Documentation

# sbiosampleerror

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

## Syntax

``sdN = sbiosampleerror(sd,errormodel,errorparam)``

## Description

example

````sdN = sbiosampleerror(sd,errormodel,errorparam)` adds noise to the simulation data `sd` using one or more error models `errormodel` and error parameters `errorparam`.```

## Examples

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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.

`sdNoisy = sbiosampleerror(sd,'constant',20);`

Plot the noisy simulation data.

`plot(t,sdNoisy);`

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.

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

Plot the noisy simulation data.

```plot(t,sdNoisy); ```

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

## Input Arguments

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Simulation results, specified as a ```SimData object``` or matrix.

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 `sd`, and each error model is applied to the corresponding column in `sd`. If it is a single character vector, string, or function handle, the same error model is applied to all columns in `sd`.

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 `sd` 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'`: $y=f+b|f|e$

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

• `'exponential'`: $y=f\ast \mathrm{exp}\left(ae\right)$

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 `sd`, and you are applying a different error model (`constant`, `proportional`, and `exponential` error models with error parameters 0.1, 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 = {0.1,2,0.5};```

## Output Arguments

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