Getting started with GEM-SA Marc Kennedy

This talk  Starting GEM-SA program  Creating input and output files  Explanation of the menus, toolbars, etc.  Description of the project window

Starting GEM-SA  Double-click the GEM-SA icon to start  The main window appears, with – Menu – Toolbar – Sensitivity analysis output grid – Log window

menu Log window toolbar Sensitivity analysis output grid

Toolbar icons New project Open project Save project Print output report Edit project Generate input design points Rescale an input Standardise design Copy input design to clipboard Convert input to integer Run the analysis Help

Sensitivity analysis output grid  This will report the sensitivity results after the analysis is complete – One line for each input parameter – One line for each pair of inputs, if joint effects are selected

Log Window output  Tells us – Which training data are being loaded/saved – Transformations applied to the data – Fitted Gaussian process parameters – Summary of the uncertainty analysis

Creating a GEM project  To build the emulator we first need 3 files: – Data file of code inputs – Data file of code outputs – GEM-SA project file

Restrictions on input/output data  Single output – Multiple outputs must be treated individually  Max 30 input parameters  Max 400 training points  The data files are plain text files – One line for each point – Input file can be space or tab delimited

Generating a new input design  Designs can be generated using the toolbar icon or the menu: Input  Generate…  The design dialog appears

Generating a new input design  Click OK and fill in the required range for each input  Click OK again

Editing input designs  If you select a column, you can rescale values of that input or round values to be integers  Designs can be loaded into or saved from this window using the Inputs menu. Use to copy the points to the clipboard for use in other programs

Types of design  GEM-SA can generate 2 types of design – LP-  – Maximin Latin Hypercube designs  Both have good space-filling properties – Ensure all regions of the input space are well represented

LP-  design  Very quick to generate  Deterministic set of uniform points  Increasing the sample size just adds points to the smaller design – Making it useful for sequential analysis – Only have to generate the extra runs

Maximin Latin hypercube design  Maximin Latin Hypercube designs – Maximise the minimum distance amongst all pairs of points – Can take a long time to generate  Univariate projections are equally spaced – Each input has all its range represented – Good when only a few inputs are active

Creating output points from these inputs  This is the tricky part…  Each row from the input design must be used to generate a single output, e.g. using – Spreadsheet  Simple, but requires functional form – Script  Only need executable code  Loop through inputs, modify code input file – Modify code to loop through the points  Messy, need source code

Example: using a spreadsheet  Copy the input design to the clipboard using  Open Excel and paste inputs  Create formula in final column  Copy formula for all rows of the design  Cut and paste special (values) in a new sheet  Save as text file

Example: using a script  Read base input file  Read training inputs file  Loop through training file lines – Replace target inputs using training line – Write new base input file – Run code – Calculate single output and add to training output file

my $pftchangeline = 21; # change line 21 within the input file for each run = (11,14,23,19); # columns within pftchangeline to modify = (0,1,2,3); # ordering of these parameters within training inputs open(BASEINFILE, "input.dat"); # getinitial (fixed) input file used by sdgvmd = ; # and store the input lines close BASEINFILE; open(LHFILE, "training_inputs.txt"); my $newpftline = $lines[$pftchangeline]; = split(" ", $newpftline); while ( ){ # assigns each line in turn to $_ chomp; split; open(INFILE, "> inputfile.dat"); = # modify lines $lines[$pftchangeline] = join(' print close INFILE; `sdgvm0 input.dat`; # run sdgvm0 with modified input # now do something with the output files }

The project window  Appears whenever you – Load a project – Edit a project – Create new project  This window has 3 tabs – Options – Files – Simulations

How many inputs? What are the input names?

Which joint effects should be calculated? What should be calculated, and how?

Are the inputs uncertain? What prior mean for the output?

What kind of prediction? What kind of cross validation?

Names for the input files Names for the output files

MCMC control parameters How many points used to calculate main effects, joint effects How many realisations of predictions, main and joint effects to generate

Input parameter names  This window appears if you press the Names… button – Giving names is optional, but useful later when looking at GEM-SA output – Ordering can be changed using the arrows

Selecting joint effects  If you select calculate joint effects, individual items in the joint effects window can be highlighted for inclusion in joint effect calculations  Need to unselect the default all inputs first – Unless you want to consider all pairs

Other checkboxes  Sum effects – Use this if you want main effects of the 2 inputs to be included in the realisations of the joint effect of a pair – The sensitivity measure, which computes joint sensitivity indices separately from the component main effects

Other checkboxes  Code has numerical error – Use this if your code has numerical errors which you want to smooth out – The variance of the error will be estimated as part of the fitting process – Can make the fitting process quite unstable, so avoid if possible!

Other checkboxes  Use MCMC for emulator parameters – For serious Bayesians only! – Takes into account uncertainty in the fitting of the emulator – Slows down the computation substantially, usually with minimal effect on the results  Auto-tune Metropolis algorithm – Use only with MCMC

Input uncertainty options  All unknown, product normal – Inputs are independent, normally distributed  All unknown, uniform – Inputs are independent, distributed uniformly between the min and max values of the training data  All known – No uncertainty analysis required

Input uncertainty options  Some known, rest product normal – Some input values will be fixed (in the dialog window or in a prediction file) – Others will be given normal input parameters

Prior mean options  If you believe the output is roughly linear function of its inputs, select ‘linear term for each input’ – Otherwise a single value will be used to represent the prior overall level of the output

Input normal parameters  Window appears if you click OK having selected normal inputs

Input fixed and normal parameters  Window appears if you click OK having selected some fixed inputs, rest normal  For fixed inputs, tick the box and enter the fixed value in the first test box

Selecting prediction type  Predictions can be – Correlated realisations of outputs at the prediction inputs  Similar to main effect outputs – Marginal means and variances of outputs at the prediction inputs  Faster to compute, especially with many prediction points  Easy to interpret

Selecting cross validation type  Choice of none, leave-one-out or leave final 20% out  Leave-one-out – Hyper-parameters use all data and are then fixed when prediction is carried out for each omitted point  Leave final 20% out – Hyper-parameters are estimated using the reduced data subset