sbiosampleerror

Sample error based on error model and add noise to input data

Syntax

noisydata = sbiosampleerror(inputdata,errormodel,errorparam)

Description

noisydata = sbiosampleerror(inputdata,errormodel,errorparam) adds noise to the input data using one or more error models and error parameters.

Examples

Add Noise to Simulation Data

This example adds noise (or error) to the simulation data from a radioactive decay model with the first-order reaction: $$\frac{dz}{dt}=c\cdot x$$, where x and z are species and c is the forward rate constant.

Load the sample project containing the radiodecay model m1.

sbioloadproject radiodecay;

Simulate the model.

[t,sd,names] = sbiosimulate(m1);

Plot the simulation results.

plot(t,sd);
legend(names,'AutoUpdate','off');
hold on

Add noise to the simulation results using the constant error model with the error parameter set to 20.

noisydata = sbiosampleerror(sd,'constant',20);

Plot the noisy simulation data.

plot(t,noisydata);

Define a Custom Error Model Using a Function Handle

This example defines a custom error model using a function handle and adds noise to simulation data of a radioactive decay model with the first-order reaction , where x and z are species, and c is the forward rate constant.

Load the sample project containing the radiodecay model m1.

sbioloadproject radiodecay;

Suppose you have a simple custom error model with a standard mean-zero and unit-variance (Gaussian) normal variable e, simulation results f, and two parameters p1 and p2:

Define a function handle that represents the error model.

em = @(y,p1,p2) y+p1+p2*randn(size(y));

Simulate the model.

[t,sd,names] = sbiosimulate(m1);

Plot the simulation results and hold the plot.

plot(t,sd);
legend(names,'AutoUpdate','off');
hold on

Sample the error using the previously defined custom function with two parameters set to 0.5 and 30, respectively.

noisydata = sbiosampleerror(sd,em,{0.5,30});

Plot the noisy simulation data.

plot(t,noisydata);

You can also apply a different error model to each state, which is a column in sd. Suppose you want to apply the custom error model (em) to the first column (species x data) and the proportional error model to the second column (species z data).

hold off
noisydata = sbiosampleerror(sd,{em,'proportional'},{{0.5,30},0.3});
plot(t,sd);
legend(names,'AutoUpdate','off');
hold on
plot(t,noisydata);

Input Arguments

inputdata — Input data

SimData object | vector of SimData objects | numeric matrix

Input data, specified as a SimData object, vector of SimData objects, or numeric matrix. If it is a vector of SimData objects, the error is added to each of the columns in the Data property. If it is a numeric matrix, the error is added to each column in the matrix.

errormodel — Error model

character vector | string | function handle | string vector | cell array of character vectors

Error model(s), specified as a character vector, string, function handle, string vector, cell array of character vectors, or cell array containing a mixture of character vectors and function handles.

If it is a string vector or cell array, its length must match the number of columns (responses) in inputdata, and each error model is applied to the corresponding column in inputdata. If it is a single character vector, string, or function handle, the same error model is applied to all columns in inputdata.

The first argument of a function handle must be a matrix of simulation results. The subsequent arguments are the parameters of the error model supplied in the errorparam input argument. The output of the function handle must be a matrix of the same size as the first input argument (simulation results).

For example, suppose you have a custom error model with a standard mean-zero and unit-variance (Gaussian) normal variable e, simulation results f, and two parameters p1 and p2: $$y=f+p1+p2\ast e$$. You can define the corresponding function handle as follows.

em = @(y,p1,p2) y+p1+p2*randn(size(y));

where y is the matrix of simulation results and p1 and p2 are the error parameters. The output of the function handle must be the same size as y, which is the same as the simulation results specified in the inputdata input argument. The parameters p1 and p2 are specified in the errorparam argument.

There are four built-in error models. Each model defines the error using a standard mean-zero and unit-variance (Gaussian) variable e, simulation results f, and one or two parameters a and b. The models are:

• 'constant': $$y=f+ae$$

• 'proportional': $$y=f+b\left|f\right|e$$

• 'combined': $$y=f+(a+b\left|f\right|)e$$

• 'exponential': $$y=f\ast \exp (ae)$$

errorparam — Error model parameter

scalar | vector | cell array

Error model parameter(s), specified as a scalar, vector, or cell array. If errormodel is 'constant', 'proportional', or 'exponential', then errorparam is specified as a numeric scalar. If it is 'combined', then errorparam is specified as a row vector with two elements [a b].

If errormodel is a cell array, then errorparam must be a cell array of the same length. In other words, errorparam must contain N elements, where N is the number of error models in errormodel. Each element must have the correct number of parameters for the corresponding error model.

For example, suppose you have three columns in inputdata, and you are applying a different error model (constant, proportional, and exponential error models with error parameters 0.1, 0.2, and 0.5, respectively) to each column, then errormodel and errorparam must be cell arrays with three elements as follows.

errormodel = {'constant','proportional','exponential'};
errorparam = {0.1,0.2,0.5};

Output Arguments

noisydata — Data with added noise

vector of SimData objects | matrix

Data with added noise, returned as a vector of SimData objects or numeric matrix. If inputdata is a vector of SimData objects, noisydata is also a vector of SimData objects, and the error is added to each column in the inputdata.Data property. If inputdata is specified as a matrix, noisydata is a matrix, and the error is added to each column in the matrix.

Version History

Introduced in R2014a