the toy e.g. (5 attributes)

An Inferred Bayesian Network

details of the network's nodes next...

{CTleaf N(1.0,0.41)(+-0.1),_,_,_,_}, --@0

{CTleaf _,mState[0.5,0.5],_,_,_},   --@1

{CTfork @0<|>=1.4[                  --@2|@0,@1
  {CTleaf _,_,mState[0.99,0.01],_,_},
  {CTfork @1=False|True[
    {CTleaf _,_,mState[0.98,0.02],_,_},
    {CTleaf _,_,mState[0.02,0.98],_,_}]}]}, 

{CTleaf _,_,_,mState[0.5,0.5],_},   --@3

{CTfork @2=False|True[              --@4|@0,@2
  {CTfork @0<|>=1.0[
    {CTleaf _,_,_,_,N(0.55,0.2)(+-0.1)},
    {CTfork @0<|>=1.4[
      {CTleaf _,_,_,_,N(1.0,0.2)(+-0.1)},
      {CTleaf _,_,_,_,N(1.45,0.2)(+-0.1)}]}]},
  {CTleaf _,_,_,_,N(3.45,0.2)(+-0.1)}]}

Components

mState[p0,p1,...] -- multi-state distribution[*].

N(m,s) -- normal (Gaussian) distribution[*].

"classification" tree[*],

    CTleaf -- model[*] an attribute,

    CTfork -- test[*] an attribute.

([*] message lengths, i.e. complexities, direct search & prevent over-fitting.)

2. A Real Example: Lost Person

data Tipe = Alzheimers | Child | Despondent | Hiker | ...

type Age = Double

data Race = White | Black deriving (Eq, Enum,...

data Gender = Male | Female deriving (Eq, Enum,...

data Topography = Mountains | Piedmont | Tidewater deriving...

data Urban = Rural | Suburban | Urban deriving (Eq,Ord,...

type HrsNt = Double -- hours notified

type DistIPP = Double -- distance
...

Estimators

type MissingPerson = (Maybe Tipe, Maybe Age, ...)

e0 = (estModelMaybe estMultiState)   --Tipe

e1 = (estModelMaybe (estNormal 0 90 1 70 0.5))   --Age

...

e7 = (estModelMaybe (estNormal 0 50 0.5 30 0.2)) --DistIPP

estimator = estVariate15 e0 e1 e2 e3 e4 e5 e6 e7 e8 e9 e10 e11 e12 e13 e14

NB. There is(n't:-) a lot of missing data.

1st Inferred Network for 8 attributes

Inferred Network's Trees...

Net:[
 -- @1, Age:
 {CTleaf _,(Maybe 50:50,N(40.6,27.5)... },

 ... etc. ...

 -- @6, HrsNt:
 {CTfork @1(<|>=62.0|?)[
  {CTleaf...,(Maybe 50:50,N( 8.7, 7.6)...},
  {CTleaf...,(Maybe 50:50,N(21.4,26.3))...},
  {CTleaf...,(Maybe 50:50,N(20.0,..1-case)..}
]},

... ]

network: 115.1 nits + data: 5396.6 nits
null:   5935.6 nits (@0..@7)

E.g. A High-Order Function of an Estimator

estModelMaybe estModel dataSet =
 let
  present (Just _) = True
  present Nothing  = False
  m1 = uniformModelOfBool          -- [*]
  m2 = estModel (map (\(Just x) -> x)
                (filter present dataSet))
 in modelMaybe m1 m2

    m1 = estMultiState (map present dataSet)

Classes e.g.

class Project t where   -- as in `projection'
 select :: [Bool] -> t -> t
 selAll :: t -> [Bool]  -- all True flags

A type, t, in class Project can be projected onto a select-ed sub-space.
E.g. A 15-dim'n estimator, such as estVariate15 e0...e14.

Also a related class for select-ive partitioning of data within trees.

e.g.				@0: Tipe = Alzheimers | Child |... @1: Age   @2: Race = ...| ... @3: Gender = ...| ... @4: Topography = ...| ...| ... @5: Urban = ...| ...| ... @6: HrsNt   @7: DistIPP   @8: TrackOffset   @9: Health = Well | Hurt | Dead --after!   @10: Outcome = Find | Suspended | Invalid @11: FindRes = Ground | Air |...| Dog @12: FindLoc = Brush | Woods |... @13: HrsFind   @14: HrsTot
A Network Inferred for all 15 Attributes of `lost persons'

Summary

Have types and type-classes for Models, Function-Models and Time-Series models. Polymorphic types, type classes, high-order functions, lazy-evaluation -- all useful.

Easy to write a new model, e.g. ModelMaybe & Bayesian network, to suit a new problem.

Other case studies include -- mixture models (clustering), time-series, Markov models, mixtures of Markov models, function models (regressions), etc..