Learning Bayes

prob.js

var sum = function(members) {
    var sumvalue = 0;
    for(var key in members) {
        if (members.hasOwnProperty(key)) {
            sumvalue += members[key]
        }
    }
    return sumvalue
}

var prob = function(i,looking,choose){
    return choose * i.members[looking] / sum(i.members)
};

////////////////////////////////////////////////
//
// P(FromBox)
// : P(A)
//
console.assert(1/2 == prob({members:{X: 1, Y: 1}}, "X", 1)) // P(FromBox="X")
console.assert(1/2 == prob({members:{X: 1, Y: 1}}, "Y", 1)) // P(FromBox="Y")

//
// P(GotTicket)
// : P(B)
//
console.assert(5/20 == prob({members:{Yes: 5, No: 15}}, "Yes", 1)) // P(GotTicket="Yes")
console.assert(15/20 == prob({members:{Yes: 5, No: 15}}, "No", 1)) // P(GotTicket="No")

//
// กำหนดให้มีตั๋วในกล่อง X จำนวน 3 ใบ
// และที่เหลือในกล่อง Y จำนวน 2 ใบ
// และแบ่งตั๋วไว้กล่องละ 10 ใบ
//

//
// P(GotTicket|FromBox="X")
// : P(B|A="X")
//
console.assert(3/10 == prob({members:{Yes: 3, No: 7}}, "Yes", 1)) // P(GotTicket="Yes"|FromBox="X")
console.assert(7/10 == prob({members:{Yes: 3, No: 7}}, "No", 1))  // P(GotTicket="No"|FromBox="X")

//
// P(GotTicket|FromBox="Y")
// : P(B|A="Y")
//
console.assert(2/10 == prob({members:{Yes: 2, No: 8}}, "Yes", 1)) // P(GotTicket="Yes"|FromBox="Y")
console.assert(8/10 == prob({members:{Yes: 2, No: 8}}, "No", 1))  // P(GotTicket="No"|FromBox="Y")

//
// Joint probability
// : P(B,A) = P(B|A) * P(A)
//
// P(GotTicket,FromBox="X")
// : P(B,A="X")
//
console.assert(3/20 == (
    prob({members:{Yes: 3, No: 7}}, "Yes", 1) * prob({members:{X: 1, Y: 1}}, "X", 1) // P(GotTicket="Yes",FromBox="X")
))
console.assert(7/20 == (
    prob({members:{Yes: 3, No: 7}}, "No", 1) * prob({members:{X: 1, Y: 1}}, "X", 1)  // P(GotTicket="No",FromBox="X")
))

//
// P(GotTicket,FromBox="Y")
// : P(B,A="Y")
//
console.assert(2/20 == (
    prob({members:{Yes: 2, No: 8}}, "Yes", 1) * prob({members:{X: 1, Y: 1}}, "Y", 1) // P(GotTicket="Yes",FromBox="Y")
))
console.assert(8/20 == (
    prob({members:{Yes: 2, No: 8}}, "No", 1) * prob({members:{X: 1, Y: 1}}, "Y", 1)  // P(GotTicket="No",FromBox="Y")
))

//
// จาก
// : P(B,A) = P(B|A) * P(A)
// : P(A,B) = P(A|B) * P(B)
// เมื่อ
// : P(A,B) = P(B,A)
// จะได้
// : P(A|B) * P(B) = P(B|A) * P(A)
//
// เมื่อย้ายข้างสมการ 
// จะสรุปความสัมพันธ์เป็นสูตรได้
// : P(A|B) = P(B|A) * P(A) / P(B)
// หรือ
// : P(B|A) = P(A|B) * P(B) / P(A)
//
// P(FromBox="X"|GotTicket="Yes") == 3/5
// = P(GotTicket="Yes|FromBox="X") * P(FromBox="X") / P(GotTicket="Yes")
//
console.assert(3/5 == (
    prob({members:{Yes: 3, No: 7}}, "Yes", 1)  // P(GotTicket="Yes"|FromBox="X")
  * prob({members:{X: 1, Y:1}}, "X", 1)        // P(FromBox="X")
  / prob({members:{Yes: 5, No: 15}}, "Yes", 1) // P(GotTicket="Yes")
))

//
// P(FromBox="Y"|GotTicket="Yes") == 2/5
// = P(GotTicket="Yes|FromBox="Y") * P(FromBox="Y") / P(GotTicket="Yes")
//
console.assert(2/5 == (
    prob({members:{Yes: 2, No: 8}}, "Yes", 1)  // P(GotTicket="Yes"|FromBox="Y")
  * prob({members:{X: 1, Y:1}}, "Y", 1)        // P(FromBox="Y")
  / prob({members:{Yes: 5, No: 15}}, "Yes", 1) // P(GotTicket="Yes")
))

//
// P(Dice) when have ticket
// : P(C)
//
console.assert(1/6 == prob({members:{Highest: 1, Lowest: 5}}, "Highest", 1)) // P(Dice="Highest")
console.assert(5/6 == prob({members:{Highest: 1, Lowest: 5}}, "Lowest", 1))  // P(Dice="Highest")

//
//  P(FromBox="X"|GotTicket="Yes"|Dice="Highest")
// : P(A="X"|B="Yes"|C="Highest")
//
console.assert(3/5 * 1/6 == (
    prob({members:{Yes: 3, No: 7}}, "Yes", 1)             // P(GotTicket="Yes"|FromBox="X")
  * prob({members:{X: 1, Y:1}}, "X", 1)                   // P(FromBox="X")
  / prob({members:{Yes: 5, No: 15}}, "Yes", 1)            // P(GotTicket="Yes")
  * prob({members:{Highest: 1, Lowest: 5}}, "Highest", 1) // P(Dice="Highest")
))

const Loves = () => (Math.floor(Math.random() * Math.floor(2)) ? "Love" : "Liar")