# namin/spots

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 package probabilisticModeling object probabilisticModeling { import scala.collection.immutable.Set1 import scala.util.Random abstract class Distribution[A] { def Sample: A def Support: Set[A] def Expectation(H: A => Double): Double def map[B](k: A => B) = flatMap((x: A) => always(k(x))) def flatMap[B](k: A => Distribution[B]): Distribution[B] = bind(this)(k) } def always[A](x: A) = new Distribution[A] { def Sample = x def Support = new Set1(x) def Expectation(H: A => Double) = H(x) } val rnd = new Random def coinFlip[A](p: Double)(d1: Distribution[A])(d2: Distribution[A]) = { if (p < 0.0 || p > 1.0) error("invalid probability") new Distribution[A] { def Sample = if (rnd.nextDouble() < p) d1.Sample else d2.Sample def Support = d1.Support ++ d2.Support def Expectation(H : A => Double) = p * d1.Expectation(H) + (1.0-p) * d2.Expectation(H) } } def bind[A,B](dist: Distribution[A])(k: A => Distribution[B]): Distribution[B] = new Distribution[B] { def Sample = (k(dist.Sample)).Sample def Support() = dist.Support.flatMap(k(_).Support) def Expectation(H : B => Double) = dist.Expectation(k(_).Expectation(H)) } def weightedCases[A](inp: List[(A,Double)]): Distribution[A] = { def coinFlips[A](w: Double)(l: List[(A,Double)]): Distribution[A] = { l match { case Nil => error("no coinFlips") case (d,_)::Nil => always(d) case (d,p)::rest => coinFlip(p/(1.0-w))(always(d))(coinFlips(w+p)(rest)) } } coinFlips(0)(inp) } def countedCases[A](inp: List[(A,Int)]): Distribution[A] = { val total = 1.0*(inp map { case (_,v) => v } reduceLeft (_+_)) weightedCases(inp map { case (x,v) => (x,v/total) }) } sealed trait Outcome final case object Even extends Outcome final case object Odd extends Outcome final case object Zero extends Outcome val roulette = countedCases(List((Even,18),(Odd,18),(Zero,1))) val roulettePayoff = roulette.Expectation(x => x match { case Even => 10.0 case Odd => 0.0 case Zero => 0.0 } ) sealed trait Light final case object Red extends Light final case object Green extends Light final case object Yellow extends Light def trafficLightD: Distribution[Light] = weightedCases(List((Red,0.50),(Yellow,0.10),(Green,0.40))) sealed trait Action final case object Stop extends Action final case object Drive extends Action def cautiousDriver(light: Light): Distribution[Action] = light match { case Red => always(Stop) case Yellow => weightedCases(List((Stop,0.9),(Drive,0.1))) case Green => always(Drive) } def aggressiveDriver(light: Light): Distribution[Action] = light match { case Red => weightedCases(List((Stop,0.9),(Drive,0.1))) case Yellow => weightedCases(List((Stop,0.1),(Drive,0.9))) case Green => always(Drive) } def otherLight(light: Light): Light = light match { case Red => Green case Yellow => Red case Green => Red } sealed trait CrashResult final case object Crash extends CrashResult final case object NoCrash extends CrashResult def crashExplicit(driverOneD: Light => Distribution[Action])(driverTwoD: Light => Distribution[Action])(lightD: Distribution[Light]): Distribution[CrashResult] = lightD.flatMap(light => driverOneD(light).flatMap(driverOne => driverTwoD(otherLight(light)).flatMap(driverTwo => (driverOne, driverTwo) match { case (Drive,Drive) => weightedCases(List((Crash,0.9),(NoCrash,0.1))) case _ => always(NoCrash) }))) def crash(driverOneD: Light => Distribution[Action])(driverTwoD: Light => Distribution[Action])(lightD: Distribution[Light]): Distribution[CrashResult] = for (light <- lightD; driverOne <- driverOneD(light); driverTwo <- driverTwoD(otherLight(light)); caseBothDrive <- weightedCases(List((Crash,0.9),(NoCrash,0.1)))) yield (driverOne,driverTwo) match { case (Drive,Drive) => caseBothDrive case _ => NoCrash } val model = crash(cautiousDriver)(aggressiveDriver)(trafficLightD) val model2 = crash(aggressiveDriver)(aggressiveDriver)(trafficLightD) def H(x: CrashResult) = x match { case Crash => 1.0 case NoCrash => 0.0 } def main(args: Array[String]) = { println("roulette sample: " + roulette.Sample) // roulette sample: Odd println("roulette sample (again): " + roulette.Sample) // roulette sample (again): Even println("roulette payoff: " + roulettePayoff) // roulette payoff: 4.864864864864865 println("model sample: " + model.Sample) // model sample: NoCrash println("model2 sample: " + model2.Sample) // model2 sample: NoCrash println("model crash expectation: " + model.Expectation(H)) // model crash expectation: 0.036899999999999995 println("model2 crash expectation: " + model2.Expectation(H)) // model2 crash expectation: 0.08909999999999998 } }