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a.
Hypothesis Testing vs. Bayes’ Theorem — Which One?
We have discussed two logical frameworks for the consideration of forensic
science data, hypothesis testing, and likelihood ratios in the context of Bayes’
theorem. In hypothesis testing, one proposition at a time is considered; failing
to falsify the proposition, the uncertainty associated with the truth of the
proposition is usually expressed as a frequency. In an LR, alternative hypoth-
eses are compared and the relative uncertainty associated with the truth of
the propositions is calculated. Frequencies are incorporated with other infor-
mation in this calculation.
Perhaps these logical frameworks are not as antithetical as extremists of
both persuasions might have us believe. Stoney (1991) wrote that “The like-
lihood ratio is a generalization of the more generally used ‘match frequen-
cies.’” We believe that it is useful to study and understand the ideas inherent
in both of these schools of scientific philosophy. Considerable research and
refinement will be necessary before the profession of forensic science evolves
a unified understanding and application of the various tools available to
express the strength of forensic evidence. Certainly, the Bayesian model is
more sophisticated and allows for the logical consideration of more complex
situations. However, we believe that the concept of hypothesis falsification is
still fundamental to the applied sciences. We are not willing to discard one
set of ideas wholesale; rather, we take from both as the situation demands.
We continue to draw from both schools of thought throughout the rest of
this volume.
4.
Individualization
Neither the Bayesian model using likelihood ratios nor hypothesis testing is
very helpful in expressing an individualization. Strict Bayesians exclude the
possibility that one alternative is ever completely wrong, allowing us to accept
the other one as true; strict frequentists insist that a number must always be
proffered, however irrational such a number might be in the context of an
actual population.
Although it may seem irrelevant to discuss probabilities for evidence that
has been individualized to a single source, we must remember that an opinion
of unique common source still relies on a body of data. Consciously or not,
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Principles and Practice of Criminalistics
the data convince the analyst to make the leap. No evidence to the contrary
would change the analyst’s belief that the evidence and reference share a
common source. The state of the practice of forensic science is that examiners
do provide opinions of individualization.