Some Intrinsic Limitations of Sample Variances in Stock Assessment Models
C.E. Porch
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Description
Most modern stock assessment algorithms incorporate multiple catch and abundance estimates, with differing levels of precision. Often these estimates are weighted by their corresponding variances, but estimates of variance are even less precise than estimates of expectation. For this reason, transformations and weighting schemes based on a presumed variance to expectation relationship have often been suggested. Since the true variance to expectation relationship is seldom known, it is usually inferred from regressions of sample variance on sample mean. Unfortunately, the sample variances of non-negative variates like catch per unit effort lie within bounds that are functions of the sample size, sample mean, and maximum possible catch (density). Furthermore, the sample mean and sample variance are self-correlated because the sample mean appears in the expression for sample variance. This paper demonstrates that these, and other mathematical artifices, can force a strong spurious correlation between the sample variance and sample mean regardless of the statistical distribution of the data. Therefore, plots of sample variance against sample mean are unlikely to reveal the true variance to mean relationship for any given population. Moreover, stock assessments that use sample variance to weight the input observations will tend to be biased. Underestimates will tend to receive too much weight and overestimates too little, particularly if the resource in question is uncommon and the sample sizes are small.
Item details
- Item number: AK-SG-98-01s
- Year: 1998
- DOI: https://doi.org/10.4027/fsam.1998.19
