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Glossary of Terms for ModelMaker
Accuracy
The Monte Carlo facility allows you to specify model parameters as random distributions. The Binomial distribution has the form:  where P(k) is the probability for the whole number k. The user-supplied parameters are:
ModelMaker can use Boolean expressions in defining event actions and conditions (for conditional components). The expressions allowed are listed in the Available Functions panel of the Event Actions Definition dialog and the conditional component dialogs. Boundary Conditions As ModelMaker is designed to solve 'initial value' type problems, the boundary conditions are defined as the values of the variables at the start of the problem. Bulirsch-Stoer One of the five integration methods used by ModelMaker. Provides similar accuracy to the (default) Runge-Kutta method but is only recommended for smooth or well behaved functions and should be avoided for models with discontinuities. CCompartmentsCompartments are ModelMaker's integrators. They are defined by a symbol, a differential equation and an initial value, and produce a series of values as output. The differential equation is solved as a function of the independent variable t by default. Conditional components Compartments, flows, variables and defined values can be defined as conditional or unconditional components. A conditional component is defined from a list of conditions which have associated equations. When the component is evaluated, ModelMaker works down the list of conditions until it finds one which is true. The associated equation is then used to determine the value of the component. Constraint Range Define a constraint range to limit the value a parameter can take during optimization and minimization - set on the Constraints tab of the Parameter Definition dialog box. Continuous Distributions The Monte Carlo facility allows you to specify model parameters as random distributions. The probability distributions fall into the two classes - Continuous and Discrete. A random variable is said to be continuous in a given range if it can assume any value in that range. The continuous distributions are Normal, Triangular, Uniform, Exponential, Weibull, Beta, Gamma, Logistic, Pareto, Extreme Value and Lognormal. Control Series When using lookups you can define one of the series as being a control series. A control series does not have a value or symbol of its own but uses the value of a model component to determine which data points are to be used to calculate the value of a controlled series. Controlled Series Used in lookups. The column of data from which the value of the series is to be evaluated using the interpolation method indicated on the lookup definition dialog. Controlled series have their own unique symbol which is used by other model components to refer to its value. Convergence A term used to determine when an optimization or minimization should stop. The run converges when the changes occurring reach small enough values so as to be considered zero i.e. continuing the run would not get significantly better results. DData SeriesData series are the columns of data in lookup files and tables. Lookups are ModelMaker's way of linking models to external data, i.e., using real data to control the model components. There are four types of data series, Control, Controlled, Data and unused. Data series cannot be interpolated and are used to extract single values. Defined Value Defined Values are similar to Variables in that they are defined by an ordinary (not differential) equation. However Defined Values are only calculated at the start of a model run or as a result of an event action. If you know that a component value only needs to be calculated once or a limited number of times then they can be used to save computational overhead instead of a Variable whose value is calculated at every time step. Delay A delay is a model component that holds the value of another model component for a specified time. Differential Equation A differential equation tells you how a function changes. Solving a differential equation with the appropriate boundary conditions will give the function itself and values of the variables involved. ModelMaker uses a choice of five integration methods to solve differential equations defined in 'Compartments'. Using these numerical methods you can solve systems of differential equations that either could not be solved analytically or would need expert mathematicians to do so. Discontinuities You can model discontinuous systems in ModelMaker using Events (see below). Discrete Distributions The Monte Carlo facility allows you to specify model parameters as random distributions. The probability distributions fall into the two classes - Continuous and Discrete. Discrete random variables may only take on distinct values. The discrete distributions are Binomial, Poisson and Geometric. DLL The DLL component is used to link the model to an external program in the form of a DLL. You might want to do this, for example if you wish to use your own functionality not currently included in ModelMaker. In short, the component passes values to the DLL and then receives the results allowing them to be transferred to other model components. EEuler The simplest of the integration methods used by ModelMaker to solve differential equations. This is included mainly for educational purposes and we recommend that you use one of the more advanced methods.Events Events are used to model discontinuous systems. An event action occurs when the event is triggered, the trigger being the value of a component (Component Event) or the independent variable (Independent Event). Event actions can include changes in values of components, changing data used in lookups and event to add user interactivity. Experimental Data Import experimental data using the Model Data view. This Model Data is used to optimize your model and should not be confused with data in Lookup tables and Files. Lookup data is used to drive the model through fixed data points and using interpolation methods to calculate the interim values. Explorer The new ModelMaker window is divided into two panels. On the left is the Model Explorer. This lists all ModelMaker views in a 'file-tree' manner allowing you easy access to all model views. Exponential Distribution The Monte Carlo facility allows you to specify model parameters as random distributions. The exponential distribution has the form:  where p(x) is the Probability Density Function. There are no user-supplied parameters for this distribution. Extended Least-Squares In ModelMaker, optimization is the minimization of the difference between the calculated values and observed experimental values. The measure of difference is the residual sum of squares (RSS). Extended Least Squares (ELS) is one of three alternative methods of calculating this value and is recommended when the user does not know the error magnitude of data values. Extreme Value Distribution The Monte Carlo facility allows you to specify model parameters as random distributions. The Extreme Value distribution has the form:  where p(x) is the Probability Density Function. The user-supplied parameters are:
FFile TypesModelMaker creates three types of file:
GGamma DistributionThe Monte Carlo facility allows you to specify model parameters as random distributions. The Gamma distribution of order a>0 is defined by:  where p(x) is the Probability Density Function. In ModelMaker 4, the scale factor b in the above expression equals 1.0. The user-supplied parameter is:
New in Version 4 this integration method is recommended for solving stiff systems of equations. Geometric Distribution The Monte Carlo facility allows you to specify model parameters as random distributions. The Geometric distribution has the form:  where P(k) is the probability for the whole number k. The user-supplied parameters are:
When a component is defined as Global its value is available to all other components in the same sub-model and lower sub-models. Graphics You can add graphics to your models in the form of a bitmap image to enhance you model diagram. Most component definition dialogs include a bitmap tab for importing the image. text boxes are particularly useful for adding graphic images as you do not need to define any other function other then the location of the image file. IIf..else.The ModelMaker scripting language, used for defining Event Actions includes many common programming statements such as if...else. Initial Value ModelMaker Compartments solve differential equations using initial value methods of integration. As such compartments must be defined with an initial value - even if this is zero. If all the compartments in the model have zero initial value then you will be warned of this when you try to run the model. Delays also use an initial value. Integration In ModelMaker integration is the solution of differential equations. ModelMaker has a choice of five numerical methods of integration: Euler, Mid-point, Runge-Kutta (default), Bulirsch-Stoer and Gears method. LLocal MinimumExercise caution when performing optimization runs as most optimization methods move towards the nearest minimum value. if this is a local minimum rather than the global minimum then you may not be able to calculate the best parameter set for your model. Version 4 can now perform parameter estimation - itself an optimization technique. In this case you can choose to use the simulated annealing algorithm which is much better at avoiding local minima and finding the true global minimum. Logistic Distribution The Monte Carlo facility allows you to specify model parameters as random distributions. The logistic distribution has the form:  where p(x) is the Probability Density Function. This expression describes the distribution about a mean value of zero. The user-supplied parameters are:
The Monte Carlo facility allows you to specify model parameters as random distributions. The Lognormal distribution has the form:  where p(x) is the Probability Density Function. Lognormal random numbers are the exponentials of Gaussian random numbers. The user-supplied parameters are:
Lookups are used to link models to external data. Lookups are used to calculate model values during a model run. For example if your were modeling rainfall and had actual measurements of rainfall in a data file then you could use a lookup to use these values directly in your model. Lookup data should not be confused with Model Data which is used for model optimization. MMarquardtMarquardt (also known as Levenberg-Marquardt) is the default optimization method used by ModelMaker. The Marquardt method is selected on the Run Optimization dialog and configured on the Optimization Settings dialog. Mid-Point One of the five integration methods used by ModelMaker. Minimization In ModelMaker minimization is the adjustment of parameters to find the minimum value of a model component. Minimization requires that you select parameters to be included (in the Parameters View) and create a sample point in the Sample Points view. Convergence options are configured in the Minimization settings dialog. Monte Carlo Also known as Global Sensitivity Analysis is included in ModelMaker 4 for the first time. Monte carlo allows you to test the model and see a statistical analysis of the sensitivity of selected component values to variations in parameter values. The Monte Carlo configuration allows a choice of several distribution functions for each parameter. Results are plotted on a histogram and statistical analysis results are displayed in the Global Sensitivity Analysis dialog. Model Definition The Model Definition view is a tree like structure displaying all model component details. A model definition is also included when results are archived, providing a snap-shot of the model when those results were created. NNormal DistributionThe Monte Carlo facility allows you to specify model parameters as random distributions. The Normal distribution generates random numbers according to a Gaussian distribution:  where p(x) is the Probability Density Function. The user-supplied parameters are:
OObserved Data ModelMaker can use observed data in two ways. Lookups use data to calculate values during a model run. Model data is experimental data which can be compared to model values during optimization.PParameterParameters are fixed values used by a model during a model run. They may, however be varied between model runs in order to analyze and optimize the model:
The Monte Carlo facility allows you to specify model parameters as random distributions. The Pareto distribution has the form:  where p(x) is the Probability Density Function. The user-supplied parameter is:
The Monte Carlo facility allows you to specify model parameters as random distributions. The Poisson distribution has the form:  where P(k) is the probability for the whole number k. The user-supplied parameters are:
RRandom NumberRandom numbers may be generated in three ways, as a uniform distribution between two values, as a normal distribution where the user defines the mean and standard distribution and as an exponential function between 0 and 709.7827. When developing stochastic models you may reset the random seed generation between runs or let modelmaker use a new seed to ensure a different set of numbers. Repeated Run The repeated run feature allows you to run a model several times in succession. One use of this is when you are using stochastic models and want to get a good statistical result by running the model over and over again. Other uses may be the use of different data sets for different runs and in sensitivity analysis where the values of parameters are changed between the runs. Runge-Kutta Also known as Fourth Order Runge-Kutta this is the default integration method used by ModelMaker. This tends to give good results for most kinds of model though can have problems when simulating stiff systems of equations. In this case you should use the new Gear method. SSample PointsA sample point is a simulation result - the value of a component at a particular moment in time. Sample points are configured in the Sample Points view, and must be defined in order to run minimization and Monte Carlo analysis. Sensitivity Analysis Sensitivity analysis is a good way of observing the effect of changes in your model when parameters are changed. A more rigorous approach is to use the Monte Carlo feature but if you want to find out what happens when parameters are changed the sensitivity analysis allows you to change parameter values in a stepwise (linear or logarithmic) manner. Sensitivity is configured as part of the Repeated Run settings on the Run Options dialog. Shading ModelMaker shades components in several ways:
One of the methods used for optimization and minimization. Stiff equations A stiff system of equations are typically those exhibiting extremes of behaviour - in some periods the functions are changing slowly and in others they are changing rapidly whose solutions remain wholly bounded. For example, simulating a set of chemical reactions often results in a stiff set of equations because although a set of chemical reaction may start out rapidly when they approach equilibrium the timescale decreases greatly. Gear's method of integration, implemented in ModelMaker 4 is ideal for solving stiff systems of equations. TTriangular DistributionThe Monte Carlo facility allows you to specify model parameters as random distributions. The Triangular distribution can be configured to produce both symmetrical and asymmetrical distributions:  where p(x) is the Probability Density Function. The user-supplied parameters are:
UUnconditional ComponentsCompartments, flows, variables and defined values can be defined as conditional or unconditional components. An unconditional component is defined using a single equation which is always used when evaluating the component. This is the default state for new components. Uniform Distribution The Monte Carlo facility allows you to specify model parameters as random distributions. The form of the Uniform distribution in the range a to b is:  where p(x) is the Probability Density Function. The user-supplied parameters are:
WWeibull DistributionThe Monte Carlo facility allows you to specify model parameters as random distributions. The Weibull distribution has the form:  where p(x) is the Probability Density Function. The user-supplied parameters are:
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