IMIS | Vlaams Instituut voor de Zee

Vlaams Instituut voor de Zee

Platform voor marien onderzoek


Publicaties | Instituten | Personen | Datasets | Projecten | Kaarten
[ meld een fout in dit record ]mandje (0): toevoegen | toon Print deze pagina

Refined parameter and uncertainty estimation when both variables are subject to error. Case study: estimation of Si consumption and regeneration rates in a marine environment
de Brauwere, A.; De Ridder, F.; Elskens, M.; Schoukens, J.; Pintelon, R.; Baeyens, W.F.J. (2005). Refined parameter and uncertainty estimation when both variables are subject to error. Case study: estimation of Si consumption and regeneration rates in a marine environment. J. Mar. Syst. 55(3-4): 205-221.
In: Journal of Marine Systems. Elsevier: Tokyo; Oxford; New York; Amsterdam. ISSN 0924-7963; e-ISSN 1879-1573, meer
Peer reviewed article  

Beschikbaar in  Auteurs 
    VLIZ: Open Repository 70163 [ OMA ]

    Analysis > Mathematical analysis > Numerical analysis > Approximation
    Characteristics > Uncertainty
    Cycles > Chemical cycles > Geochemical cycle > Biogeochemical cycle > Nutrient cycles > Silicon cycle
    Environments > Aquatic environment > Marine environment
Author keywords
    marine environment; Monte-Carlo simulations; nonlinearity; silicon cycling; uncertainty estimation; weighted least squares method

Auteurs  Top 
  • de Brauwere, A., meer
  • De Ridder, F., meer
  • Elskens, M., meer
  • Schoukens, J., meer
  • Pintelon, R., meer
  • Baeyens, W.F.J., meer

    The problem of estimating parameters and their uncertainty from experimental measurements in marine ecosystems is a common task and often necessitates solving nonlinear equations. If the measurements are subject to individually varying errors (i.e., heteroscedastic data), the parameters are often estimated using a Weighted Least Squares (WLS) method. For estimating the parameter uncertainties, a linearized expression for the covariance matrix exists. Yet, both methods assume that the errors on the independent variable, also called “input”, is negligible, which is often not true. For instance, in order to determine uptake and regeneration rates of silicic acid by phytoplankton, concentration and isotopic abundance measurements are performed at the beginning (input) and at the end (output) of an incubation experiment. Here, the so-called input and output are measurements of the same quantities, i.e., determined in exactly the same way, only differing by the time at which the measurements were performed. Clearly, there is no reason to assume that the input measurements are subject to less error than the output measurements. We propose a refinement of the two abovementioned estimation methods which enlarges their applicability to cases where input noise is not negligible. The refined methods are evaluated on the uptake and regeneration processes of silicic acid and compared to the original procedures using Monte-Carlo simulations. The results reveal a smaller bias for the refined WLS estimator compared with the original one. An additional advantage of using the refined WLS cost function is that its residual value can be interpreted as a sample from a ?2 distribution. This property is especially useful because it enables an internal quality control of the results. In addition, the parameter uncertainty estimation is significantly improved. By neglecting the effect of the input noise, a (potentially) important origin of the parameter variation is simply ignored. Therefore, without the refinement, the parameter uncertainties are systematically underestimated. Using the refined method, this systematic error disappears and on the whole, the parameter standard deviations are accurately estimated.

Alle informatie in het Integrated Marine Information System (IMIS) valt onder het VLIZ Privacy beleid Top | Auteurs