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<!DOCTYPE html><html><head>
  <meta http-equiv="content-type" content="text/html; charset=UTF-8">
  <title>Probability Calculator - jsFiddle demo</title>

      <script type="text/javascript" src="https://ajax.googleapis.com/ajax/libs/angularjs/1.1.4/angular.min.js"></script><style type="text/css">@charset "UTF-8";[ng\:cloak],[ng-cloak],[data-ng-cloak],[x-ng-cloak],.ng-cloak,.x-ng-cloak{display:none;}ng\:form{display:block;}</style>

      <script type="text/javascript" src="https://rawgithub.com/prajwalkman/angular-slider/master/angular-slider.min.js"></script><style type="text/css"></style>

      <link rel="stylesheet" type="text/css" href="https://rawgithub.com/prajwalkman/angular-slider/master/angular-slider.min.css">

      <script type="text/javascript" src="http://d3js.org/d3.v3.js"></script>

      <link rel="stylesheet" type="text/css" href="http://twitter.github.io/bootstrap/assets/css/bootstrap.css">

  <style type="text/css">
    .axis path, .axis line {
    fill: none;
    stroke: #000;
    shape-rendering: crispEdges;
}
.line {
    fill: none;
    stroke: steelblue;
    stroke-width: 1.5px;
}
.vertex {
    fill: #1f77b4;
    fill-opacity: 1;
    stroke: #999;
    stroke-opacity: .5;
}
  </style>


<script type="text/javascript">//<![CDATA[

var app = angular.module('app', ['uiSlider']);

function km(days, day, prob) {
    daily = 1 - Math.pow(1.0 - prob / 100, 1.0 / days);
    bottom = Math.pow(1 - daily, days) / days;
    top_terms = d3.range(1, days - day + 2).map(function (i) {
        return daily * Math.pow(1 - daily, days - i) / (days + 1 - i);
    });
    top_sum = d3.sum(top_terms);
    return (top_sum / (top_sum + bottom)) * 100;
};

function Controller($scope) {
    $scope.probability = 75;
    $scope.days = 10;

    function refresh() {
        days = parseInt($scope.days);
        prob = parseInt($scope.probability);
        data = d3.range(1, days + 1).map(function (i) {
            return {
                day: i,
                prob: km(days, i, prob)
            }
        });

        x.domain([1, days]);
        d3x.call(xAxis);

        svg.select("path.line")
            .attr("d", line(data));

        svg.selectAll("circle.vertex")
            .remove();

        svg.selectAll("circle.vertex")
            .data(data)
        .enter().append("circle")
            .attr("cx", function (d, i) {return x(d.day)})
            .attr("cy", function (d, i) {return y(d.prob)})
            .attr("r", 2)
            .attr("class", "vertex")
            .append("title")
            .text(function (d, i) {
                return "Day " + d.day + " : " + Math.round(d.prob) + "%";
            });
    }

    $scope.$watch('days', refresh, true);
    $scope.$watch('probability', refresh, true);
}
//]]>

</script>


</head>
<body ng-app="app" class="ng-scope">
  <div class="container">

    <h1>Probability Calculator</h1>

<p>
This computes the "optimal" (as opposed to "honest") probability estimate that will minimize your averaged daily Brier score on a "contingent stopping" question, i.e. one which closes when an event is realized.
</p>
<p>
The calculator takes two inputs:</p>
<ol>
<li>the number of days until the event's deadline <b>when the question opened</b></li>
<li>your best estimate <b>at that time</b> of the overall probability over that entire period</li>
</ol>
<p>The calculator will assume that the event has equal and independent probability of happening on any given day, and will infer that daily probability from the overall probability you gave.
</p>
<p>
The calculator will then compute for all days until the deadline the probability forecast that minimizes your Brier score, at least "in theory" (that is, if a number of assumptions are verified, none of which will be spelled out here).
</p>

<div ng-controller="Controller" class="ng-scope">
    <label for="prob">Starting probability</label>
    <slider style="width:40%" floor="1" ceiling="99" step="1" precision="0" ng-model="probability" id="prob" class="ng-isolate-scope ng-scope ng-pristine ng-valid"><span class="bar"></span><span class="pointer" style="left: 117.040816326531px;"></span><span ng-bind-html-unsafe="translate({value: floor})" class="bubble limit ng-binding" style="opacity: 1;">1</span><span ng-bind-html-unsafe="translate({value: ceiling})" class="bubble limit ng-binding" style="left: 159px; opacity: 1;">99</span><span class="bubble ng-binding" ng-bind-html-unsafe="translate({value: ngModel})" style="left: 119px;">75</span></slider>
    <label for="days">Total number of days</label>
    <slider style="width:40%" floor="2" ceiling="365" step="1" precision="0" ng-model="days" id="days" class="ng-isolate-scope ng-scope ng-pristine ng-valid"><span class="bar"></span><span class="pointer" style="left: 3.41597796143251px;"></span><span ng-bind-html-unsafe="translate({value: floor})" class="bubble limit ng-binding" style="opacity: 0;">2</span><span ng-bind-html-unsafe="translate({value: ceiling})" class="bubble limit ng-binding" style="left: 152px; opacity: 1;">365</span><span class="bubble ng-binding" ng-bind-html-unsafe="translate({value: ngModel})" style="left: 5px;">10</span></slider>
</div>

<script>
    var margin = {
        top: 20,
        right: 20,
        bottom: 30,
        left: 50
    },
    width = 760 - margin.left - margin.right,
        height = 300 - margin.top - margin.bottom;

    var parseDate = d3.time.format("%d-%b-%y").parse;

    var x = d3.scale.linear()
        .range([0, width]);

    var y = d3.scale.linear()
        .range([height, 0]);

    var xAxis = d3.svg.axis()
        .scale(x)
        .orient("bottom");

    var yAxis = d3.svg.axis()
        .scale(y)
        .orient("left");

    var line = d3.svg.line()
        .x(function(d) {
        return x(d.day);
    })
        .y(function(d) {
        return y(d.prob);
    });

    var svg = d3.select("div.container").append("svg")
        .attr("width", width + margin.left + margin.right)
        .attr("height", height + margin.top + margin.bottom)
        .append("g")
        .attr("transform", "translate(" + margin.left + "," + margin.top + ")");

    x.domain([1, 2]);
    y.domain([0, 100]);

    var d3x = svg.append("g")
        .attr("class", "x axis")
        .attr("transform", "translate(0," + height + ")")
        .call(xAxis);

    svg.append("g")
        .attr("class", "y axis")
        .call(yAxis);

    svg.append("path")
        .attr("class", "line");

</script>


</body></html>