of the Inference
LR 2. Assuming the absence of the Boyfriend
The results can be summarized as follows: The probability of the evidence under Hypothesis 1, the boyfriend and the suspect, is many orders of mag- nitude greater than any of the others. How should this be expressed? We take LR 1 as an example. We could say either of the following:
• The evidence profile is at least 1.5 billion times more likely to be of the type seen if the boyfriend and the suspect are the donors, than if the boyfriend and any other random man are the donors.
• The probability of someone other than the suspect having the requisite profile to complete the observed mixture, assuming the boyfriend is present, is 1 in 1.5 billion.
* The details of these calculations are given in Appendix E. We use the Caucasian popu- lation frequencies for the example.
P E Boyfriend + Suspect( ) P E Boyfriend + random man( )
--- = 1.5 billion
P E Suspect + random man( ) P E two 2( ( )random men)
--- = 45,000,000 8127/frame/ch06 Page 146 Friday, July 21, 2000 11:47 AM
case, that is, that the victim indicates a consenting intercourse with a named donor whose sample is available, at least three orders of magnitude of infor- mation are lost.
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,
148 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.
a. Individualization and Opinion — A Special Case
How do we reconcile an opinion of individualization with the hypothesis testing model, in which we accept a hypothesis only by failing to disprove it?* By definition, we are left with only a provisional explanation which, at any time, may be disproved by further work. This presents an interesting dilemma for any applied science, including forensic science. If no hypothesis is ever proved, merely disproved, how can an analyst ever draw any firm conclusions from the data? Scientists understand that no fact is ever proved, yet the criminal justice system looks to science for help in establishing facts. The lawyers roll their eyes at the inability of the scientist to make up her mind, for the attorney’s life is made up of practical events that require practical decisions. In its purest form, science is of no value to the judicial system.
However, as a hypothesis continues to be tested, repeated failure to dis- prove it strengthens our conviction that it is correct and weakens our skep- ticism that it is wrong. Another way to say this is that, with each piece of additional information, our uncertainty regarding the truth of the hypothesis decreases. Finally, the analyst judges that no other potential reference source could possess the observed traits. Therefore, the chance of encountering a different reference with these characteristics by chance alone is zero.
Using LRs, the analyst judges the denominator (the probability of the evidence assuming a different source) to be zero. Dividing by zero drives the LR to infinity and, consequently also, the posterior odds. Purists, of course, contend that the denominator can never be zero. Robertson and Vignaux (1995), of the Bayesian persuasion, recognize this dilemma and suggest an interim solution.
In these cases it seems that the expert is giving evidence of identity when, and only when, in his judgment the probability of getting the evidence assuming the alternative hypothesis is so small that it does not matter what the numerator or even the prior are. At what point this is reached seems to be a matter of judgment and experience and there most writers on expert evidence are content to let the matter rest. This may have had the unfortunate effect of removing the incentive to carry out the basic research necessary to build appropriate models. Intellectually, this is unsatisfactory and further
* This must be an intelligent failure to disprove the hypothesis using discriminating tests. For instance, failure to prove that an individual is not the donor of a stain using secretor status (80% of the population are secretors ) is virtually meaningless and would not alter our certainty very much one way or the other.
As a practical matter, we suggest that:
At some subjective point, most qualified authorities would agree that, for
practical applications, the likelihood that the hypothesis is untrue is so small
that it can be ignored.
This concept is critical to moving forward in any applied science. Before we continue discussing its implications, let’s clarify the meaning of several key concepts.
Subjective. This implies a criteria that is personal and, as such, may be different for each individual. It is important to understand that any endeavor in which humans participate involves a subjective component; it is the nature of human existence that we each operate from a slightly different perspective, and all of our decisions are shaped by our cumulative experiences. Science is no different and the subjective element makes our conclusions no less valid. According to Popper, “We must distinguish between truth, which is objective and absolute, and certainty, which is subjective.”* (Horgan, 1996).
One fingerprint expert may be “certain” when she can find 9 points of comparison between two prints; another expert may require 10 points of comparison to be “certain.” Even if the two experts agree that 9 points of comparison exist, they may come to different conclusions based on their subjective uncertainty. The chromatogram of a suspected ignitable liquid is an objective piece of data. Everyone can agree on the number of peaks and their size. Two qualified analysts might disagree about whether they are comfortable concluding that the chromatogram represents a highly evapo- rated sample of gasoline.
Most. Not all qualified observers might agree with the assessment. This derives in part from the subjective nature of the evaluation, and in part from the nature of our culture, which seems to require disagreement to instigate progress.** However, if you are hanging in the wind all by yourself with a conclusion of singular common source, and none of your lab-mates is willing to brave the storm with you, you might wish to reconsider your conclusion.
* Popper believed that a theory could be absolutely true, but rejected the belief that we could ever know that a theory is true (Horgan, 1996).
** “The reasonable man adapts himself to the world. The unreasonable man persists in trying to adapt the world to himself. Therefore all progress depends upon the unreasonable man” — George Bernard Shaw.
150 Principles and Practice of Criminalistics
Qualified authority. One who has undertaken a formal study of the subject or who has extensive experience with it, has communicated with others on the topic, and can speak to the majority and minority opinions. To proffer an opinion on a particular case, one must also have reviewed the evidence and data relevant to that case, and synthesized an independent conclusion. Simply criticizing another’s conclusion is insufficient.
Small. How small does small need to be for the likelihood of untruth to be ignored? The uncomfortable part of this is that there is no absolute answer because “small” is necessarily relative. One is always comparing hypotheses rather than considering any hypothesis in a vacuum solely on its own merits. We’ve discussed likelihood ratios as a means for comparing hypotheses in this chapter.
Practical application. This brings us back around to the idea of subjective certainty. Although we have beat to death the idea that a hypothesis can only be disproved, never proved, we also embrace the reality that forensic science is an applied science whose purpose is to supply facts to the trier of the same. When we analyze the evidence and reference samples and see no differences, we conclude from this analysis that the two items could share a common source. For individualizable evidence, the inference may be so strong that we believe it to be true, even though we could not prove it with absolute certainty. We state this conclusion of common singular source as an opinion. Based on the experience and knowledge of both the forensic community and the indi- vidual, we may reasonably accept a properly qualified conclusion as fact.
G.
Summary
Charles Sanders Peirce, the founder of the Philosophy of Pragmatism, defined absolute truth as: “whatever scientists say it is when they come to the end of their labors” (Horgan, 1996). This is a particularly appealing bit of philoso- phy for those of us working in the applied sciences, particularly one such as forensic science where an entirely unrelated discipline depends on us to provide it with “facts.” Although we govern ourselves by the rules of science, we also embrace the practical nature of our endeavor. Pragmatism provides the philosophical foundation for Stoney’s clarification that individualization cannot be proved, we can only become convinced of it (Stoney, 1991).
However, to become convinced of an individualization, one must first be convinced that such a possibility exists. This conviction grows from an understanding of the nature of the evidence, including its inherent possibilities 8127/frame/ch06 Page 150 Friday, July 21, 2000 11:47 AM
tion, each practitioner must rely on an individual body of education, training, and most of all experience, to justify his conclusion of individuality. The greater the common wisdom and the more extensive the individual experi- ence, the more confidence we have that the leap of faith is both appropriate and justified. Equally important are the checks and balances that a working community provides in helping the individual analyst determine when the limitations of the evidence or the tests prevent individualization as a reason- able conclusion in any specific case.
When individualization is not legally necessary, and identification is sufficient, no further information is required. However, when individualiza- tion is desirable, but not possible, we default to classification. In this situation, more than one source could have produced the evidence, and we must provide an estimate of how many more than one this might be.
Lest we lose sight of why we care, remember that at this point in the paradigm (Figure 3.1) we are attempting to infer the source of a piece of evidence. Classification establishes a nonexclusive relationship between some evidence and its source; individualization establishes a singular relationship between a piece of evidence and its source. Whether we arrive at a classifi- cation or an individualization, that information will be used as a link to infer
associations between objects (for instance, a suspect and the crime scene).
The processes of association and reconstruction will be the topic of the next chapter.
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