Creating a prediction interval with monte carlo simulation

[#1]

Hi,

I was wondering if anyone could help me.  

I have a set of data in two columns.  Column one contains a Run ID while Column 2 contains data generated by the run.  My end goal is to plot the 95% prediction interval of the confidence intervals produced by N, N-1, N-2, N-3... until you only have two datapoints per Run, where N = initial number of replicates.  Therefore step by step, If for example I had 40 replicates per run, I would like for JMP to randomly select 39 replicates for each run, conduct a lower 95% and upper 95% confidence interval for each Run, then conduct a lower 95% Prediction interval for the lower 95% confidence intervals of each run and a upper 95% prediction interval for the upper 95% confidence intervals of each run.  This would get repeated with 38 replicates, 37 replicates... until there is only 2 replicates.  I would like to graph on the x-axis the replicate number and plot both the upper 95% Preidiction interval and lower 95% prediction interval similar to what is shown below:

[#2]

Hi,

I believe I have an answer for you.  It makes use of the Bootstrapping functionality in JMP Pro, and for that reason will only work with JMP Pro.  Please take a look and let me know if it does what you are after.

Names Default To Here( 1 );
dt = Open( "$SAMPLE_DATA/Big Class.jmp" );

dist=dt<<Distribution(Y(:Weight));//Create Distribution report of column "Weight""

//JMP PRO REQUIRED FOR NEXT STEP
boot_dt=(dist << Report)[TableBox( 2 )] << Bootstrap(
	40,
	Fractional Weights( 1 ),
	Split Selected Column( 1 )
);//Bootstrap 40 samples of Summary Statistics

boot_dist=boot_dt[2]<<Distribution(Y(Column(3)));//Create Distribution of Bootstrap samples for whichever statistic ends up in Column 3 - "Lower 95% Mean"" in our case. 

	lowCL = {};//container for lower confidence limits
	upCL = {};//container for upper confidence limits
	nsims = {};	//container for number of simulations - for x-axis of GB report
	
	lowCL[1] = Report( boot_dist )["Bootstrap Confidence Limits"][Number Col Box( 2 )][1];//lower a=0.05 limit
	upCL[1] = Report( boot_dist )["Bootstrap Confidence Limits"][Number Col Box( 3 )][1];//upper a=0.05 limit
	boot_dist << Close Window;
	
	nsims[1] = N Rows( boot_dt[2] ) - 1;//Estimates were taken using all rows of table, except the first.
	
//	dist << Close Window;
	
	For( i = 2, i <= N Rows( boot_dt[2] ) - 2, i++, //Create distribution reports after excluding rows one-at-a-time, save values in lowCL, upCL and nsims containers.
	
		boot_dt[2] << Select Where( Row() == i );
		boot_dt[2] << Exclude;
	
		boot_dist=boot_dt[2]<<Distribution(Y(Column(3)));
		lowCL[i] = Report( boot_dist )["Bootstrap Confidence Limits"][Number Col Box( 2 )][1];//lower a=0.05 limit
		upCL[i] =  Report( boot_dist )["Bootstrap Confidence Limits"][Number Col Box( 3 )][1];//upper a=0.05 limit
		boot_dist << Close Window;
	
		nsims[i] = N Rows( boot_dt[2]) - i;
	);//end of For-loop, containers now have values for each row.
	
	

	
	graphdt = New Table(); //create new table to generate GB report
	lowCLcolumn = graphdt << New Column( "Lower Confidence limit" );	//column of lower confidence limits
	graphdt << add Rows( N Items( lowCL ) ); //add rows 
	lowCLcolumn << Set Values( lowCL ); // set values from lowCL into column
	
	upCLcolumn = graphdt << New Column( "Upper Confidence limit" );	//column of upper confidence limits
	upCLcolumn << Set Values( upCL );//set values from upCL into column
	
	Nsimscol = graphdt << New Column( "N" );	//column of number of rows in simulated estimates table that were not exlcuded (x-axis of GB report)
	Nsimscol << Set Values( nsims ); // set values from nsims into column
	
	//create GB report
	gb = graphdt << Graph Builder(
		Size( 531, 456 ),
		Show Control Panel( 0 ),
		Variables( X( :N ), Y( :Lower Confidence limit ), Y( :Upper Confidence limit, Position( 1 ) ) ),
		Elements( Line( X, Y( 1 ), Y( 2 ), Legend( 7 ) ) )
	);

[#3]

By the way, this solution makes use of bits of a script from an add-in presented at the JMP Discovery Summit Europe 2020.