Model

An algebraic effect embedding of probabilistic models.

Documentation

newtype Model env es a

Models are parameterised by:

1) a model environment env containing random variables that can be provided observed values

2) an effect signature es of the possible effects a model can invoke

3) an output type a of values that the model generates.

A model initially consists of (at least) two effects: Dist for calling primitive distributions and ObsReader env for reading from env.

Constructors

Model

Fields

• runModel :: (Member Dist es, Member (ObsReader env) es) => Prog es a

Instances

Monad (Model env es)

Defined in Model

Methods

(>>=) :: Model env es a -> (a -> Model env es b) -> Model env es b

(>>) :: Model env es a -> Model env es b -> Model env es b

return :: a -> Model env es a

Functor (Model env es)

Defined in Model

Methods

fmap :: (a -> b) -> Model env es a -> Model env es b

(<$) :: a -> Model env es b -> Model env es a

Applicative (Model env es)

Defined in Model

Methods

pure :: a -> Model env es a

(<*>) :: Model env es (a -> b) -> Model env es a -> Model env es b

liftA2 :: (a -> b -> c) -> Model env es a -> Model env es b -> Model env es c

(*>) :: Model env es a -> Model env es b -> Model env es b

(<*) :: Model env es a -> Model env es b -> Model env es a

handleCore :: (Member Observe es, Member Sample es) => Env env -> Model env (ObsReader env ': (Dist ': es)) a -> Prog es a

The initial handler for models, specialising a model under a certain environment to produce a probabilistic program consisting of Sample and Observe operations.

Distribution smart constructors

Smart constructors for calling primitive distribution operations inside models, where each distribution comes with a primed and an unprimed variant.

An unprimed distribution takes the standard distribution parameters as well as an observable variable. This lets one later provide observed values for that variable to be conditioned against:

   exampleModel :: Observable env "b" Bool => Model env es Bool
   exampleModel = bernoulli 0.5 #b
   

A primed distribution takes no observable variable and so cannot be conditioned against; this will always representing sampling from that distribution:

   exampleModel' :: Model env es Bool
   exampleModel' = bernoulli' 0.5
   

bernoulli :: forall env es x. Observable env x Bool => Double -> ObsVar x -> Model env es Bool

bernoulli'

Arguments

:: Double

probability of True

-> Model env es Bool

beta :: forall env es x. Observable env x Double => Double -> Double -> ObsVar x -> Model env es Double

beta'

Arguments

:: Double

shape 1 (α)

-> Double

shape 2 (β)

-> Model env es Double

binomial :: forall env es x. Observable env x Int => Int -> Double -> ObsVar x -> Model env es Int

binomial'

Arguments

:: Int

number of trials

-> Double

probability of successful trial

-> Model env es Int

number of successful trials

categorical :: forall env es a x. (Eq a, Show a, Member a PrimVal, Observable env x a) => [(a, Double)] -> ObsVar x -> Model env es a

categorical'

Arguments

:: (Eq a, Show a, Member a PrimVal)

=> [(a, Double)]

primitive values and their probabilities

-> Model env es a

cauchy :: forall env es x. Observable env x Double => Double -> Double -> ObsVar x -> Model env es Double

cauchy'

Arguments

:: Double

location

-> Double

scale

-> Model env es Double

halfCauchy :: forall env es x. Observable env x Double => Double -> ObsVar x -> Model env es Double

halfCauchy'

Arguments

:: Double

scale

-> Model env es Double

deterministic :: forall env es a x. (Eq a, Show a, Member a PrimVal, Observable env x a) => a -> ObsVar x -> Model env es a

deterministic'

Arguments

:: (Eq a, Show a, Member a PrimVal)

=> a

value to be deterministically generated

-> Model env es a

dirichlet :: forall env es x. Observable env x [Double] => [Double] -> ObsVar x -> Model env es [Double]

dirichlet'

Arguments

:: [Double]

concentration parameters

-> Model env es [Double]

discrete :: forall env es x. Observable env x Int => [Double] -> ObsVar x -> Model env es Int

discrete'

Arguments

:: [Double]

list of n probabilities

-> Model env es Int

integer index from 0 to n - 1

gamma :: forall env es x. Observable env x Double => Double -> Double -> ObsVar x -> Model env es Double

gamma'

Arguments

:: Double

shape (k)

-> Double

scale (θ)

-> Model env es Double

normal :: forall env es x. Observable env x Double => Double -> Double -> ObsVar x -> Model env es Double

normal'

Arguments

:: Double

mean

-> Double

standard deviation

-> Model env es Double

halfNormal :: forall env es x. Observable env x Double => Double -> ObsVar x -> Model env es Double

halfNormal'

Arguments

:: Double

standard deviation

-> Model env es Double

poisson :: forall env es x. Observable env x Int => Double -> ObsVar x -> Model env es Int

poisson'

Arguments

:: Double

rate (λ)

-> Model env es Int

number of events

uniform :: forall env es x. Observable env x Double => Double -> Double -> ObsVar x -> Model env es Double

uniform'

Arguments

:: Double

lower-bound

-> Double

upper-bound

-> Model env es Double