When chatting with Dan the other day about design matrices, learning and inference, I thought I saw a potentially interesting analogy to PL.

PlanOut programs have a simple syntax:

Program ::= Stmt*
Stmt ::=
| if <Bexpr> { <Stmt>* } else { <Stmt>* } <Stmt>*
| **id** <- <Expr> ; <Stmt>*
| return <Bexpr> ; <Stmt>*

Expr ::=
| <Aexpr> | <Bexpr> | <Cexpr> | <Sexpr>
| <Get>
| <ExternalGet>
| coalesce ( <Expr> , <Expr> )
| <Cexpr> [ <Expr> ]
| <RandomVariable>

RandomVariable ::=
| bernoulliTrial( p = <Aexpr> , unit = <Uexpr> ) | bernoulliTrial( p = <Aexpr> , unit = <Uexpr>, salt = <Sexpr> )
| weightedChoice( weights = <Cexpr> , choices = <Cexpr> , unit = <Uexpr>) | weightedChoice( weights = <Cexpr> , choices = <Cexpr> , unit = <Uexpr>, salt = <Sexpr> )
| uniformChoice( choices = <Cexpr> , unit = <Uexpr> ) | uniformChoice( choices = <Cexpr> , unit = <Uexpr> , salt = <Sexpr>)
| randomFloat ( min = <Aexpr> , max = <Aexpr> , unit = <Uexpr> ) | RandomFloat ( min = <Aexpr> , max = <Aexpr> , unit = <Uexpr> , salt = <Sexpr> )
| randomInteger ( min = <Aexpr> , max = <Aexpr> , unit = <Uexpr> ) | RandomInteger ( min = <Aexpr> , max = <Aexpr> , unit = <Uexpr> , salt = <Sexpr> )
| sample ( choices = <Cexpr> ) | sample ( choices = <Cexpr> , num_draws = <Aexpr> ) | sample ( choices = <Cexpr> , num_draws = <Aexpr> , unit = <Uexpr> ) 

I made the decision to port my blog over to a Github hosted Jekyll blog from a university-hosted Wordpress blog because I had no way to render custom Javascript in the Wordpress blog. In particular, I had wanted to be able to render interactive graphs using d3.

Unfortunately, I can’t just add a link to d3 in my _includes/head.html file and embed my Javascript directly in a mardown-ified blog post: Jekyll (or maybe Liquid?) strips out the Javascript. There is a workaround, but since the process is more than one step, I wanted to document how one includes custom Javascript in a Jekyll blog.

When inferring contrasts for a simple difference in means estimator for a (between subjects) PlanOut experiment, we take the unit of randomization to uniquely identify a subject. We also assume that the assignment of one unit does not affect the outcomes of other units. And finally, we assume that the parameter of interest can be determined by the variables in the PlanOut program, since these variables are subsequently read by an Internet application to determine the user experience.

Without more specific domain knowledge, we must treat each PlanOut script as a procedure parameterized by the unit of randomization (e.g., the userid) and the parameter of interest (i.e., the dependent variable in the analysis we will do at the end).

PlanOut programs are just sets of assignments with some conditions imposed on top of them. If we generate the dependencies between variables in a PlanOut program, we can use this information to determine which contrasts are valid.