How can I make many runs of a simulation and plot all the results with one expression evaluation?

Question

I have many cells, starting with this first cell:

mcRun = 20;
randomWalk[n_] := RandomVariate[NormalDistribution[0, 1], n]; 

RandVar = Table[randomWalk[5], {mcRun}];
Length[RandVar] 
MatrixForm[RandVar[[1 ;; 10]]] (* only display first 10 *)
ListPlot[RandVar]

Then later in a 2nd cell:

CorRandVar = RandVar * 10;

Still later in a 3rd cell:

InvCor = CDF[NormalDistribution[], CorRandVar];

And there are many more cells that depend on the value of the initial parameter mcRun that I defined in the first cell.

At the moment I use 'Evaluate Notebook' to get my results. I wait for one 'Evaluate Notebook' to complete, note down the result from running with mcRun = 20 (20 monte carlo simulations), edit mcRun = 20 to another value and repeat.

So how could I automate what 'Evaluate Notebook' does and plot, for example, InvCor (or any function/value) as a function of the input parameter mcRun, say, from 20 to 20,000? ? Or better, how could I incorporate my simulation into a Manipulate to add interactivity?

Answer 1

You might write a master function, call it runSim, that evaluates all the functions you have already defined and takes the parameter needed to make a single run as it argument. Then evaluate

Map[runSim, {p1, p2, ... }]

to get several runs at once. If several parameters need to be given for a single run, then you would evaluate

MapThread[runSim, {{p11,p12, ...}, {p21, p22, ...}, ... }

Edit

As a concrete example, I have converted part of your code into a runSim function. I hope it will start you down the path to automating your evaluations.

randomWalk[n_] := RandomVariate[NormalDistribution[0, 1], n]

runSim[runs_Integer] /; runs >= 10 := 
   Module[{randVar}, 
      randVar = Table[randomWalk[5], {runs}];
      Column[{MatrixForm[randVar[[1 ;; 10]]] ,
              ListPlot[randVar]}]]

runSim[10]

The output looks like this: