State Supreme Court Approves of Variable-Prior-Odds Presentation of the Bayesian Probability of Paternity

In 2002, the Supreme Court of Kentucky wrote a disappointing opinion on the admissibility of the "probability of paternity" in a case of rape and sexual abuse of a minor. In 2016, the court corrected its mistakes in a similar case. The more recent opinion is a welcome addition to the jurisprudence on probability evidence in criminal cases.

Butcher

In the first case, Butcher v. Commonwealth, 96 S.W.3d 3 (Ky. 2002), Larry Butcher lived with a woman and her young daughter in Johnson County. After the woman had twin girls fathered by Larry, he "began a pattern of sexual abuse with H.B., who was then ten years old. . . . H.B. became pregnant in April 1987, at age fourteen. H.B. gave birth to a baby girl on January 19, 1988." Larry was convicted of eleven counts of first-degree rape and other offenses.

The evidence against him included "a DNA paternity test indicating a 99.74 percent likelihood that [he] was the father of H.B.'s child." The court explained that a "Mr. DeGuglielmo testified that tests performed on the eight genetic markers previously discussed yielded a paternity index of 388/1, meaning Appellant was 388 times more likely to be the father of the child than a randomly selected male of the same race."

The meaning the court ascribed to the paternity index is clearly wrong. The paternity index of 388 meant that the genotypes were 388 times more probable if Larry were the father than if a randomly selected man was. The probability that Larry was the father instead of a different man is something else. To mechanically equate the two is to transpose conditional probabilities. As is now widely recognized, the "probability of paternity" is a posterior probability that depends on both the likelihood ratio and the prior probability of paternity. If and only if the prior probability is one-half are the prior and the posteriors exactly equal.

Having initially conflated the paternity index with the posterior probability, the Butcher court went on to explain that the "final part of the paternity test translates the paternity index into a percentage that is more understandable . . . using Bayes' Theorem, a formula that takes into account actual events and circumstances, as opposed to random sequences of events." It thought that "[i]n paternity tests generally, this formula combines the paternity index and another value representing the prior probability that an event occurred, including such factors as access to the mother, fertility, and date of conception."

Of course, paternity test reports in both civil and criminal cases do not generally consider these factors. Rather, they "typically insert a standard prior probability of .5 regardless of any other factors, which indicates a fifty percent chance that the alleged father actually had sexual intercourse with the mother." (This is not quite right either, since not all intercourse leads to children.)

In any event, Butcher concluded that "there was a 99.74 percent likelihood that Appellant was the father of H.B.'s child. Although Mr. DeGuglielmo did not testify that he had used a prior probability value of .5 in reaching his expert conclusions, the mathematical results of the test suggest that he did."

In response to a garbled argument from Butcher that the use of a prior probability of one-half offended the presumption of innocence in a criminal case, the court relied on a 1998 Texas Court of Appeals opinion’s strange conclusion that "[t]he use of a prior probability of .5 is a neutral assumption. The statistic merely reflects the application of a scientifically accepted mathematical theorem which in turn is an expression of the expert's opinion testimony."

This is strange because any value from 0 to 1 for the prior probability would be part of "the application of a scientifically accepted mathematical theorem"—namely, Bayes’ rule. The expert supposedly has no opinion about the prior probability and is using the midpoint of 0.5 to express ignorance about what the value actually is. Yet, to assign a probability of 0.5 to the defendant is to credit the fact that he—as opposed to all other men in the population—has been charged with a crime. Letting an accusation of criminality create a substantial probability of guilt does seem to offend the presumption of innocence.

Ivey

This year’s case, Ivey v. Commonwealth, No. 2014-SC-000345-MR, 2016 WL 671153 (Ky. Feb. 18, 2016), is a major leap forward. Alfred Ivey, Jr., lived in Hardin County with his half-sister and her daughter from a previous relationship. The daughter became pregnant at the age of 13. Seven years later, she revealed that Ivey was the father and had repeatedly raped her before then. A paternity test confirmed that Ivey was the father, and a jury convicted him of two rapes of a minor.

Ivey objected that the probability of paternity—a whopping 99.9999%—was inadmissible under Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579 (1993). At a pretrial hearing on his motion to exclude,

Ivey proffered an academic article, Ernest P. Chiodo et al., An Error in Statistical Logic in the Application of Genetic Paternity Testing, J. Mod. Applied Stat. Methods, Winter 2002, Vol. 1, Issue 1, at 126, but did not offer any additional proof, such as expert testimony. His argument at that hearing was based solely on the article, which criticizes the use of the 50% prior probability to calculate the probability of paternity in some circumstances because it "highlights a serious error in statistical methodology known as the ‘principle of indifference.’"

The trial court admitted testimony about the parentage test anyway, and the state supreme court revisited its opinion in Butcher. This time around, it recognized that

The paternity index "does not measure the chance of defendant's paternity compared to that of a randomly selected man." D.H. Kaye, Plemel as a Primer on Proving Paternity, 24 Willamette L.Rev. 867, 877 (1988). . . . Technically speaking, the paternity index is the ratio of "the probability of the alleged father transmitting the alleles and the probability of selecting these alleles at random from the gene pool." D.H. Kaye, The Probability of an Ultimate Issue: The Strange Cases of Paternity Testing, 75 Iowa L.Rev. 75, 89 (1989–1990). It has been described as a "likelihood ratio," that is, "a ratio of two conditional probabilities," but "is not itself a probability." 1 McCormick on Evidence § 211 n. 17 (7th ed. 2013) "Unlike probabilities, which are bounded by 0 and 1, the likelihood ratio can exceed one. The larger the ratio, the more probative the evidence."

As such, the court acknowledged that its understanding of the paternity index in Butcher was "not, strictly speaking, completely accurate." Likewise, Ivey is more careful in describing the nature of a prior probability.

Nevertheless, the court seemed uncertain whether "the use of the 50% prior probability is a logical error." It wrote that "the ‘error,’ to the extent it is one, appears to matter only under unrealistic conditions." It noted that the likelihood ratio of 11,900,000 in the case swamped any plausible prior probability:

[I]n this case, even with very low assumed prior probabilities, the probability of paternity exceeded 99.99%. The Commonwealth's expert explained generally to the jury how the prior-probability notion affected the probability of paternity, albeit without getting into the details of Bayes' theorem, and postulated several variations less than the assumed standard 50%. For example, the expert explained that if the prior probability were only 1%, or .01, then the probability of paternity dropped only to 99.9991%. The extreme example of a low prior probability, .1%, or .001, used in the Chiodo article also results in very high probability of paternity for Ivey. Though the expert did not testify to this number, it can easily be calculated with the formula laid out elsewhere in this opinion, with the resulting probability of paternity being 99.9916%.

After seemingly sidestepping the question of whether the 0.5 prior probability is "a logical error," however, the court agreed with the commentary correcting the claims of "neutrality" for this number: "Those critical of using a 50% prior probability have a point. [T]hat prior probability is fairly high (almost satisfying the civil burden of proof by itself). Despite our assertions in the past, it is not a truly neutral number. It, at best, gives us a ‘useful working hypothesis.’" That said, "a 50% prior probability is far from neutral."

Yet, the court was unfazed by the fact that the prosecution’s expert testified that "she tried to be neutral, though ‘ideally’ the probability of paternity would take into account all the other evidence. . . . She testified that 50% was the only neutral number that would not weigh the results one way or the other."

What, then, can be done to enable a laboratory to explain the import of its genetic findings? Not being in a position to evaluate the nongenetic evidence in a case, the laboratory has no basis for estimating a case-specific prior probability. Neither does it have a usable statistic for the prevalence of paternity on the part of defendants in criminal conduct that results in pregnancies. Consequently, it cannot apply Bayes’ rule to give a single posterior probability to the jury.

One solution would be to forget Bayes’ rule—to eschew talk of the posterior of paternity and restrict testimony to the likelihood ratio and its components. Citing publications of the Royal Statistical Society, 1/ a concurring justice urged this approach. The paternity tester might testify along these lines: X% of all children would be expected to inherit the genetic characteristics that the child has if the defendant (or an identical twin) were the father. Only Y% would be expected to have these characteristics if an unrelated man were the father. Only Z% of children with (an unknown) brother to the defendant would be expected to inherit the child’s characteristics. Thus, the DNA types in this case strongly support the conclusion that the defendant is the father. (Obviously, this conclusion only follows if X is much greater than Y and Z, as was the case in Ivey.)

Ivey considered, but did not settle on another approach—sometimes called "variable prior odds" 2/ —which involves presenting jurors with a spectrum of prior and posterior probabilities to show them how the posterior probability changes as a function of the prior probability.

The Ivey court observed that

Though this proposed approach has drawn some criticism, see Meyerson & Meyerson, supra 3/, at 789 (stating that “[t]his proposal, though well-meaning, is hopelessly misguided”), it is not without its charm. It avoids the problem of the expert using a 50% prior probability without disclosing what that figure means, and allows the jury to use “Bayes's rule merely ... as a heuristic device, displaying the force of the evidence across a wide range of prior probabilities.” Kaye, DNA Evidence, supra, at 167. And this approach has been used in some courts, especially before DNA testing became as refined as it is today. See State v. Spann, 130 N.J. 484, 617 A.2d 247, 264–65 (1993); Plemel v. Walter, 303 Or. 262, 735 P.2d 1209, 1219 (1987).

But the court was not sufficiently charmed to insist on the use of variable prior odds:

We need not decide today whether such an approach is required. We note it only as one possible solution to the problem of the 50% prior probability. Whether presenting a spectrum is definitively a better method than simply assuming a 50% prior probability is a question better left, in the first instance, to a trial court presented with evidence to evaluate whether it better fits under Daubert and KRE 702. And it is likely that such an examination will be unnecessary, as even in Butcher, we noted that the use of a 50% prior probability could be disregarded by the jury and that it could “be weakened on cross and in argument.” 96 S.W.3d at 8 . . . . And defendants are free to offer their own expert witness critical of the 50% prior probability, as happened in this case.

Inviting a debate before a jury over Laplace's principle of insufficient reason and assertions of "neutrality," however, is less than ideal. Experts should avoid these dubious rationales in favor of

what was used in this case. [T]he Commonwealth's expert testified as to the effect of several lesser prior probabilities, including 1%, on the resulting probability of paternity. In each instance, the probability of paternity remained above 99.99%. Thus, the jury could see the effect of different prior probabilities on the resulting probability of paternity. ... [¶] As Professor Kaye noted in 1989, as genetic testing becomes "more refined ... the controversy over [probability of paternity] will wither." . . . This prophesy has not completely born out, as questions are still being raised more than 25 years later. But as testing improves, we are convinced those questions are becoming of little consequence.

Notes

1. Colin Aitken, Paul Roberts, & Graham Jackson, Communicating and Interpreting Statistical Evidence in the Administration of Criminal Justice: Practitioner Guide No. 1, Fundamentals of Probability and Statistical Evidence in Criminal Proceedings 35–36 (Royal Statistical Society 2010); Roberto Puch–Solis, Paul Robert, Susan Pope & Colin Aitken, Practitioner Guide No. 2, Assessing the Probative Value of DNA Evidence (2012); Graham Jackson, Colin Aitken, & Paul Roberts, Communicating and Interpreting Statistical Evidence in the Administration of Criminal Justice: Practitioner Guide No. 4, Case Assessment and Interpretation of Expert Evidence 37 (2015).
2. David H. Kaye, David E. Bernstein & Jennifer L. Mnookin. The New Wigmore: A Treatise on Evidence: Expert Evidence §14.3.2(c) (2d ed. 2011).
3. Michael I. Meyerson & William Meyerson, Significant Statistics: The Unwitting Policy Making of Mathematically Ignorant Judges, 37 Pepp. L.Rev. 771 (2010).

District of Columbia Court of Appeals Delivers Coup de Grâce to "Unqualified" Pattern-matching Testimony

Earlier this year, the highest court for the District of Columbia indicated that it was not disposed to testimony that “that when a bullet is fired from a particular gun, the gun leaves ‘unique’ identifying marks, 'similar to a fingerprint, basically.'" See Traditional Forensic Pattern-matching Testimony in Williams v. United States, June 18, 2016. Forensic Sci., Stat. & L., http://for-sci-law.blogspot.com/2016/06/traditional-forensic-pattern-matching.html (discussing Williams v. United States, 130 A.3d 343 (D.C. 2016)).

Last month, in Gardner v. United States, 140 A.3d 1172 (D.C. 2016), the court declared that "in this jurisdiction a firearms and toolmark expert may not give an unqualified opinion, or testify with absolute or 100% certainty, that based on ballistics pattern comparison matching a fatal shot was fired from one firearm, to the exclusion of all other firearms."

The defendant, Eric Gardner, was on trial (for a second time) for shooting Andrew Kamara, a taxicab driver. Part of the case against him consisted of expert testimony about bullet cartridges associated with the shooting. Defense counsel wanted the trial court to rule that "what is appropriate is for the expert to testify specifically in this case that the bullet that was recovered from the decedent is consistent with ... one of the pistols that he was given to examine but not state that it was ... [with] any scientific certainty." The trial court replied that he would let the expert "state his conclusions—his reasonable conclusions and you can impeach him up and down, if you want."

And so the government's expert, Lyndon Watkins, "stated that the silver gun was the murder weapon." Furthermore, he

confirmed his unqualified opinion on cross-examination and redirect examination. From his analysis, Mr. Watkins testified unequivocally that in his opinion, the silver gun fired the killing shot, reiterating that conclusion on cross examination when defense counsel stated, "I believe your ... expert opinion was the bullet recovered from Mr. Kamara . . . was consistent with having been fired from the silver pistol; is that correct?" Mr. Watkins responded, "It was fired from the pistol, yes sir." On redirect examination, . . . "It was identified as having been fired from Government Exhibit 71."

The Court of Appeals noted that despite the long history of judicial acceptance of bullet-matching testimony, "[b]eginning around 2008, however, questions about pattern matching generally, and bullet pattern matching specifically, surfaced in the scientific community." Although it cited only law review articles for this assessment, it then pointed to reports of the National Research Council and the fact that "some jurisdictions began to limit the scope of a ballistics expert's testimony."

After noting that the issue had not been resolved in Williams and an earlier case on the subject, the court announced that

[W]e now hold that the trial court erred by allowing Mr. Watkins to give an unqualified opinion about the source of the bullet that killed Mr. Kamara. We further hold that in this jurisdiction a firearms and toolmark expert may not give an unqualified opinion, or testify with absolute or 100% certainty, that based on ballistics pattern comparison matching a fatal shot was fired from one firearm, to the exclusion of all other firearms.

Apparently, the government did not directly defend its prosecutor’s use of "that’s the gun" testimony, but contended that "any possible error in the admission of Watkins' testimony without 'qualification' was harmless."

Where this leaves the law of the District of Columbia is unclear. Apparently, error can arise short of the tag phrase "to the exclusion of all other guns in the world," but what "qualification" of the testimony that "This is the gun!" is required? Defense counsel maintained "that the error in admitting Mr. Watkins' unqualified opinion was not harmless because . . . ‘the difference between whether the silver gun was definitely the murder weapon or whether it was simply believed by the ballistician to be the murder weapon may well have affected the jury's deliberations.’" But it hardly seems satisfactory to draw the line between the statement of an expert toolmark examiner that (1) "This is the gun that fired the bullet" and (2) “"his is the gun that, in my opinion as an expert trained and experienced in these matters, fired the bullet."

In earlier cases, the government represented that its policy was to permit testimony that to "a reasonable scientific certainty," this is the gun. That is a "qualification," I suppose, but it is no better than the "unqualified" one in resolving "questions about pattern matching . . . in the scientific community."

Of course, the beauty of the common law is that courts need not (and cannot) definitively resolve the myriad of factual patterns not yet presented, but the absence of any real explanation in Gardner of why a positive identification of a gun from expended bullets is unacceptable means that the opinion leaves a wide range of "qualified" testimony up in the air.

Traditional forensic pattern-matching testimony in Williams v. United States

The opinion of the District of Columbia's highest court in Williams v. United States, 130 A.3d 343 (D.C. 2016), is straightforward, but it is worth noting a modern example of traditional forensic pattern-matching testimony.

The case

In 2010, the bullet-riddled body of Min Soo Kang was discovered on the side of a road in Southeast D.C. Police retrieved three bullets that had penetrated the driver’s seat and fingerprints from his Cadillac Escalade in Northeast D.C. A trawl of the national Automated Fingerprint Identification System (AFIS) led police to suspect Marlon Williams. Pursuant to a search warrant, police took a High Point brand firearm from the bedroom of his apartment.

Bullets tested fired from the gun had impression from passing through the barrel that matched the ones on the bullets the car. The criminalistics evidence and “the testimony of an individual to whom Mr. Williams had made incriminating statements while they were in the courthouse cellblock formed the bulk of the government's case.” Id. at 346. The case was persuasive—the jury convicted Williams of first-degree murder and other crimes.

The firearms evidence

The firearms and toolmark examiner, Luciano Morales, testified on direct examination that when a bullet is fired from a particular gun, the gun leaves “unique” identifying marks, “similar to a fingerprint, basically.” He then testified that he had compared the markings on the bullets recovered from Mr. Kang's car with the markings on the bullets test-fired from the gun recovered from Mr. Williams's apartment (manufactured by High Point and admitted as Exhibit No. 58), and he had concluded that the bullets were fired by the same gun. On redirect, when the prosecutor asked whether there was “any doubt in [his] mind” that the bullets recovered from Mr. Kang's Escalade were fired from the gun found in Mr. Williams's room, the examiner responded, “[n]o sir.” He elaborated that “[t]hese three bullets were identified as being fired out of Exhibit No. 58. And it doesn't matter how many firearms High Point made. Those markings are unique to that gun and that gun only.” The prosecutor then asked the examiner whether, “judging from the markings that you find in 58, it's your conclusion that those three bullets were fired from 58?” The examiner was unequivocal: “Item Number 58 fired these three bullets.”

Id. The Court of Appeals held that the admission of this testimony was not error—because defense counsel did not object to it at the trial. Of course, the court recognized a standard exception to the need for a contemporaneous objection—the "plain error" rule. However, under this exception, “it is not enough for an appellant to demonstrate error; the appellant must also show that the error is ... ‘so egregious and obvious as to make the trial judge and prosecutor derelict in permitting it, despite the defendant's failure to object.’” Id. at 347.

Some readers might think that resorting to hyperbole could amount to a dereliction of a prosecutor's duty not to overstate its case and of an expert's obligation to stay within the bounds of what the expert discipline validly can claim to know. Indeed, the government conceded on appeal “that, at Mr. Williams's trial, it violated its policy ‘to only elicit firearms examiners' opinions to a reasonable degree of scientific certainty.’” Id. at 348. But the court balked at the idea that the trial judge should have demanded the phrase “reasonable scientific certainty.” It noted that

[W]e question whether this court would want to endorse a policy of “only elicit[ing] firearms examiners' opinions to a reasonable degree of scientific certainty,” in light of criticism that firearms examination does not involve any “scientific” measure of certainty. See National Research Council, Committee on Identifying the Needs of the Forensic Sciences Community, Strengthening Forensic Science in the United States: A Path Forward 154–55 (2009); National Research Council, Committee to Assess the Feasibility, Accuracy, and Technical Capability of a National Ballistics Database, Ballistic Imaging 3, 81–82 (2008).

Id. at 348 n.11.

The "reasonable scientific certainty" mantra definitely has its problems, 1/ but the better argument was that the dereliction of duty evident in Williams was not the kind of error that could satisfy the plain-error doctrine: “The government's internal policy does not constitute binding law—let alone a ‘clear’ or ‘obvious’ rule—that a trial court should be presumed to know.” Id. at 348–49 (notes omitted). “[O]nly when an error is ‘clear under current law’ can it be “plain.” Id. at 347.

But what is "current law"? Does it take a previous opinion in the same jurisdiction to make a proposition "clear under current law," or can the result clearly be immanent the fabric of such opinions, or even in those of other jurisdictions?

Although not without ambiguity, the opinion seems to accept the latter, more expansive understanding of "current law." First, it reads its previous opinions as too tentative or reserved to establish a legal rule precluding testimony of 100% confidence.

The closest this court has come to addressing this issue was in (Ricardo) Jones v. United States, 27 A.3d 1130 (D.C.2011). In that case the defense argued inter alia that toolmark and firearms examiners could not “stat[e] their conclusions with ‘absolute certainty excluding all other possible firearms.’ ” Id. at 1138. In response, the government assured this court, both in its appellate brief and at oral argument, that it was the government's policy not to present such testimony. “In light of the government's representation,” this court “assume[d], without deciding, that such experts should not be permitted to testify that they are 100% certain of a match, to the exclusion of all other firearms.” Id. at 1139. The court then determined that any such error was harmless. Id. Jones did not plainly bar the toolmark examiner in this case from testifying as he did and does not provide a foundation for a determination of plain error.

Id. at 348. Thus, “[t]here [was] no precedent in this jurisdiction that limits a toolmark and firearms examiner's testimony about the certainty of his pattern-matching conclusions.” Id. at 347-48. Although the court was willing to consider "the weight of non-binding authority outside this jurisdiction," it could locate very few appellate opinions condemning expressions of absolute certainty. Id. at 348. Hence, Williams’ objection, raised for the first time on appeal, came too late.

The future

If Williams had objected at trial, would it have made any difference to the outcome? The established view is that the expert can express total certainty in a “unique” identification. But if the expression of 100% confidence in Williams is legally (or professionally) unpalatable (as a concurring opinion by the author of the panel opinion suggested), how should a firearms examiner testify? The legal contrivance of “reasonable scientific certainty” is not a viable alternative. 1/ Statements about “likelihoods”—the probabilities of the matching patterns being seen (1) when the sample gun fires the bullet, and (2) when different guns fire the bullet—are widely recommended by students of forensic inference. Subjectively assessed likelihoods are appealing if they are frankly and transparently explained and the expertise underlying them has been demonstrated to exist. In the longer term, will efforts to achieve objective measurements and to use machine learning or other statistical tools to quantify the likelihoods for those measurements 2/ lead to a better, or at least a complementary approach?

Notes

1. See Is "Reasonable Scientific Certainty" Unreasonable?, Forensic Sci., Stat. & L., Feb. 26, 2016, http://for-sci-law.blogspot.com/2016/02/is-reasonable-scientific-certainty.html .
2. John Song, Xiaoping Liu. A Review of NIST Projects in Surface and Topography Metrology for Firearm Evidence Identification in Forensic Science, 1 J. Sci. & Industrial Metrology 1 (2016); T.V. Vorburger et al., Topography Measurements and Applications in Ballistics and Tool Mark Identifications, Surface Topography: Metrology and Properties, Dec. 17, 2015, http://iopscience.iop.org/article/10.1088/2051-672X/4/1/013002

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Proposed Uniform Language for Forensic Serology

The second document listed in the announcement of "Uniform Language" (UL) documents for forensic science is the “Proposed Uniform Language for Testimony and Reports For the Forensic Examination of Serology.” It pertains to the detection of sera, not the examination of serology, but you get the idea. The task is one of classification: Is this a blood stain? Is it a semen stain?

The approved statements (with emphasis added) are

• blood or semen may be present on an item of evidence [using "the appropriate presumptive testing procedure(s)"]
• blood or semen was identified on an item of evidence [using "the appropriate confirmatory procedure"].

In terms of accuracy, the difference between "presumptive" and "confirmatory" is that presumptive tests are less specific — more substances will be test positive with a presumptive test. A supporting document explains that confirmatory testing can include either a highly specific test — or just a second, presumptive test, if based on “different chemical principles” and “not subject to the same limitations.” (Or maybe a second and a third screening test are required; it is hard to tell from the document.)

Although the examiner is not allowed to say that a positive result is "infallible," that is only because an examiner might goof in following a protocol that is perfectly discriminating. The confirmatory procedure “identif[ies] blood or semen to the exclusion of all other substances.” (P. 5.)

The documents display little sympathy for probabilistic thinking. Apparently, examiners may not give an error probability for an "identification," for "the analytical processes and procedures ... do not have a calculable error rate due to the unpredictability of human error." This observation motivates the proscription of statements of a "zero error rate," but by this logic, the probability of commercial pilot error, of a mishap in a nuclear power plant, or of medication errors in ICUs could not be calculated.

Aside from this allegedly unquantifiable risk of strictly "human error," identifications are subject to no uncertainty:

• when crystals are formed under the proper testing conditions, there is no doubt of the nature of the stain tested ... no false positives.
• [if] the Takayama test ... is positive, blood is conclusively present.

Despite this certitude in the supporting document, the UL document itself cautions that

An examiner may not state or imply that a level of numerical certainty is calculated to support the identification of blood or semen.

The claims of "no doubt" and "conclusively" positive results can be reconciled with the prohibition on what can be said or reported; after all, that the number corresponding to certainty is not "calculated" is literally true. But if the examiner can report that (1) the testing conditions were proper, (2) a positive result means that "blood is conclusively present," then why cannot the examiner state that (3) "my tests demonstrate that the stain surely contains blood — the probability is 1 — unless I have done something wrong"? An argument might be that expressing conditional certainty as the number 1 is not necessary and might unduly impress readers of reports or legal factfinders.

Closely related postings

• Proposed Uniform Language for Forensic Toxicology, June 6, 2016, http://for-sci-law.blogspot.com/2016/06/proposed-uniform-language-for-forensic.html
• The Department of Justice's "Proposed Uniform Language for Testimony and Reports," June 4, 2016, http://for-sci-law.blogspot.com/2016/06/the-department-of-justices-proposed.html