var ARMS = [0,0,0,0,0,0];
    var _PROBS = [ rbeta(2,9), rbeta(5,9), rbeta(5,9) ];
    var BB_RUN = 0;
    
    d3.select( "#reveal-div" )
        .selectAll("p")
        .data( _PROBS )
        .enter()
        .append("p")
        .text( function(d,i){ return "Arm " + (i + 1) + ": " +d.toFixed(4); } )
    
    
    function pdfbeta(x_array,a,b){
        //x is an array
        _beta = Beta(a,b);
        function _pdfbeta(x){
            return ( Math.pow(x,a-1)*Math.pow(1-x, b - 1) )/_beta 
        }
        
        return x_array.map( _pdfbeta )
    }
    
    function Beta(a,b){
        //stirlings approx
        // use logs and exponentials to avoid underflow
        // with logs is still giving me errors
        
        //var n = Math.pow(a, a - 0.5)*Math.pow(b, b-0.5)
        
        var log_n = Math.log(a)*(a - 0.5) + Math.log(b)*( b-0.5)
        //var d = Math.pow( a + b, a+ b-0.5)
        var log_d = Math.log( a + b)*(a+ b-0.5)
        return Math.sqrt( 2*Math.PI)*Math.exp(log_n - log_d)
        }

    
    function rbeta(a,b){
            //from Simulation and MC, Wiley
            
            var p = a/b;
            if (Math.min(a,b) <= 1){
                var lambda =  Math.min(a,b)
            }else{
                var lambda = Math.sqrt( (2*a*b - a - b)/(a+b-2) )
            }
            
            while (1){
               var R1 = Math.random();
               var R2 = Math.random();
               var y = Math.pow( ( 1./R1 - 1.), 1./lambda );
               if ( 4*R1*R2*R2 < (Math.pow(y, a - lambda)*Math.pow(  (1.+ p)/(1 + p*y) , a + b ) )){
                    return (p*y)/(1+ p*y) 
               }
            }
        }
        
    function rbeta_array( arm_counts){
        // to be used with ARMS with uniform prior.
        samples = []
        for (var i=0; i < arm_counts.length/2; i++){
            samples.push( 
                    rbeta(arm_counts[2*i + 1]+1, 1+arm_counts[2*i] - arm_counts[2*i+1] ) 
                    )
        }
        return samples
    }
        
    function draw_arm( p ){
        if (  Math.random() < p){ return 1 } else { return 0 }
    }
     
    
    function update_arm( arm_number ){
        var result = draw_arm(_PROBS[arm_number] );
        ARMS[2*arm_number] += 1;
        ARMS[2*arm_number+1] += result;
        redraw(arm_number);
        return
    }
     
    
    function bayesian_bandits(){
        //for (var i = 0; i < n_pulls; i++ ){
            //sample from Beta distributions
            var samples = rbeta_array(ARMS);
            var select = samples.indexOf( d3.max( samples) );
            update_arm( select );
            if (BB_RUN < 300){
                BB_RUN += 1;
                window.setTimeout( bayesian_bandits, 100 )
            }
            else{
                return 
            }
        //}
    }
    
    var x_array = [];
    var _N = 100;
    var max_data = 10
    for ( var i =0; i < _N; i++ ){
        x_array.push( .01*i )
    }

    var colors = ["#348ABD", "#A60628", "#7A68A6"]; 
    var fill_colors = [ "rgba(52, 128, 189,0.1)", "rgba(166, 6, 40, 0.1 )", "rgba( 122, 104, 166,0.1 )"]; 
    
    var w = 600,
    h = 150,
    margin = 15,
    y = d3.scale.linear().domain([0, max_data]).range([h - margin,0 + margin ]),
    x = d3.scale.linear().domain([0,_N]).range([0 + margin, w - margin])
       
    var vis = d3.select("#beta-graphs")
        .append("svg:svg")
        .attr("width", w )
        .attr("height", h )
        
    var g = vis.append("svg:g")
        
    var line = d3.svg.line()
        .x(function(d, i) { return x(i); })
        .y(y)

    
    for ( var i =0; i < 3; i++){
        var _data = pdfbeta(x_array, 1 + ARMS[2*i+1],1+ARMS[2*i] - ARMS[2*i+1] );
        g.selectAll('path.line')
            .data( [_data] )
            .enter()
            .append("svg:path")
            .attr("stroke", colors[i] )
            //.attr("fill", fill_colors[i] )
            //.attr("fill", fill_colors[i] )
            //.attr("stroke-width", 0 )
            .attr("d", line )
            .attr("id", "line-" + i );
    }
    

    g.append("svg:line")
        .attr("x1", x(0))
        .attr("y1",  y(0))
        .attr("x2", x(w))
        .attr("y2", y(0))
     
    g.append("svg:line")
        .attr("x1", x(0))
        .attr("y1", y(0))
        .attr("x2", x(0))
        .attr("y2", y(max_data))
        
    g.selectAll(".xLabel")
        .data( d3.range(0,1.2,.2) )
        .enter().append("svg:text")
        .attr("class", "xLabel")
        .text(String)
        .attr("x", function(d) { return x(100*d) })
        .attr("y", h)
        .attr("text-anchor", "middle")
        .attr("dy", 0.0 )
    /*
    g.selectAll(".yLabel")
        .data(y.ticks(4))
        .enter().append("svg:text")
        .attr("class", "yLabel")
        .text(String)
        .attr("x", 0)
        .attr("y", function(d) { return y(d) })
        .attr("text-anchor", "right")
        .attr("dy", 4)
    */
    g.selectAll(".xTicks")
        .data(x.ticks(5))
        .enter().append("svg:line")
        .attr("class", "xTicks")
        .attr("x1", function(d) { return x(d); })
        .attr("y1", y(0))
        .attr("x2", function(d) { return x(d); })
        .attr("y2", y(-0.1))

    vis.append("text")
        .attr("x", (w / 2))             
        .attr("y", 15 )
        .attr("text-anchor", "middle")  
        .style("font-size", "17px") 
        .text("Posterior Distributions");
     
    /*
    g.selectAll(".yTicks")
        .data(y.ticks(4))
        .enter().append("svg:line")
        .attr("class", "yTicks")
        .attr("y1", function(d) { return -1 * y(d); })
        .attr("x1", x(-0.3))
        .attr("y2", function(d) { return -1 * y(d); })
        .attr("x2", x(0))
    */
    



    <!-- Data for bar chart: Two time-series, alternating to form a single series. Bar Color will switch back & forth -->
    
    var data = ARMS;
    var labellist = ["Arm 1", "", "Arm 2", "", "Arm 3", ""];

    var w_bar = 600,
        h_bar = 170,
        labelpad = 50,
        x_bar = d3.scale.linear().domain([0, 100]).range([0, w_bar]),
        y_bar = d3.scale.ordinal().domain(d3.range(data.length)).rangeBands([0, h_bar], .2);

    var vis = d3.select("#paired-bar-chart")
      .append("svg:svg")
        .attr("width", w_bar + 40)
        .attr("height", h_bar + 20)
      .append("svg:g")

    var bars = vis.selectAll("g.bar")
        .data(data)
      .enter().append("svg:g")
        .attr("class", "bar")
        .attr("transform", function(d, i) { return "translate(" + labelpad + "," + y_bar(i) + ")"; })

                   
    bars.append("svg:rect")
        .attr("fill", function(d, i) { return (i%2)? colors[i]: fill_colors[i]; } )   //Alternate colors
        .attr("width", function(d,i){ return x_bar(d)*0.5 })
        .attr("height", y_bar.rangeBand());

    bars.append("svg:text")
        .attr("x", 0)
        .attr("y", 10 + y_bar.rangeBand() / 2)
        .attr("dx", -6)
        .attr("dy", ".50em")
        .attr("text-anchor", "end")
        .text(function(d, i) { return labellist[i]; });
    
    var counts = bars.append("svg:text")
        .attr("x", 0)
        .attr("y", 10 + y_bar.rangeBand() / 2)
        .attr("dx", -6)
        .attr("dy", "-.40em")
        .attr("text-anchor", "end")
        .text(function(d, i) { return ""; });
    

    var rules = vis.selectAll("g.rule")
        .data(x.ticks(10))
      .enter().append("svg:g")
        .attr("class", "rule")
        .attr("transform", function(d) { return "translate(" + x_bar(d) + ", 0)"; });


    rules.append("svg:line")
        .attr("y1", 0)
        .attr("y2", h_bar)
        .attr("x1", labelpad)
        .attr("x2", labelpad)
        .attr("stroke", "white")
        .attr("stroke-opacity", .3);


    
    function redraw(arm_number){
                    
        var _data = []
        for ( var i =0; i < 3; i++){
            _data.push( pdfbeta(x_array, 1 + ARMS[2*i+1],1+ARMS[2*i] - ARMS[2*i+1] ) );  
        
        }
        //update what is max.
        max_data = d3.max( [ 
                    10, 
                    d3.max(_data[0]),
                    d3.max(_data[1]),
                    d3.max(_data[2]) ])
        
        y = d3.scale.linear().domain([0, max_data]).range([h - margin,0 + margin ])
        line = d3.svg.line()
            .x(function(d, i) { return x(i); })
            .y(y)
    
        for ( var i =0; i < 3; i++){
            g.select("#line-" + i)
                 .data( [_data[i]] )
                .attr("d", line )
        }
    
    

        
        
        
        bars.data(ARMS)
            .enter().append("svg:g")
            .attr("class", "bar")
            .attr("transform", function(d, i) { return "translate(" + labelpad + "," + y(i) + ")"; });
    
        
        bars.append("svg:rect")
            .attr("fill", function(d, ix) {_ix = Math.floor(ix/2); return (ix%2)? fill_colors[_ix]: colors[_ix]; } )   //Alternate colors
            .attr("width", function(d,i){ return x_bar(d)*0.5 })
            .attr("height", y_bar.rangeBand());
        
        
        counts
            .attr("x", 0)
            .attr("y", 10 + y_bar.rangeBand() / 2)
            .attr("dx", function( d,i) { return !(i%2) ? 50 + 3.2*data[i] : 67 + 3.2*data[i] ;})
            .attr("dy", "-.40em")
            .attr("text-anchor", "end")
            .text(function(d, i) { return !(i%2) ? data[i] + " pulls" : data[i] + " rewards" ;});
    
        //update scoreboard
        var rewards =  ARMS[1] + ARMS[3] + ARMS[5];
        var pulls = ARMS[0] + ARMS[2] + ARMS[4];
        document.getElementById("rewards").innerHTML = rewards ;
        document.getElementById("pulls").innerHTML = pulls ;
        document.getElementById("ratio").innerHTML = (rewards/pulls).toFixed(3) ;
    
    }
    
    
    d3.select( "#reveal-div" )
        .selectAll("p")
        .data( _PROBS )
        .enter()
        .append("span")
        .attr( "style", "margin-left:15; margin-right: 30px; margin-top:0" )
        .text( function(d,i){ return  d.toFixed(4) ; } )
    //redraw() //to initialize