Definition
The Fisher information is a measure for the amount of information about parameters provided by experimental data (Fisher 1912). It is a well-established characteristic of an experimental design used to assess and optimize the design for maximizing the expected accuracy of parameter estimates (Kreutz 2009). The Fisher information is calculated for each pair of parameters and is in this notation denoted as the Fisher information matrix.
In the following, the Fisher information is introduced in some commonly used notations. Some calculations require additional assumptions in a strict mathematical derivation. Because the assumptions are usually fulfilled for models applied in systems biology, these restrictions are not stated explicitly.
Because the log-likelihood \( LL\left( {y|\theta } \right) \) depends on the noise realization, the log-likelihood and its derivatives can be considered as random variables. The Fisher information I of a design \( \mathcal{D} \)is defined as...
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Kreutz, C., Timmer, J. (2013). Optimal Experiment Design, Fisher Information. In: Dubitzky, W., Wolkenhauer, O., Cho, KH., Yokota, H. (eds) Encyclopedia of Systems Biology. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9863-7_1222
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DOI: https://doi.org/10.1007/978-1-4419-9863-7_1222
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