RENDERED: FEBRUARY 18, 2016 

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ALFRED IVEY JR. 

2014-SC-000345-MR oxpre 1N•C 

APPELLA 

I .412,kikt NAStiz I 1 

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ON APPEAL FROM HARDIN CIRCUIT COURT 

V. HONORABLE KELLY M. EASTON, JUDGE 

NO. 12-CR-00382 

COMMONWEALTH OF KENTUCKY APPELLEE 

OPINION OF THE COURT BY JUSTICE NOBLE 

AFFIRMING 

The Appellant, Alfred Ivey, Jr., was convicted of two counts of rape of a 

minor. The crime resulted in a child, and a DNA paternity test was used as 

evidence against Ivey. On appeal, he alleges two errors related to expert 

testimony about the DNA evidence of his paternity: (1) that the trial court erred 

in allowing the expert to testify about the probability of paternity based on an 

improper statistical method; and (2) that the expert invaded the province of the 

jury by instructing it on how to consider the evidence. Finding no error, we 

affirm. 

I. Background 

Ivey was in a long-term sexual relationship with his half-sister, Novina 

Peel.' They lived together in Hardin County, Kentucky, from 1994 to 2007. Peel 

had a daughter, Karen, 2from a previous relationship. 

1They shared the same father, Alfred Ivey, Sr. 

2We refer to the daughter with a pseudonym to protect her identity. 
In 2003, when Karen was thirteen years old, she became pregnant. When 

Peel asked her who had fathered the child, Karen replied that she did not 

know. Peel speculated that Karen had been raped at a school dance, a story 

that Karen went along with. Karen gave birth to a daughter the following year, 

and Peel raised the child as her own. 

By 2010, Karen had become an adult, moved to Oregon, and gotten 

married. At that time, she revealed that Ivey was the father of her child. She 

claimed that when she was between nine and eleven, Ivey had forced her to 

have sexual intercourse on multiple occasions, and that when she got old 

enough to understand ' that it was wrong, Ivey had threatened her and her 

mother. She claimed that he raped her again when she was thirteen, and that 

she got pregnant at that point. 

Not knowing what to do, Peel contacted the child-support office in 

Garrard County. The office obtained a court order for paternity testing, which 

showed that Ivey was the father. Peel also contacted the police in Hardin 

County about criminal proceedings. Police obtained a search warrant for a 

second DNA sample. An expert later testified that paternity testing of this 

sample showed a 99.9999% probability of Ivey being the father of Karen's 

child. 3 

Ivey was indicted on two counts of first-degree rape. Before trial, his 

counsel moved for an evidentiary hearing on the reliability of the method used 

to calculate the 99.9999% probability of paternity and to exclude that evidence 

from the trial. The court held a hearing and denied the motion, and the DNA 

3This figure is based on certain assumptions and is discussed further below. 

2 
evidence was admitted at trial. Karen did not wish to testify, but she did so 

nevertheless, describing the abuse she suffered from Ivey. 

The jury convicted Ivey on both counts, and he was sentenced to life in 

prison. He appeals to this Court as a matter of right. Ky. Const. § 110(2)(b). 

II. Analysis 

Ivey raises two issues on appeal. First, he claims that the trial court 

erred in not holding an evidentiary hearing on one of the statistical methods 

used in evaluating the DNA test and in admitting the testimony about the 

method because it was unreliable. Second, he claims that the Commonwealth's 

DNA expert improperly instructed the jury on how to weigh the evidence. 

A. The statistical DNA evidence was properly admitted. 

As to the DNA evidence, Ivey's complaint is narrowly focused. He does 

not challenge the DNA test itself, nor does he challenge all of the statistical 

conclusions that can be drawn from that test. Instead, he complains about the 

use of a 50% "prior probability" of paternity in calculating the final probability 

of paternity, which is the last of three conclusions that can be drawn from the 

DNA test. This Court previously upheld the use of that 50% figure in Butcher v. 

Commonwealth, 96 S.W.3d 3, 7 (Ky. 2002), concluding that it did not violate 

the presumption of innocence. Ivey claims that he was nevertheless entitled to 

a hearing under Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579 

(1993), because no scientific method is forever beyond challenge, and that the 

method used by the expert was improper and unreliable. 

The trial court held a hearing on Ivey's motion at which the reliability of 

the probability-of-paternity calculation was questioned. In support of his 

3 
position, 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."' Id. at 128. 

The trial court concluded that the evidence would be admissible. The 

court specifically concluded that Butcher had decided the question of the use of 

the 50% prior probability, and declined to hold a "new" Daubert hearing 

because the use of the 50% figure was a reliable method. Instead, the court 

concluded, Ivey was free to challenge the use of the figure on crossexamination and inquire about the .expert's statistical assumptions. 

DNA paternity tests and the various statistical methods used to analyze 

the results of those tests have consistently been upheld as sufficiently reliable 

to be admitted under KRE 702. Indeed, they are considered so reliable that 

they no longer require a pre-trial Daubert hearing before they may be admitted. 

See Fugate v. Commonwealth, 993 S.W.2d 931, 937 (Ky. 1999) (concluding that 

reliability of DNA testing "has been sufficiently established as to no longer 

require a Daubert hearing"); Goodyear Tire and Rubber Co. v. Thompson, 11 

S.W.3d 575, 579 (Ky. 2000) ("[A] trial court may take judicial notice of the 

reliability of these methods of analysis."). 
Ivey, of course, is correct that even these well-established methods "are 

not forevermore beyond the reach of the application of Daubert," Goodyear Tire, 

11 S.W.3d at 579, and that "a party still may challenge the reliability of ... 

methods of DNA analysis," id. But there are limits to what a defendant may 

demand. In essence, Ivey sought a "reverse" Daubert hearing on the 50% figure 

at which he would "bear[] the burden of proving that the methods of analysis 

are not, or are no longer, reliable under KRE 702." Id. But the problem with 

Ivey's claim is that he was given a hearing. As noted above, he presented 

evidence, in the form of the statistics article, but the trial court was not 

convinced that it undermined the reliability of the method. Though the court 

stated that no "new" Daubert hearing was needed, the hearing that was held 

was, in fact, the reverse Daubert hearing that Ivey was entitled to. 

Thus, to the extent that Ivey's complaint is that he did not receive a 

Daubert hearing, there was no error. He received all that he was entitled to: a 

hearing on his motion at which he presented and argued the one item of 

evidence he discussed in that motion. He was not denied the opportunity to 

present further proof; he simply failed to do so. (In fact, he did present further 

proof at trial, in the form of his own expert.) 

Ivey's real complaint is that the trial court erred in concluding that the 

statistical method used to calculate what is called a probability of paternity is 

reliable in the face of the proof he offered. In essence, he now complains that 

by presenting the statistics article, he satisfied the burden laid out in Goodyear 

Tire of proving the unreliability of this method, and that the trial court erred in 

admitting it. This Court concludes that he has not met his burden. 

5 
Ivey's claim, however, cannot be understood without some context, if 

only because the statistical method at issue is not common knowledge. It is 

thus necessary to lay out the basics of how paternity testing works, at least in 

a summary fashion. 

Like other types of DNA testing, paternity testing first requires that a set 

of DNA profiles be developed for comparison. Paternity testing compares three 

profiles, one of the child, one of the mother, and one of the putative father. This 

is the standard type of DNA profiling that is commonly discussed in other 

cases. But as in every case, DNA profiles do not speak for themselves; they 

must instead be compared to each other. 

When it comes to the comparison, paternity testing is not the same as 

other kinds of DNA testing, such as that typically used for a criminal case in 

which a biological sample is compared to a defendant's to see if there is a 

match. This is because a child receives half its DNA from each parent. Thus, 

there will never be a complete match between the two DNA profiles, that of 

(putative) father and child. Instead, paternity testing looks at whether there is 

shared or common DNA. Using this comparison, an examiner first determines 

whether the putative father is excluded as a possible contributor to the child. If 

not, the examiner can then calculate a "paternity index, and [a] probability of 

paternity." Butcher, 96 S.W.3d at 6. 4 

4 Butcher also referred to a "probability of exclusion," 96 S.W.3d at 6, which is a 

different concept from excluding the putative father. The probability of exclusion looks 

at the percentage of the male population that can be excluded from possibly being the 

father. Michael I. Meyerson & William Meyerson, Significant Statistics: The Unwitting 

Policy Making of Mathematically Ignorant Judges, 37 Pepp. L. Rev. 771, 781 (2010). If 

the defendant is included in the relevant population, the probability of exclusion is 

probative of paternity, in that it reduces the size of the population that could have 

6 
The first step, determining exclusion, looks at whether an alleged father's 

DNA could have contributed at all to the child's DNA. In other words, at its 

most basic, a DNA paternity test has two possible outcomes: the putative father 

is excluded, meaning he is shown not to be the father, or he is "included," 

meaning he is possibly the father. Butcher, 96 S.W.3d at 6; Griffith v. State, 976 

S.W.2d 241, 242-43 (Tex. App. 1998). To conduct the exclusionary 

determination, a DNA examiner compares locations on the child's and putative 

father's DNA—frequently called loci. If the putative father is "included," then 

his DNA necessarily matches portions of the child's DNA. In Butcher, the 

examiner compared eight different genetic markers. In this case, fifteen loci 

were compared. Ivey was found not to be excluded because his DNA matched 

portions of the child's DNA at all fifteen loci. 

The next step, if the putative father is not excluded, is to calculate the 

paternity index. 5Rather than a physical test, this process employs "a statistical 

evaluation to say how likely that match that we see is." Butcher, 96 S.W.3d at 

6. As the Commonwealth's expert in this case described it, the statistical 

examination is "to assess that potential relationship that is being supported by 

the DNA" and to "give a significance to how strong of a potential relationship 

fathered the child. But this calculation is different from excluding the defendant. The 

defendant is either excluded or not, to the extent that the DNA test itself is accurate. 

The DNA expert in this case did not testify as to the probability of exclusion. 

5As some commentators have noted, this value is actually the combined 

paternity index, though it is often simply called the paternity index. See Meyerson 86 

Meyerson, supra, at 782 n.62. A paternity index is calculated for each loci tested, and 

those indexes are multiplied together to arrive at the combined paternity index, which 

is the figure admitted into evidence. Id. 

7 
could that be." The result is "expressed numerically as a paternity index." 

Butcher, 96 S.W.3d at 6. We have described the paternity index as follows: 

The paternity index is a value reflecting the likelihood that a tested 

man is the father of the child as opposed to an untested man of the 

same race. It is expressed as a number. If a paternity index can be 

assigned to a man, it means that he is that many more times likely 

to be the father than any other randomly selected male of his race. 

Id. at 6-7 (quoting Griffith, 976 S.W.2d at 243). 

This description, however, is not completely accurate. 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). 6That would be the 

"probability of paternity," id., which is a different calculation, discussed below. 

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." Id. Thus, the paternity index is probative of paternity, 

but it does not actually tell us the probability the person tested is the father. 

6Professor Kaye's works are cited throughout because he has written frequently 

on the subject, perhaps more frequently than any other commentator, and is an expert 

in the field. 

8 
For example, in Butcher, the paternity index was 388/1 (or simply 388). 

We said that this meant the defendant was "388 times more likely to be the 

father of the child than a randomly selected male of the same race." 96 S.W.3d 

at 7. Again, this is not, strictly speaking, completely accurate. See 1 McCormick 

on Evidence § 211 n.18 (7th ed. 2013) (noting that Butcher's formulation 

commits "the transposition fallacy" and is a "misinterpretation"); see also id. 

§ 210 ("A juror who hears that only one out of every five, or for that matter, one 

out of every 10,000 persons, possesses the traits that characterize the true 

offender, may be tempted to subtract this statistic from one to arrive at the 

incorrect conclusion that the remainder is the probability that the defendant is 

guilty. In the statistical literature, this reasoning is known as the transposition 

fallacy."). Instead, a paternity index of 388 "means that it is [388] times more 

likely that a union of [the defendant] and [the mother] would produce a child 

with the observed set of markers than would a union of [the mother] and a set 

of alleles picked at random from men of [the defendant's] race." Kaye, Plemel as 

a Primer, supra, at 874. Or to apply a simpler description by Professor Kaye, to 

Butcher's facts: "Men of [the defendant's] phenotype, when crossed with the 

mother, would produce offspring with the child's phenotype [388] times as 

frequently as would randomly selected men." Kaye, The Probability of an 

Ultimate Issue, supra, at 91. 

In Ivey's case, the paternity index was 11,900,000. (This likelihood ratio 

is substantially higher than that in Butcher, at least in part, because many 

more loci were compared.) Ivey's index is therefore that much more probative of 

paternity than the index in Butcher. 

9 
The third step is to calculate a probability of paternity, which is usually 

expressed as a percentage. This calculation uses Bayes' theorem,? Butcher, 96 

S.W.3d at 7, which "show[s] the effect of a new item of evidence on a previously 

established probability," 1 McCormick on Evidence § 211 (7th ed. 2013). "On its 

most basic level, the formula is nothing more than a mathematical way of 

representing how we incorporate new information into our reasoning." Michael 

I. Meyerson 86 William Meyerson, Significant Statistics: The Unwitting Policy 

Making of Mathematically Ignorant Judges, 37 Pepp. L. Rev. 771, 783 (2010). 

The new evidence in paternity testing is the result of the DNA test, specifically 

the paternity index. The established probability (of paternity), often referred to 

as a "prior probability," depends on other evidence, such as "access to the 

mother, fertility, and date of conception." Butcher, 96 S.W.3d at 7; see also 

Meyerson 86 Meyerson, supra, at 785 (noting that the other evidence can 

include "whether [the defendant] had sexual relations with the mother and ... 

how many other men she had sexual relationships with, as well as the timing 

of each sexual encounter"). Applying Bayes' theorem to the prior probability 

results in what is called a posterior probability; in the context of paternity 

testing, the posterior probability is simply referred to as the probability of 

paternity. 

7When applied to paternity testing, assuming a paternity index has been 

calculated, the formula is: 

Paternity Index x Prior Probability 

( Paternity Index x Prior Probability) + (1 — Prior Probability) 

Butcher, 96 S.W.3d at 7. This gives a decimal that is the probability of paternity and 

which may then be expressed as a percentage. 

10 
Because Bayes' theorem is a ratio of probabilities, a lower prior 

probability will necessarily result in a lower final probability of paternity than 

would a higher prior probability. The prior probability can thus have a 

significant effect on the probability of paternity. Ideally, the other, non-DNA 

evidence in the case could be evaluated to assess a prior probability, which 

could then be compared with the DNA test to arrive at a final number. 

In theory, the prior probability could vary dramatically depending on the 

proof in a case. The prior probability can be any number between zero and one 

(that is, more than 0% and less than 100%). 8For example, very strong, but not 

unassailable, proof of an alibi should result in a lower prior probability than 

proof showing that the defendant was present but simply denies having had 

sex with the victim. Similarly, evidence that a defendant had had a 

vasectomy—an effective but imperfect method of sterilization—would also 

result in a very low prior probability that he was the father. 

"In the context of criminal cases, however, those using this formula to 

determine paternity 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." Butcher, 96 S.W.3d at 

7. This again is somewhat of a misstatement. Rather than showing a 50% 

chance that the alleged putative father had intercourse with the mother, the 

50% prior probability indicates a 50% probability, before the DNA test, that the 

alleged father is the biological father. This distinction is crucial because having 

8Zero could never be used, because that would mean that we are certain that 

the defendant is not the father. Nor can one (or 100%) be used, as that would mean we 

are certain that he is the father. 

11 
intercourse does not guarantee a pregnancy, a fact acknowledged elsewhere in 

Butcher. In Ivey's case, using the 50% prior probability, his probability of 

paternity was calculated to be 99.9999%. 

In Butcher, this Court specifically approved of the use of a 50% prior 

probability, over two dissents. The defendant in that case had claimed that use 

of that figure violated the presumption of innocence. But this Court instead 

concluded: "The 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." Id. 

at 8 (quoting Griffith, 976 S.W.2d at 247). The Court also noted: "The jury is 

free to disregard it. It can be weakened on cross and in argument." Id. (quoting 

Griffith, 976 S.W.2d at 247). 

Butcher, however, was not directly about whether the use of a 50% prior 

probability satisfies the reliability requirement of Daubert. In fact, Butcher 

mentions neither Daubert nor KRE 702. Nor did Butcher address the scholarly 

criticism now raised by Ivey or other criticism that has turned up in the Court's 

legal research. 9Ivey claims now that the use of the 50% prior probability fails 

the requirement of reliability, at least in light of the statistics article he 

submitted to the trial court. Because Butcher did not directly address this 

question, we cannot rely on that decision as dispositive. 

9The Court that decided Butcher appears to have been at least aware of some of 

the criticism, however. It cited, for example, an article criticizing the use of the 50% 

prior probability, albeit for a different proposition. See Butcher, '96 S.W.3d at 6 (citing 

Kaye, The Probability of an Ultimate Issue, supra). 

12 
The statistics article Ivey presented claims that paternity testing "can 

lead to incorrect conclusions," where there is a problem with the "statistical 

assumptions," specifically in "assuming equal prior (pre-test) probabilities for 

an event in the face of ignorance concerning the actual probabilities." Chiodo et 

al., supra, at 126. In other words, the authors claim that the use of the 50% 

prior probability is a logical error. 

But the "error," to the extent it is one, appears to matter only under 

unrealistic conditions. The article uses as an example paternity testing based 

on a single genetic marker occurring in only 1% of the population. Id. at 127. 

With a 50% prior probability, the probability of paternity in such 

circumstances is 99.01%. Id. But the article points out that lower prior 

probabilities result in significantly lower probabilities of paternity under the 

hypothetical scenario. For example, if the prior probability was 0.001 (or 0.1%), 

which is a fairly low prior probability, the probability of paternity would be only 

.091, or 9.1%. Id. Or, to employ an example more germane to this case, as will 

become apparent shortly, if the prior probability was .01, or 1%, then the 

resulting probability of paternity would be only 50.25%. 10 

10This figure can be arrived at by first calculating the paternity index resulting 

from the hypothetical in the article, since that figure is not given. (This is because the 

authors used a slightly different formulation of Bayes' theorem.) As noted above, the 

probability-of-paternity calculation shows the relationship between three numbers: the 

paternity index, the prior probability, and the resulting probability of paternity. 

Because we know two of these numbers used in the article, the prior probability and 

the probability of paternity, we can calculate the paternity index through a simple 

application of algebra. The formula is 

P1 x PP 

(PI x PP) + (1 — PP) = PoP 

where PI is the paternity index, PP is the prior probability, and PoP is the probability of 

paternity. In the example in the article, the PP is .5 (or 50%), and the resulting PoP is 

.9901. With those figures plugged into the formula, we have 

13 
But in 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%. 

Presumably, this is because the genetic testing used in Ivey's case is 

simply more extensive than what was used in Butcher. In Butcher, only eight 

loci were compared, whereas fifteen were tested in this case. More importantly, 

the number of loci tested is significantly higher than the number used in the 

hypothetical example in the Chiodo article, which again looked at but one 

genetic marker. 

P1 x .5 

(P1 x .5) + (1 — .5) — .9901 

Simplified, it is 

.5P1 

= .9901 .5PI + .5 

Solving algebraically for PI, we get 100.01. That number is likely an approximation, 

given that the PoP was rounded to four digits, but it is close enough for our present 

purposes. 

With the paternity index, 100.01, we can easily calculate other probabilities of 

paternity based on other prior probabilities, again with the same formula. A prior 

probability of .01 (or 1%) results in a probability of paternity of .5025, or 50.25%. 

14 
The simple fact is that the hypothetical used by the article is unrealistic. 

Modern genetic testing is not going to rely on a single genetic marker—for 

exactly the reasons argued in the article. Ivey's evidence, again consisting of 

but a single statistics article, was insufficient to require the trial court to 

question the reliability of the statistical techniques used in this case. Paternity 

testing of this sort is regularly used in the courts of this Commonwealth and 

across the United States. 

Interestingly, the example used in the Chiodo article appears to have 

been chosen very intentionally. As noted in footnote 10 above, the paternity 

index describing the scenario in the article's hypothetical appears to be 

approximately 100.01. The Uniform Parentage Act creates a rebuttable 

presumption of paternity in cases where "the man has at least a 99 percent 

probability of paternity, using a prior probability of 0.50, as calculated by using 

the combined paternity index obtained in the testing," and there is "a combined 

paternity index of at least 100 to 1." Uniform Parentage Act § 505(a) (2002); see 

also KRS 406.111 (applying same probability of paternity and paternity index 

requirements but having no requirement as to prior probability). The example 

used in the article barely meets this threshold. To that extent, it ably 

demonstrates the absurdity of using the 50% prior probability with threshold 

cases, at least if only that number is used to calculate a probability of 

paternity. 

But again, in this case, the paternity index far exceeds the minimum 

threshold. And though the Kentucky presumption statute was not at issue in 

this case, as it was a criminal prosecution, the paternity index was sufficiently 

15 
high, and resulted in such high probabilities of paternity with even very low 

prior probabilities, that Ivey's paternity is all but guaranteed. We cannot say 

■ 

that the method was unreliable in this case, even given the criticism in the 

Chiodo article. 

That, of course, does not mean that use of the 50% prior probability is 

forever beyond a reverse Daubert challenge. 11Most commentators outside the 

blood-testing community, such as statisticians and law professors, have 

objected to the use of a 50% prior probability because the notion that it is 

neutral is demonstrably false. See, e.g., Meyerson 86 Meyerson, supra, at 786-

87 (noting that it cannot be a neutral number because it assumes a 50% 

chance that the defendant is the father); Kaye, The Probability of an Ultimate 

Issue, supra, at 94 (noting the "neutral" argument is "unconvincing" and laying 

out several arguments for why that is the case); 1 McCormick on Evidence § 211 

(7th ed. 2013) (noting that the conception of .5 as neutral "cannot withstand 

examination"); id. § 211 n.26 ("Virtually all commentators outside of the 

paternity testing community concur."). And former members of this Court, 

albeit a minority at the time, have agreed. See Butcher, 96 S.W.3d at 12 

(Cooper, J., concurring); id. (Stumbo, J., dissenting). 

Those critical of using a 50% prior probability have a point. That number 

assumes that there is a prior probability at all that the defendant is the father, 

which may be inescapable since a 0% probability cannot be used. But, more 

11That is the case at least until the General Assembly adopts the 50% prior 

probability by statute, as is in the Uniform Parentage Act. But even then, that 

calculation would only be required in civil paternity suits, not criminal cases where 

proof of paternity would be relevant. 

16 
importantly, that 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." Meyerson 86 

Meyerson, supra, at 788 n.96 (quoting Jack P. Abbott et al., Joint AMA-ABA 

Guidelines: Present Status of Serologic Testing in Problems of Disputed 

Parentage, 10 Fam. L.Q. 247, 262 (1976)). 

Perhaps a hypothetical, suggested by Professor Kaye, best illustrates why 

a 50% prior probability is far from neutral. See Kaye, Plemel as a Primer, supra, 

at 874. Assume a situation where the paternity index is 178. Further assume 

the uncontradicted proof is that a year before the child's conception, the 

defendant had a vasectomy, and that the medical proof shows, beyond 

question, "the odds are one to a million that he could father a child." Id. 

Despite the nearly astronomical pre-DNA test odds against the defendant being 

the father, using the 50% prior probability results in a 99.44% probability of 

paternity. Surely in such a case, it would be absurd to allow an expert to testify 

to a 99.44% probability of paternity, or to affirm a conviction based on such 

evidence. 12Of course, to their credit, it is unlikely that DNA experts would give 

such testimony under those circumstances. But if followed literally, Butcher 

would allow it. 

12The hypothetical is not without some basis in reality. In several instances of 

pre-DNA genetic testing, such as,HLA typing, a sterile man was calculated to have had 

a probability of paternity exceeding 95% and approaching 100%. See, e.g., O'Bannon v. 

Azar, 435 So. 2d 1144 (La. Ct. App. 4th Cir. 1983) (affirming verdict for defendant who 

had 99.91% paternity probability but who previously had a successful vasectomy); 

Cole v. Cole, 74 N.C. App. 247, 328 S.E.2d 446 (1985) (reversing finding of paternity 

based on a 95.98% paternity probability where it was undisputed that the alleged 

father previously had a successful vasectomy). 

17 
The problem is that the paternity index measures only the strength of the 

evidence, in this case, the DNA test itself Id. But DNA testing, at this point, is 

simply not 100% accurate, especially in the context of paternity, nor is it likely 

ever to be since we do not have DNA profiles of everyone on the planet. And the 

paternity index "tells us nothing about the prior odds." Id. It "reveals how far 

we can move from a given starting point, but it does nothing to reassure us 

that we are starting at the right point." Id. Using the 50% prior probability then 

"treats the genetic findings as the very first datum, to be evaluated before any 

other evidence is available." Id. at 880. 

If it is the first evidence to be considered, "the fairest thing the laboratory 

can do is to say that as far as it can tell, considering only the untested vials of 

blood, the accused man is no more likely than any other male in the relevant 

population to be the father." Id. But that means that "if there are more than 

two men biologically capable of fathering the child, then the prior probability 

for the defendant is less than .5." Id. And with fairly low paternity indexes, it 

appears that the relevant population would include more than one possible 

father. 

Thus, some commentators have suggested that jurors be presented with 

"a spectrum of prior and posterior probabilities." Id. at 881; see also 1 

McCormick on Evidence § 211 (7th ed. 2013) ("[T]he expert could show the jury 

how the test results would affect not merely a prior probability of one-half, but 

a whole spectrum of prior probabilities."); David H. Kaye, DNA Evidence: 

Probability, Population Genetics, and the Courts, 7 Harv. J.L. 86 Tech. 101, 167 

(1993-1994) (urging that an "expert present[] the jury with a table or graph 

18 
showing how the posterior probability changes as a function of the prior 

probability"). Though this proposed approach has drawn some criticism, see 

Meyerson 85 Meyerson, supra, at 789 (stating that "[t]his proposal, though wellmeaning, 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, 617 A.2d 247, 264-65 (N.J. 1993); Plemel v. 

Walter, 735 P.2d 1209, 1219 (Or. 1987). 

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 (quoting Griffith, 976 S.W.2d at 247). 

And defendants are free to offer their own expert witness critical of the 50% 

prior probability, as happened in this case. 

But we also note the spectrum approach because it is, in essence, what 

was used in this case. As noted above, the Commonwealth's expert testified as 

19 
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. If this is the norm in the testimony of 

paternity experts, then it appears they have anticipated the primary objections 

that Ivey has brought to bear. If there is any prejudice from ever using a 50% 

number, even as a "working hypothesis," that prejudice is likely attenuated by 

spectrum testimony like that given in this case. 

That said, as much as anything, improvements in DNA testing 

techniques have lessened the need for testimony about a spectrum of prior 

probabilities. The example used in the Chioda statistics article, for example, 

used only one genetic marker. One of the cases discussed by Meyerson 86 

Meyerson, State v. Spann, 130 N.J. 484, 617 A.2d 247 (1993), used only two 

genes. Our own case, Butcher, had evidence of but eight loci, which resulted in 

a paternity index of only 388/1. But in this case, the testing was of fifteen loci, 

and the resulting paternity index approached 12 million. And that number, 

when run through Bayes' theorem, consistently results in probabilities of 

paternity over 99.99%, even with very low prior probabilities. 

As Professor Kaye noted in 1989, as genetic testing becomes "more 

refined ... the controversy over [probability of paternity] will wither." Kaye, The 

Probablity of an Ultimate Issue, supra, at 88 n.64. 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. 

20 
In the end, Ivey's complaints do not undermine the reliability of the 

evidence in this case. The evidence, therefore, was properly admissible. Rather 

than going to the admissibility of the evidence, his complaints go to its weight. 

And the jury was presented with ample proof to allow it to determine the proper 

weight to assign to the testimony. 

B. The DNA expert's testimony was not erroneous. 

Ivey next complains that the trial court erred in allowing the 

Commonwealth's expert to "instruct jurors on how to weigh the evidence." 

Specifically, he complains about the expert's testimony about prior 

probabilities other than 50%, as discussed above. 

After the expert testified to the 99.9999% probability of paternity based 

on the 50% prior probability, the Commonwealth asked her whether that 

number took into account "all DNA evidence and non-DNA evidence." The 

expert replied that it did not and reflected only the DNA evidence. The 

Commonwealth then asked what the "other evidence" would be. Ivey objected, 

and the court stated it was a legal issue, presumably referring to what things 

in this case would constitute the evidence. Instead, the court allowed the expert 

to give examples of other types of evidence. She answered: "testimony provided 

by other individuals, any testimony other than what I'm talking about right 

now." 

The Commonwealth then asked the expert whether the probability of 

paternity, the final percentage she had calculated, took into account the other 

evidence. The expert testified that it did not because she did not know what 

that evidence was. Instead, she said, she tried to be neutral, though "ideally" 

21 
the probability of paternity would take into account all the other evidence. She 

said that instead, she assumed a 50% probability, as discussed above, to avoid 

"giving weight to either side of the argument, and ... [to] only represent[], in the 

probability of paternity, the DNA results." She testified that 50% was the only 

neutral number that would not weigh the results one way or the other. 

The expert did not expressly describe how the probability of paternity is 

arrived at, as it is laid out above. For example, she made no mention of Bayes' 

theorem. But her testimony in this regard implicitly described it, particularly 

its evaluation of a prior probability in light of new evidence (e.g., a DNA test). 

The Commonwealth asked the expert if she had calculated a probability 

of paternity based on other prior probabilities. She said yes, noting that she 

had used 1% and several other values. In explaining her use of 1%, she said: "If 

I were to assume 1% prior probability, that means the trier of fact, in this case 

the jury, if you were to assign a probability to all the other evidence other than 

the DNA evidence—" Ivey then objected and asked to approach; the trial court 

stated, "No. Overruled." The expert then continued with her answer: 

If the trier of fact were to assign a probability of all the other nonDNA evidence, before anything about DNA, and at that time, based 

off all the non-DNA evidence, believed there was only a 1% 

probability that the alleged father was the biological father, that's 

what assuming a one percent probability would mean. 

She then went on to explain other prior probabilities that the jury might arrive 

at in considering the non-DNA evidence. 

Ivey now claims that the expert was instructing the jury how to consider 

the evidence by this testimony. He notes our case law condemning testimony 

removing from the jury its historic function of assessing credibility, such as 

22 
Stringer v. Commonwealth, 956 S.W.2d 883, 894 (Ky. 1997). He also cites cases 

from other jurisdictions, many of which pre-date DNA testing and address 

blood-type or other early forms of genetic testing, stating that expert proof of 

probabilities of paternity exceeding 99% cannot be viewed as conclusive of the 

question of paternity. 

To some extent, this argument is a repetition of the one addressed above. 

Ivey simply wants this Court to disapprove of the probability-of-paternity 

calculation because it inherently requires an assessment of the proof in the 

case to arrive at a prior probability. We decline to do so, as explained above. 

Rather than instructing the jury on how it had to consider the evidence, 

or hiding the probability-of-paternity calculation behind a veil of assumed 

scientific authority, the expert's testimony actually opened the options for the 

jury. We already approved in Butcher the use of the 50% prior probability in 

that calculation because it is purportedly neutral, even though it also includes 

an implicit assumption about the other evidence in the case. But here, the 

expert explained the significance of that figure and how the other evidence of 

paternity would "ideally" be taken into account. She also explained to the jury 

the results of the probability-of-paternity calculation if it had believed the other 

non-DNA evidence weighed strongly against paternity (thus the 1% figure). The 

expert's testimony thus opened up the available options, albeit only slightly 

given the very high probability of paternity even with a very low prior 

probability. Rather than invading the province of the jury, the expert gave 

testimony that would assist the jury "to understand the evidence or to 

23 
determine a fact in issue." KRE 702. That is exactly what expert witnesses are 

for. There was,,therefore, no error. 

III. Conclusion 

The trial court held the only hearing requested by Ivey, and did not err in 

allowing the DNA expert to testify about a probability of paternity based on a 

50% prior probability of paternity, especially since she also testified about 

lesser prior probabilities. And the expert did not invade the province of the jury 

by explaining how the other lesser prior probabilities, which would depend on 

the evidence in the case, would affect the probability of paternity. Finding no 

error, this Court affirms the judgment of the Hardin Circuit Court. 

All sitting. Minton, C.J.; Cunningham, Hughes, Keller and Wright, JJ., 

concur. Venters, J., concurs in result only by separate opinion. 

VENTERS, J., CONCURS IN RESULT ONLY: I concur in result only. The 

majority rejected Ivey's complaint that the calculation used to determine the 

probability of paternity in this sexual assault case was unreliable. I submit 

that the method was improper, but would hold that error to be harmless. The 

issue, however, is more appropriately framed as whether the probability of 

paternity as calculated for a paternity determination is a relevant fit for a rape 

or sexual assault case. "Tit' is not always obvious, and scientific validity for 

one purpose is not necessarily scientific validity for other, unrelated purposes." 

Daubert v. Merrell Dow Pharmaceuticals, Inc., 509 U.S. 579, 591 (1993) (citation 

omitted). 

Like all evidence, statistical and probability evidence must be relevant to 

a fact in issue. Bayes Theorem consists of a prior probability multiplied by a 

24 
likelihood ratio, which results in a posterior probability. The theorem is 

routinely applied in paternity cases. Federal Judicial Center, Reference Manual 

on Scientific Evidence 172 (3d ed., National Academies Press 2011) However, 

the logic that justifies its use for proving paternity does not necessarily apply 

for proving sexual assault. Specifically, using the prior probability that the 

putative father had sexual relations with the mother makes logical sense in a 

paternity case; but using it to determine the likelihood that a male suspect had 

sexual relations with the female victim in a sexual assault case is illogical 

because it presupposes the truth of the issue it purports to prove. 

The likelihood ratio, by itself, is a probability-based method for 

evaluating the probative value of forensic evidence and may be presented 

without the prior probability estimation. Colin Aitken, Paul Roberts, 86 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 86 Colin 

Aitken, Practitioner Guide No. 2, Assessing the Probative Value of DNA Evidence 

(2012). The likelihood ratio expresses "the extent to which evidence supports a 

particular proposition in terms of two likelihoods: (i) the likelihood of the 

evidence if one proposition is true; and (ii) the likelihood of the evidence if the 

other proposition is true." Colin Aitken, Paul Roberts & Graham Jackson, 

Practitioner Guide No. 1, Fundamentals of Probability and Statistical Evidence in 

Criminal Proceedings at 35. 

25 
In criminal proceedings, the likelihood ratio is obtained by comparing the 

likelihood of the evidence given the prosecutor's proposition that the accused is 

guilty to the likelihood of the evidence given the defense's proposition that the 

accused is not guilty. Id. at 35. "The relative values of these two likelihoods 

provide a measure of the meaning and probative value of the evidence." Id. at 

36. The larger the likelihood ratio, the more probative is the first proposition 

as compared to the second proposition. In this case, the paternity index, based 

on the DNA evidence alone, without the Bayes prior probability estimation, 

results in a likelihood ratio highly favorable to the prosecutor's proposition that 

the defendant had sex with the alleged victim. 

Bayes Theorem's introduction of the prior probability of the ultimate fact 

in issue (that the defendant had sex with the victim) is not appropriate when, 

as part of its inferential reasoning, "it involves making selection between 

(potentially) contested facts, a role properly reserved to the fact-finder." 

Graham Jackson, Colin Aitken, 85 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). The probability of paternity formula used here included the prior 

probability that Ivey had sexual intercourse with the victim, and thereby 

interjected an assumption of sexual intercourse, the very fact the 

Commonwealth was required to prove. 

Simply stated, it is improper to prove that sexual intercourse, the corpus 

delicti of the rape charge, occurred by using a statistical formula that 

presupposes the probability that sexual intercourse occurred with the 

26 
defendant. Consequently, with the incorporation of this assumption, the 

probability of paternity is not a relevant calculation for deciding whether a 

defendant committed sexual assault. The formula is not "fit" for the purposes 

of proving sexual assault. Moreover, by excluding the use of the prior 

probability, and presenting only the paternity index derived from the DNA 

analysis, the jury's "common sense" inferential reasoning for assessing the 

disputed facts is not usurped. 

Nevertheless, given the high paternity index obtained in this case, and 

the other evidence from which the fact of intercourse is easily inferred, the use 

of the irrelevant prior probability was very plainly harmless error. 

COUNSEL FOR APPELLANT: 

Erin Hoffman Yang 

Assistant Public Advocate • 

Department of Public Advocacy 

100 Mill Creek Park, Building #5 

Frankfort, Kentucky 40601 

COUNSEL FOR APPELLEE: 

Andy Beshear 

Attorney General 

Christian Kenneth Ray Miller 

Assistant Attorney General 

Office of Criminal Appeals 

Office of the Attorney General 

1024 Capital Center Drive 

Frankfort, Kentucky 40601 

27