Design

The design problem considers the expected information gain of measurements for the experimental design \(s\), given by

\[U(s)=\int_{\mathcal{Y}} \int_{\mathcal{T}} \ln \frac{p(y \mid \vartheta, s)}{p(y \mid s)} p(y \mid \vartheta, s) p(\vartheta) \mathrm{d} \vartheta \mathrm{d} y\]

where \(y\) denotes the measurements for parameters \(\vartheta\). The goal is to determine the optimal experimental design

\[s^\star = \arg\max_s U(s)\]

Usage

e["Problem"]["Type"] = "Design"

Compatible Solvers

This problem can be solved using the following modules:

Variable-Specific Settings

These are settings required by this module that are added to each of the experiment’s variables when this module is selected.

Type

  • Usage: e[“Variables”][index][“Type”] = string

  • Description: Indicates what the variable descibes.

  • Options:

    • “Design”: The variable describes a design.

    • “Parameter”: The variable describes an parameter.

    • “Measurement”: The variable describes an measurement.

Lower Bound

  • Usage: e[“Variables”][index][“Lower Bound”] = real number

  • Description: Lower bound for the variable’s value.

Upper Bound

  • Usage: e[“Variables”][index][“Upper Bound”] = real number

  • Description: Upper bound for the variable’s value.

Distribution

  • Usage: e[“Variables”][index][“Distribution”] = string

  • Description: Indicates the distribution of the variable.

Number Of Samples

  • Usage: e[“Variables”][index][“Number Of Samples”] = unsigned integer

  • Description: Number of Samples per Direction.

Name

  • Usage: e[“Variables”][index][“Name”] = string

  • Description: Defines the name of the variable.

Configuration

These are settings required by this module.

Model

  • Usage: e[“Problem”][“Model”] = Computational Model

  • Description: Stores the model function.

Variable Defaults

These following configuration will be assigned to each of the experiment variables by default. Any settings defined by the user will override the given settings specified in these defaults.

{
"Distribution": " ",
"Lower Bound": -Infinity,
"Number Of Samples": 0,
"Upper Bound": Infinity
}