| Maintainer | atloomis@math.arizona.edu |
|---|---|
| Stability | Experimental |
| Safe Haskell | None |
| Language | Haskell2010 |
Markov.Example
Description
Several examples of Markov chains. It is probably more helpful to read the source code than the Haddock documentation.
Synopsis
- newtype FromLists = FromLists Char
- newtype Simple = Simple Int
- newtype Urn = Urn (Int, Int)
- newtype Extinction = Extinction Int
- data Tidal = Tidal {}
- newtype Room = Room Int
- data FillBin
- initial :: [Int] -> FillBin
- expectedLoss :: (Fractional a, Markov ((,) (Product a)) FillBin) => [Product a :* FillBin] -> a
Documentation
An example defined from a matrix.
>>>chain [pure (FromMatrix 't') :: (Product Double, FromMatrix)] !! 100[ (0.5060975609756099,'a') , (0.201219512195122,'t') , (0.29268292682926833,'l') ]
Instances
| Eq FromLists Source # | |
| Ord FromLists Source # | |
| Show FromLists Source # | |
| Combine FromLists Source # | |
| Markov ((,) (Product Double)) FromLists Source # | |
A simple random walk. Possible outcomes of the first three steps:
>>>take 3 $ chain0 [Simple 0][ [0] , [-1,1] , [-2,0,2] ]
Probability of each outcome:
>>>take 3 $ chain [pure 0 :: (Product Double, Simple)][ [(1.0,0)] , [(0.5,-1),(0.5,1)] , [(0.25,-2),(0.5,0),(0.25,2)] ]
Number of ways to achieve each outcome:
>>>take 3 $ chain [pure 0 :: (Product Int, Simple)][ [(1,0)] , [(1,-1),(1,1)] , [(1,-2),(2,0),(1,2)] ]
Number of times pred was applied,
allowing steps in place (id)
for more interesting output:
>>>chain [pure 0 :: (Sum Int, Simple)] !! 2[ (2,-2), (1,-1), (1,0), (0,0), (0,1), (0,2) ]
Instances
| Enum Simple Source # | |
Defined in Markov.Example | |
| Eq Simple Source # | |
| Num Simple Source # | |
| Ord Simple Source # | |
| Show Simple Source # | |
| Combine Simple Source # | |
| Markov0 Simple Source # | |
| Markov ((,) (Product Double)) Simple Source # | |
| Markov ((,) (Product Int)) Simple Source # | |
| Markov ((,) (Sum Int)) Simple Source # | |
An urn contains balls of two colors. At each step, a ball is chosen uniformly at random from the urn and a ball of the same color is added.
>>>randomPath (mkStdGen 70) (Urn (2,5)) !! 8 :: (Product Double, Urn)(0.1648351648351649, Urn (2,13))
newtype Extinction Source #
This is the chain from the README.
Constructors
| Extinction Int |
Instances
A time inhomogenous random walk that vaguely models tides by periodically switching directions and falling back from a shore at the origin.
A hidden Markov model.
>>>:{ filter (\((_,Merge xs),_) -> xs == "aaa") $ chain[1 >*< Merge "" >*< 1 :: Product Rational :* Merge String :* Room] !! 3 :} [ ((3243 % 200000,"aaa"),Room 1) , ((9729 % 500000,"aaa"),Room 2) , ((4501 % 250000,"aaa"),Room 3) ]
Given that all three tokens recieved were "a",
there is a probability of approximately 0.34
that the current room is Room 3.
A collection of bins with gaps between them. At each step an empty space is chosen form a bin or from a gap. If it is in a bin, the space is filled. If it is in a gap, it is assigned to an adjacent bin, which expands to contain it and any intervening spaces, and then the space filled.
initial :: [Int] -> FillBin Source #
Create state where all bins start as (0,0).
>>>initial [5,7,0]5 (0,0) 7 (0,0) 0
expectedLoss :: (Fractional a, Markov ((,) (Product a)) FillBin) => [Product a :* FillBin] -> a Source #
Expected loss of a set of states of [.
Loss is the \(l^2\) distance between a finished state
and a state with perfectly balanced bins.FillBin]
>>>expectedLoss [pure $ initial [1,0,3] :: (Product Double, FillBin)]2.0