29:null 2a:["$","title",null,{"children":"Plot asymptotic vs empirical LRT distribution | Sergei Pond | Observable"}] 2f:Tc37,vegalite ({ "hconcat" : [{ "title" : "LRT CDF plots", "width" : 250, "height" : 250, "layer" : [ { "data": {"values": data}, //"transform": [{"filter": "datum.symbol==='GOOG'"}], "mark": {"type" : "line", "interpolate" : "monotone"}, "encoding": { "x": {"field": "x", "type": "quantitative", "axis" : {"grid" : false, "title" : "LRT", labelFontSize : 14}}, "y": {"field": "y", "type": "quantitative", "axis" : {"grid" : false, "title" : "CDF", labelFontSize : 14}, "scale" : {"type" : "linear"}}, } }, { "data": {"values": lrtData}, "mark": {"type" : "line", "interpolate" : "step", "color" : "firebrick"}, "encoding": { "x": {"field": lrt_column, "type": "quantitative", "axis" : {"grid" : false, "title" : "LRT", labelFontSize : 14}}, "y": {"field": "CDF", "type": "quantitative", "axis" : {"grid" : false, "title" : "CDF", labelFontSize : 14}, "scale" : {"type" : "linear"}}, } } ] },{ "title" : "LRT histogram", "width" : 250, "height" : 250, "layer" : [ { "data": {"values": binned_data}, "mark": {"type" : "rect", "color" : "firebrick", "opacity" : "0.5"}, "encoding": { "x": {"field": "x0", "type": "quantitative", "axis" : {"grid" : false, "title" : "LRT", labelFontSize : 14}}, "x2": {"field": "x1", "type": "quantitative", "axis" : {"grid" : false, "title" : "LRT", labelFontSize : 14}}, "y": {"field": "count","axis" : {"grid" : false, "title" : "Count", labelFontSize : 14}, "scale" : {"type" : "sqrt"}}, } }, { "data": {"values": binned_data}, "mark": {"type" : "line", "color" : "steelblue", "size" : 5}, "encoding": { "x": {"field": "x0", "type": "quantitative", "axis" : {"grid" : false, "title" : "LRT", labelFontSize : 14}}, "y": {"field": "asymptotic","axis" : {"grid" : false, "title" : "Count", labelFontSize : 14}, "scale" : {"type" : "sqrt"}}, } } ] },{"width" : 250, "height" : 250, "title" : "Q-Q plot", "layer" : [ { "data": {"values": [{}]}, "mark": { "type": "rule", "color": "orange", }, "encoding": { "x": { "datum": {"expr": "0"}, "type": "quantitative", "scale": {"domain": [0, 1]} }, "y": { "datum": {"expr": "0"}, "type": "quantitative", "scale": {"domain": [0, 1]} }, "x2": {"datum": {"expr": "1"}}, "y2": {"datum": {"expr": "1"}} } }, { "data": {"values": qq_data}, "mark": {"type" : "line", "interpolate" : "step"}, "encoding": { "x": {"field": "CDF", "type": "quantitative", "axis" : {"grid" : false, "title" : "Empirical", labelFontSize : 14}}, "y": {"field": "ASM", "type": "quantitative", "axis" : {"grid" : false, "title" : "Asymptotic", labelFontSize : 14}, "scale" : {"type" : "linear"}}, } } ]}] })30:[] 2d:{"id":"1eaa7ff025f56370","slug":"plot-asymptotic-vs-empirical-lrt-distribution","title":"Plot asymptotic vs empirical LRT distribution","thumbnail":"59be57638aff25d62662d7704c258a421407877d0f6ca03008640cbe2bf65ce7","access_level":"public","create_time":"$D2022-09-09T18:43:05.457Z","update_time":"$D2022-10-20T15:17:30.329Z","view_time":null,"first_public_time":"$D2022-09-12T13:27:42.482Z","has_unpublished_edits":null,"fork":false,"stars":2,"starred":false,"owner":{"type":"team","id":"9bf992815a7b66f2","login":"spond","name":"Sergei Pond","avatar_url":"https://avatars-next.observableusercontent.com/23c8c466a3ef27f1444c95a9ed8e52bcf08888403b6d4efbd039319b0761c13d","tier":"starter_2024"},"version":468,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"f439ea11e6786e12","login":"spond","name":"Sergei Pond","avatar_url":"https://avatars-next.observableusercontent.com/23c8c466a3ef27f1444c95a9ed8e52bcf08888403b6d4efbd039319b0761c13d","tier":null}],"members":[{"type":"individual","id":"f439ea11e6786e12","login":"spond","name":"Sergei Pond","avatar_url":"https://avatars-next.observableusercontent.com/23c8c466a3ef27f1444c95a9ed8e52bcf08888403b6d4efbd039319b0761c13d","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":3,"collection":null,"type":"notebook","body":{"title":"Plot asymptotic vs empirical LRT distribution","cells":[{"id":0,"value":"# Plot asymptotic vs empirical LRT distribution","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":386,"value":"Upload a .csv file which contains, as one column, likelihood ratio test values.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":136,"value":"viewof lrt_result_file = params.get (\"url\") ? localFileInput({accept: \".csv\", value : params.get (\"url\"), disable: true}) : localFileInput({accept: \".csv\"}) ","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":164,"value":"viewof lrt_column = Inputs.select(_.keys (simulatedLRT[0]), {value: \"LRT\", label: \"LRT column\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"#### Define the asymptotic distribution as mixture of χ² components with different degrees of freedom","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":33,"value":"viewof mixture = Inputs.form([\n Inputs.text( {value : 0, label: \"0df weight\", validate : validateValue}),\n Inputs.text( {value : 1, label: \"1df weight\", validate : validateValue}),\n Inputs.text( {value : 0, label: \"2df weight\", validate : validateValue}),\n])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"viewof mixture2 = Inputs.text( {value : 1 - mixture[0] - mixture[1] - mixture[2], label: \"3df weight\", \"disabled\" : true})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":333,"value":"viewof autotune = Inputs.button(\"Optimize weights\", {\"reduce\" : value => {\n const v = opt.nelderMead (mixture_loss, [0.2,0.2,0.2]);\n set (viewof mixture, _.map (v.x, (d)=> \"\" + d));\n return 1;\n}})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":393,"value":"Click on the above button to adjust mixture weights to minimize the Kolmogorov test statistics.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":358,"value":"**Table 1**. Values of asymptotic LRT for different critical (alpha) levels, and the corresponding empirical quantiles.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":302,"value":"viewof table1 = Inputs.table (critical_values[1], {\n rows : 15,\n //format: sites_table[0]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":324,"value":"md`Kolmogorov test statistic **${critical_values[0].toFixed (3)}**`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":104,"value":"$2f","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":145,"value":"simulatedLRT = _.map (await get_csv (params.get (\"url\")), (d)=>d3.autoType (d))","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":172,"value":"lrtData = {\n let rd = _.sortBy (_.map (simulatedLRT, (d)=>_.mapValues (_.pick (d, lrt_column), (d)=>Math.max (0, d))), (d)=>d[lrt_column]);\n _.each (rd, (d,i)=> {\n d['CDF'] = (i+1)/rd.length;\n })\n return rd;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":195,"value":"qq_data = {\n let dd = _.map (lrtData, (d)=> {\n let dd = _.clone (d);\n dd[\"ASM\"] = asymptotic_cdf (d[lrt_column]);\n return dd;\n });\n return _.filter (dd, (c,i)=> (i == dd.length - 1 || (c[\"LRT\"] < dd[i+1][\"LRT\"])));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":240,"value":"critical_values = {\n let kD = 0;\n let critical_values = [0.2,0.1,0.05,0.03,0.02,0.01,0.005,0.001];\n let critical_cutoffs = _.map (critical_values, (d)=> solver (0,100,0.01, (x)=>asymptotic_cdf (x)-(1-d))[0]);\n let crit_i = 0;\n let crit_table = [];\n _.each (qq_data, (d, i)=> {\n kD = Math.max (kD, Math.abs (d[\"ASM\"] - d[\"CDF\"]));\n if (crit_i < critical_values.length) {\n if (d[\"LRT\"] >= critical_cutoffs[crit_i] && (!i || qq_data[i-1][\"LRT\"] < critical_cutoffs[crit_i])) {\n crit_table.push ({\"LRT\" : critical_cutoffs[crit_i], \"alpha\" : critical_values[crit_i], \"empirical\" : 1-qq_data[i-1][\"CDF\"]});\n crit_i ++;\n \n }\n }\n });\n return [kD, crit_table];\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":249,"value":"asymptotic_cdf = (d, w)=> {\n w = w || weights;\n return w[0] + w[1] * jStat.chisquare.cdf (d, 1) + w[2] * jStat.chisquare.cdf (d, 2) + w[3] * jStat.chisquare.cdf (d, 3);\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":433,"value":"binned_data = _.map (d3.bin().thresholds(50)(_.map (lrtData, (d)=>d[lrt_column])), (d)=> {\n let r = {'x0' : d.x0, 'x1' : d.x1, 'count' : d.length, 'asymptotic' : (asymptotic_cdf (d.x1) - asymptotic_cdf (d.x0) + (d.x0 == 0 ? asymptotic_cdf(0) : 0))*lrtData.length}; return r;\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":89,"value":"data = _.map (_.range (0,10,0.01), (d)=> {\n return { 'x' : d,\n 'y' : asymptotic_cdf (d)}\n});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":101,"value":"vegalite = require (\"vega-embed\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":93,"value":"weights = [+mixture[0], +mixture[1], +mixture[2], +mixture2]","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":6,"value":"jStat = require('jstat@1.9.5/dist/jstat.js')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"validateValue = (t)=> {\n console.log (t.value);\n let tt = parseFloat (t.value);\n if (tt >= 0 && tt <= 1) return true;\n return false;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":138,"value":"import {localFileInput} from \"@mbostock/localfile\"","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":142,"value":"params = new URLSearchParams(location.search)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":149,"value":"get_csv = async (json_source)=> {\n if (json_source) {\n return d3.csv (json_source,d3.autoType);\n }\n return lrt_result_file.csv();\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":271,"value":"solver = solver_module.default","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":263,"value":"solver_module = import('https://cdn.skypack.dev/find-zero-range@3.0.0?min')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":311,"value":"mixture_loss = (X)=> {\n if (X[0] < 0 || X[0] > 1 || X[1] < 0 || X[1] > 1 || X[2] < 0 || X[2] > 1 || X[1] + X[0] + X[2] > 1) return 1;\n let w = [X[0],X[1],X[2], 1-X[0]-X[1]-X[2]];\n let dd = _.map (lrtData, (d)=> {\n let dd = _.clone (d);\n dd[\"ASM\"] = asymptotic_cdf (d[lrt_column], w);\n return dd;\n });\n dd = _.filter (dd, (c,i)=> (i == dd.length - 1 || (c[\"LRT\"] < dd[i+1][\"LRT\"])));\n return d3.max (dd, (d)=>Math.abs (d[\"ASM\"]-d[\"CDF\"]));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":307,"value":"opt = require('fmin@0.0.2/build/fmin.js')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":340,"value":"function set(input, value) {\n input.value = value;\n input.dispatchEvent(new Event(\"input\", {bubbles: true}));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W30","stdlib":"1","titling":"auto"}} 2e:"$2d:body"