Improved modeling of multivariate measurement errors based on the Wishart distribution.
The error covariance matrix (ECM) is an important tool for characterizing the errors from multivariate measurements, representing both the variance and covariance in the errors across multiple channels. Such information is useful in understanding and minimizing sources of experimental error and in the selection of optimal data analysis procedures. Experimental ECMs, normally obtained through replication, are inherently noisy, inconvenient to obtain, and offer limited interpretability. Significant advantages can be realized by building a model for the ECM based on established error types. Such models are less noisy, reduce the need for replication, mitigate mathematical complications such as matrix singularity, and provide greater insights. While the fitting of ECM models using least squares has been previously proposed, the present work establishes that fitting based on the Wishart distribution offers a much better approach. Simulation studies show that the Wishart method results in parameter estimates with a smaller variance and also facilitates the statistical testing of alternative models using a parameterized bootstrap method. The new approach is applied to fluorescence emission data to establish the acceptability of various models containing error terms related to offset, multiplicative offset, shot noise and uniform independent noise. The implications of the number of replicates, as well as single vs. multiple replicate sets are also described.
Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, PO Box 15000, Halifax, NS B3H 4R2, Canada. Electronic address: peter.wentzell@dal.ca.
Peter D
PD
Wentzell
Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, PO Box 15000, Halifax, NS B3H 4R2, Canada.
Cody S
CS
Cleary
Trace Analysis Research Centre, Department of Chemistry, Dalhousie University, PO Box 15000, Halifax, NS B3H 4R2, Canada; Institute for Advanced Studies in Basic Sciences (IASBS), GavaZang, Zanjan, 45137-66731, Iran.
M
M
Kompany-Zareh
Error covariance matrix; Error simulation; Fluorescence; Maximum likelihood; Measurement noise; Multivariate analysis; Wishart distribution