measurement categories, such as PAR (photosynthetically active radiation)
and understory diversity, so that implementation plots could avoid spatial
autocorrelation problems (Riitters et al. 1991).
10.4.5 Extrapolation: Information versus Data
Extrapolation requires that the structure and the variability in the data have
been modeled by an understandable set of relationships, and that these relationships will be valid for the population as well as the sample. In short, we
are attempting to convert data into information. For example, one use of
the modeling effort may be to calculate the results of what-if scenarios.
Models implicitly assume that the conditions under which the model was
constructed will be the same as those under which the what-if results will
be obtained. While this assumption is common and necessary for decision
making, some aspects of the data quality may make such extrapolations
more difficult. Instead of attempting a treatise on extrapolation, we attempt
to describe particular qualities of data that may compromise a manager’s
ability to make decisions based on model results.
Uncertainty in both the model structure and parameter values may
inhibit the ability to extract information from the modeling effort. During
an analysis of the effects of parameter uncertainty on model output results,
it is advisable, if possible, to separate the variation in the data caused by
process (e.g., temporal variation in survival rate) from its uncertainty to
other causes (e.g., sampling variation caused by finite sample size). Some
techniques for accomplishing this, and the rationale behind it, are given in
Gould and Nichols (1998), Steward-Oaten et al. (1995), and White (2000).
Multiple working hypotheses are encouraged (Hilborn and Mangel 1997),
yet some circumstances require a single modeling approach. In such
instances of single model formulations or when a final model formulation
has been selected, sensitivity analyses, propagation-of-error studies, or
similar methods of parameter checking are a necessity. If maximum likelihood methods are being used, a profile of the parameter likelihood can also
describe the amount of information present in the model structure. In a
Bayesian framework, both the prior distribution and the likelihood profile
should be compared to the posterior distribution to determine what effect
the data have had in shaping the parameter profile. One concern in
Bayesian analyses is that the prior may dominate the posterior, suggesting
that no new information has been added by the data. With the above
methods to obtain parameter ranges and by varying parameter values in
Monte Carlo simulations, probabilistic statements can be made about specific outcomes. While this level of information may make results less clear
and therefore more difficult for decision making, these types of results
effectively describe the role that the data have played in forming the
prediction. The USEPA’s DDRP program successfully used Monte Carlo
simulations to make probabilistic statements about long-term model
198
David Hohler et al.
and understory diversity, so that implementation plots could avoid spatial
autocorrelation problems (Riitters et al. 1991).
10.4.5 Extrapolation: Information versus Data
Extrapolation requires that the structure and the variability in the data have
been modeled by an understandable set of relationships, and that these relationships will be valid for the population as well as the sample. In short, we
are attempting to convert data into information. For example, one use of
the modeling effort may be to calculate the results of what-if scenarios.
Models implicitly assume that the conditions under which the model was
constructed will be the same as those under which the what-if results will
be obtained. While this assumption is common and necessary for decision
making, some aspects of the data quality may make such extrapolations
more difficult. Instead of attempting a treatise on extrapolation, we attempt
to describe particular qualities of data that may compromise a manager’s
ability to make decisions based on model results.
Uncertainty in both the model structure and parameter values may
inhibit the ability to extract information from the modeling effort. During
an analysis of the effects of parameter uncertainty on model output results,
it is advisable, if possible, to separate the variation in the data caused by
process (e.g., temporal variation in survival rate) from its uncertainty to
other causes (e.g., sampling variation caused by finite sample size). Some
techniques for accomplishing this, and the rationale behind it, are given in
Gould and Nichols (1998), Steward-Oaten et al. (1995), and White (2000).
Multiple working hypotheses are encouraged (Hilborn and Mangel 1997),
yet some circumstances require a single modeling approach. In such
instances of single model formulations or when a final model formulation
has been selected, sensitivity analyses, propagation-of-error studies, or
similar methods of parameter checking are a necessity. If maximum likelihood methods are being used, a profile of the parameter likelihood can also
describe the amount of information present in the model structure. In a
Bayesian framework, both the prior distribution and the likelihood profile
should be compared to the posterior distribution to determine what effect
the data have had in shaping the parameter profile. One concern in
Bayesian analyses is that the prior may dominate the posterior, suggesting
that no new information has been added by the data. With the above
methods to obtain parameter ranges and by varying parameter values in
Monte Carlo simulations, probabilistic statements can be made about specific outcomes. While this level of information may make results less clear
and therefore more difficult for decision making, these types of results
effectively describe the role that the data have played in forming the
prediction. The USEPA’s DDRP program successfully used Monte Carlo
simulations to make probabilistic statements about long-term model
198
David Hohler et al.