# Simulation

Abstract

Simulation involves calculating exact data for a chosen model which can then be displayed as a graph or surface to observe the behaviour of the model over selected ranges of independent variables given a set of parameter values. The model may be described by a simple equation or it may be defined by a nonlinear equation or differential equation which can only be solved numerically. Special models such as those required to describe flow cytometry data usually call for dedicated techniques.

Details

SIMFIT has a number of programs that can be used to simulate deterministic models or stochastic processes. `usermod define a set of user-supplied models for plotting, simulating or fitting as an ASCII text file makdat simulate data (u = f(x), v = g(x,y) or w = h(x,y,z)) deqsol solve sets of nonlinear differential equations adderr add random error to simulate experiments rannum random numbers and walks using chosen distributions makcsa generate flow cytometry profiles`

Program MAKDAT

MAKDAT comes along with a library of models, hierarchies of models and differential equations. You can choose models and parameter values required and calculate y = f(x) for a range X_start =< x =< X_stop, either by fixing X_start, X_stop, or by choosing Y_start = f(X_start), Y_stop = f(X_stop), and then allowing MAKDAT to find appropriate values for X_start and X-stop. You have to provide starting estimates for X_start, X-stop in order to use the second method, so this means that you have to understand the mathematics of the model.

Advice

With complicated models or differential equations, fix X_start and X_stop and observe how the graph of y = f(x) changes as you change parameters and/or end points. When you have a good idea where your end points lie you can then try the option to fix y and calculate X_start and X_stop. This is needed when f(x) is not monotonic in the range of interest. The output file from MAKDAT contains exact data for input into program ADDERR to add random errors.

Program ADDERR

The output file from MAKDAT contains exact data for y = f(x) which is useful for generating high resolution graphics and for data simulation.

You may want to add random errors to exact data, to simulate experimental error. To do this, the output file then becomes an input file for ADDERR. After adding this random error the input file is left unchanged (with the exact data) and a new output file is produced with the perturbed data. In this way experimental data can be simulated repeatedly.

Model => MAKDAT => Exact data => ADDERR => Simulated data

There are numerous ways to use ADDERR, including generating replicates. If in doubt pick 7% constant relative error with 3 replicates as this mimics many situations. Note:- constant relative errors cannot be used where your exact data set has elements with y = 0.

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