Abstract
When limited or no observed data are available, it is often useful to obtain expert knowledge about parameters of interest, including point estimates and the uncertainty around these values. However, it is vital to elicit this information appropriately in order to obtain valid estimates. This is particularly important when the experts’ uncertainty about these estimates is strongly skewed, for instance when their best estimate is the same as the lowest value they consider possible. Also this is important when interest is in the aggregation of elicited values. In this paper, we compare alternative distributions for describing such estimates. The distributions considered include the lognormal, mirror lognormal, Normal and scaled Beta. The case study presented here involves estimation of the number of species in coral reefs, which requires eliciting counts within broader taxonomic groups, with highly skewed uncertainty estimates. This paper shows substantial gain in using the scaled Beta distribution, compared with Normal or lognormal distributions. We demonstrate that, for this case study on counting species, applying the novel encoding methodology developed in this paper can facilitate the acquisition of more rigorous estimates of (hierarchical) count data and credible bounds. The approach can also be applied to the more general case of enumerating a sampling frame via elicitation.
Highlights
This paper addresses the problem of eliciting from an expert both point and interval estimates of a parameter of interest, where the expert data is heavily skewed
The details of encoding these distributions for elicited data were not specified in Fisher et al [7]. We provide these details and present an alternative distribution, the scaled Beta, which can be encoded to all elicited numbers
For an initial estimate, the summary statistics elicited were, in order [7]: (i) minimum (ML) and maximum (MU), so that the expert is 100% sure that the number is within this range; (ii) more realistic lower (L) and upper (U) bounds, and the uncertainty/sureness (P) around these bounds, elicited by asking how sure they are that the real number lies within these bounds; and (iii) their best estimate (B), the number they thought was most plausible
Summary
This paper addresses the problem of eliciting from an expert both point and interval estimates of a parameter of interest, where the expert data is heavily skewed. Elicited estimates of variables of interest may be useful, for example, when data gaps exist, such as in the post-Normal science situation in which inference is required before the data are available. Encoding Heavily Skewed Expert Count Data all the PLOS ONE policies on sharing data and materials as detailed online in the guide for authors. Whilst structured approaches for quantifying such expert knowledge have become more readily available in ecology [3,4,5], these generally encode expert knowledge and their uncertainty using symmetric or moderately skewed forms of distributions. There is little literature on elicitation of highly skewed distributions
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