[funshapes0]    Fun shapes: general constraints

These toy examples illustrate how to implement general inequality constraints. They generate points uniformly over a restricted region of the square with corners at (1, 1) and (-1, -1). A dummy bernoulli variable is introduced and its corresponding proportion set to the step function of the required constraint. The only useful example is the parallelagram where x + y is constrained to be less than or equal to one, this idea can be used to model proportions for binary data instead of say logistic regression.

Circle

    model
    {
       x ~ dunif(-1, 1)
       y ~ dunif(-1, 1)
       O <- 0
       O ~ dbern(constraint)
       constraint <- step(x * x + y * y - 1)
    }

 Inits ( click to open )



[funshapes1]

Square minus circle

    model
    {
       x ~ dunif(-1, 1)
       y ~ dunif(-1, 1)
       O <- 1
       O ~ dbern(constraint)
       constraint <- step(x * x + y * y - 1)
    }

 Inits ( click to open )


[funshapes2]

Ring

    model
    {
       x ~ dunif(-1, 1)
       y ~ dunif(-1, 1)
       O1 <- 0
       O1 ~ dbern(constraint1)
       constraint1 <- step(x * x + y * y - 1)   
       O2 <- 1
       O2 ~ dbern(constraint2)
       constraint2 <- step( x * x + y * y - 0.25)
    }

 Inits ( click to open )


[funshapes3]

Hollow square

    model
    {
       x ~ dunif(-1, 1)
       y ~ dunif(-1, 1)
       O <- 0
       O ~ dbern(constraint)
       constraint <- (step(0.5 - abs(x)) * step(0.50 - abs(y)))
    }

 Inits ( click to open )


[funshapes4]


Parallelagram

    model
    {
       x ~ dunif(0, 1)
       y ~ dunif(-1, 1.0)
       O1 <- 1
       O1 ~ dbern(constraint1)
       constraint1 <- step(x + y)
       O2 <- 0
       O2 ~ dbern(constraint2)   
       constraint2 <- step(x + y - 1)
    }

 Inits ( click to open )

[funshapes5]