k} out of ${n}, blue line) is ${(prob_p1_lt_p2 * 100).toFixed(0)}% likely to be less than the second (${second_k} out of ${second_n}, green line).` : md``","pinned":false,"hidden":false,"mode":"ojs"},{"id":728,"value":"md`## Appendix`","pinned":false,"hidden":false,"mode":"ojs"},{"id":797,"value":"md`### Variables`","pinned":false,"hidden":false,"mode":"ojs"},{"id":630,"value":"md`~~~js\nn = ${n}\nk = ${k}\nalpha_0 = ${alpha_0}\nbeta_0 = ${beta_0}\n~~~`","pinned":false,"hidden":false,"mode":"ojs"},{"id":803,"value":"md`Parameters of posterior:`","pinned":false,"hidden":false,"mode":"ojs"},{"id":138,"value":"alpha = alpha_0 + k","pinned":true,"hidden":false,"mode":"ojs"},{"id":164,"value":"beta = beta_0 + n - k","pinned":true,"hidden":false,"mode":"ojs"},{"id":928,"value":"hdi_percent = Math.round(hdi_prob * 100)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1478,"value":"nice_numbers = [1,2,5,10,20,100]","pinned":false,"hidden":false,"mode":"ojs"},{"id":1482,"value":"nice_denominators = nice_numbers.map(x => 100 / x)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1596,"value":"viewof success_term = Inputs.text({value: \"Success rate\", label: \"Success term:\"})","pinned":false,"hidden":false,"mode":"ojs"},{"id":271,"value":"hdis = calcHdi(xs, posteriorProbs.map(d => d.y), hdi_prob)","pinned":false,"hidden":false,"mode":"ojs"},{"id":42,"value":"xs = d3.ticks(0.0, 1.0, 1000)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1647,"value":"posteriorProbs = xs.map(d => ({x: d, y: posterior(d)})).map(\n (d, i, arr) => (\n Number.isFinite(d.y) && !Number.isNaN(d.y) ?\n d :\n {x: d.x, y: arr[i == 0 ? 1 : i - 1].y}\n )\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":689,"value":"em = parseFloat(getComputedStyle(d3.select('body').node()).fontSize);","pinned":false,"hidden":false,"mode":"ojs"},{"id":58,"value":"height = 500","pinned":false,"hidden":false,"mode":"ojs"},{"id":56,"value":"margin = ({top: 20, right: 20, bottom: 35, left: 40})","pinned":false,"hidden":false,"mode":"ojs"},{"id":1653,"value":"md`### Second distribution`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1658,"value":"second_alpha = alpha_0 + second_k","pinned":false,"hidden":false,"mode":"ojs"},{"id":1659,"value":"second_beta = beta_0 + second_n - second_k","pinned":false,"hidden":false,"mode":"ojs"},{"id":1660,"value":"second_posteriorProbs = xs.map(d => ({x: d, y: second_posterior(d)})).map(\n (d, i, arr) => (\n Number.isFinite(d.y) && !Number.isNaN(d.y) ?\n d :\n {x: d.x, y: arr[i == 0 ? 1 : i - 1].y}\n )\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1671,"value":"prob_p1_lt_p2 = 1 - d3.sum(\n posteriorProbs.map(d => d.y * jStat.beta.cdf(d.x, second_alpha, second_beta))\n) / posteriorProbs.length","pinned":false,"hidden":false,"mode":"ojs"},{"id":1661,"value":"second_posterior = x => jStat.beta.pdf(x, second_alpha, second_beta)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1417,"value":"md`### Functions`","pinned":false,"hidden":false,"mode":"ojs"},{"id":1016,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs"},{"id":1019,"value":"function attrs (selection, o) {\n for (let name in o) {\n console.log(name, o[name]);\n selection = selection.attr(name, o[name]); \n }\n return selection;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":9,"value":"posterior = x => jStat.beta.pdf(x, alpha, beta)","pinned":false,"hidden":false,"mode":"ojs"},{"id":1561,"value":"posterior_cdf = x => jStat.beta.cdf(x, alpha, beta)","pinned":true,"hidden":false,"mode":"ojs"},{"id":263,"value":"$30","pinned":false,"hidden":false,"mode":"ojs"},{"id":1462,"value":"gcd = {\n var gcd = function(a, b) {\n if (!b) {\n return a;\n }\n return gcd(b, a % b);\n }\n return gcd;\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":1432,"value":"md`### Imports`","pinned":false,"hidden":false,"mode":"ojs"},{"id":35,"value":"jStat = require('jStat')","pinned":false,"hidden":false,"mode":"ojs"},{"id":24,"value":"d3 = require('d3@6')","pinned":false,"hidden":false,"mode":"ojs"},{"id":638,"value":"import {NumberText} from \"@treszkai/number-text\"","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}