# Common Source vs. Specific Source Scenarios

In general, the inference of the identity of the donor of a trace impression from its com- parison with a control impression from a known donor requires considering two mutually exclusive hypotheses^{[1]} (Aitken and Taroni, 2004). Over the years, and perhaps because of the legacy of the inference frameworks developed to report forensic DNA evidence (see comment in Section 13.3.3), these hypotheses have not been formulated particularly rigor- ously. Unfortunately, this lack of formalism has resulted in the development of models and the collection of data that do not properly address the hypotheses that are most often of interest.

The next sections briefly develop two formal scenarios that frame the inference of the source of latent prints: the *common-source scenario* and the *specific-source scenario* (Ommen et al, 2017). These scenarios are often confused with one another. This results in models developed under one scenario that answer the question considered by the other one. Thus, understanding their differences is important and helps assess the potential and limitations of the different inference frameworks for fingerprint evidence.

## Common Source Scenario

The common source scenario considers that two impressions are *from the same source* with- out formally specifying who that source is. This scenario typically relates to the comparison of two latent prints, e_{M1} and *e _{U2}* (e.g., two impressions recovered on two different crime scenes or even on the same crime scene), with the goal of determining if they were made by the same person when that person is unknown (e.g., determining whether the two scenes are linked or the number of perpetrators). The hypotheses considered in the common source scenario can be stated as follows

^{[2]}:

*H _{Ocs}* : e

_{U1}and

*e*were left by the same, unknown, person;

_{U2}H_{)cs}: e_{U1} and *e _{U2}* were left by two different, unknown, individuals.

In this scenario, the true donor of each impression is considered to be a random individual from a population of potential donors. Under Hq_{cs}, the donor of the two impressions is the same random individual, while two different random donors from the population left the trace impressions under Hi_{cs}.

## Specific Source Scenario

The specific-source scenario typically involves the comparison of a trace impression, e_{M}, with a control impression from a known individual, *e _{s},* with the goal of determining if the trace was made by the considered individual. The hypotheses considered in the specific source scenario can be stated as follows:

*Ho _{ss}i e_{u}* and

*e*were made by Mr. X.;

_{s}H_{lss}: *e _{u}* was made by somebody other than Mr. X.

In this scenario, Mr. X is a known donor. He can be considered fixed. Under *H _{ss},* the true donor of

*e*is unknown and is considered to be a random individual from a population of potential donors, while Mr. X remains the undisputed donor of

_{u}*e*

_{s}.The distinction between both scenarios is not merely theoretical. Each scenario results in different likelihood functions for the same information, and, as we discuss below, in different interpretations of the results of fingerprint examinations.

In the vast majority of cases, the inference questions of greatest interest to the crimi- nal justice system fall under the umbrella of the specific-source scenario. Nevertheless, the determination that two latent prints were made by the same unknown person may be relevant to some investigations (e.g., for forensic intelligence-led investigations). Since these two scenarios are different and consider two radically different pairs of hypotheses, they should not be interchanged. Unfortunately, they are often confused.

## Simulations

This chapter explores the convergence of different models and inference frameworks partly through simulations. The simulations rely on generative models that give simplified rep- resentations of how the data arise under the different hypotheses laid out in Sections 13.3.1 and 13.3.2. We consider a simple univariate setting to explore the different models in the common and specific source scenarios. In the common source scenario, the genera- tive models under both hypotheses can be represented by two hierarchical random effects models:

**
**

where /z is the mean of the population of sources, *d* is a random effect due to sources, and iq and »2 are random effects due to objects within sources.^{[3]}

Under H_{Ocs}, both impressions originate from the same donor and, thus, have the same value for *d* (but not necessarily the same if both traces were left in different condi- tions). Under Hi_{cs}, both impressions originate from two different donors and are therefore independent. Thus, the joint distributions of M1 and *e _{U2}* are

**
**

The generative models in the specific source scenario differ depending on whether Hq_{ss }or *Hi _{ss}* is considered. Under Hq

_{ss}, when both impressions originate from the same donor, the models are two simple random effects models:

**
**

where /zrf represents the mean for the considered specific donor, and *u* and *s* are random effects respectively corresponding to trace and control samples.

Under *Hi _{ss},* the generative model for the control impressions from the specific donor is the same as under Hq

_{ss}(indeed, there is no dispute that

*e*originates from its donor).

_{s}However, the model for the trace impression, e_{M}, is a hierarchical random effects model to reflect that its true donor is an unknown individual from a population of donors:

and where *n, nd, d, u* and s are defined as above.^{[4]}

Under *H _{Oss},* trace and control observations are independent given

*nd,*and their joint distribution is multivariate normal. Under

*Hi*trace and control observations are inde- pendent since they are not from the same donor, and their joint distribution is also multivariate normal. We have:

_{ss},

If we take the view that forensic evidence has to be evaluated within a Bayesian paradigm, then we are interested in quantifying the weight of the evidence using Bayes factors (or, when the parameters are known, likelihood ratios). In the common source framework, the likelihood ratio for e_{H1} and e_{M2} is:

while the likelihood ratio for *e _{u}* and

*e*in the specific source framework is

_{s}

We already mentioned that, in most cases, fingerprint examiners are working under the specific source scenario. They are provided with a latent impression and they have to infer whether it was left by the same known person who provided a set of control impressions. Using the toy examples in (13.1) and (13.2), we can study the convergence of the common source likelihood ratio in (13.3) to the specific source likelihood ratio in (13.4) that should be used to quantify appropriately the weight of the evidence.

To compare these likelihood ratios, we consider pairs of *e _{u}* and

*e*generated by model (13.2) under Hq

_{s}_{ss}or

*Hi*and we calculate the likelihood ratios (13.3) and (13.4). To calculate the common source likelihood ratio using the data generated under the specific source model, we set e

_{ss}_{ui}= e

_{u},

*e*and

_{U2}= e_{s},_{2}= er

^{2}.

Figure 13.6 presents the results of three experiments in which, /z = 10, *nf* = 10 and cr^{2} = 2. All simulations were repeated 1,000 times. In the first experiment, the character- istics of the donor of *e _{s}* were chosen to be relatively common in the population of donors (/z

_{(}y = 9) but also quite variable (cr

^{2}= 1). In the second experiment, the characteristics of the donor of

*e*were chosen to be rare in the population of donors (/zs

_{s}^{2}= 1). In the last experiment, the variability of the characteristics of the known donor of the control impressions was chosen to be negligible (a

^{2}= IO

^{-5}).

^{[5]}

The results of the experiments show that likelihood ratios for the common and the specific source scenarios do not converge unless the variability of the donor of the con- trol material is negligible.^{1}^ Importantly, the results for the first two experiments in Fig. 13.6 show that the common source likelihood ratio unpredictably over- or underesti- mates the value of the specific source likelihood ratio. That said, although common-source likelihood ratios that are assigned when H_{lss} is true may underestimate the correspond- ing specific-source likelihood ratios, they have a marked tendency to overestimate their counterparts (we have not found a situation where common-source likelihood ratios consistently underestimate specific-source likelihood ratios).

The lack of convergence raises the issue of whether Hq_{ss} or *Hi _{ss}* is true. When Hq

_{ss}is true, underestimating the value of the specific-source likelihood ratio may result in the erroneous exclusion of the donor of the control impressions as the source of the trace impression. The criminal justice system considers this to be a better outcome than the erroneous identification of an innocent individual. Furthermore, when Hq

_{ss}is true, overes- timating the value of the specific-source likelihood ratio only results in being overconfident in the support of the correct conclusion that the donor of the control impressions is also the donor of the trace impressions; thus, the impact of the overestimation may be considered minimal. Unfortunately, when

*H*is true, overestimating the value of the specific-source likelihood ratio may result in exculpatory evidence not being given the appropriate weight in favour of an innocent, yet suspected, donor. In fact, Figure 13.6a,b show that some pieces of evidence result in values of their specific-source likelihood ratios that are less than one and in values of their common source likelihood ratios that are greater than one. This may result in serious miscarriages of justice if the common-source likelihood ratio is used instead of the specific-source one.

_{ss}## Summary

There are two different scenarios under which forensic evidence can be evaluated: the common-source scenario and the specific-source scenario. The former scenario focuses on evaluating whether two trace objects originate from the same unknown donor, while the latter focuses on evaluating whether a single trace object originates from a specific known donor. Forensic evidence is considered differently under these two scenarios and does not

**FIGURE 13.6**

Comparisons between LRs in the common source and specific source scenarios. Columns: the left column reports the results when *e _{u}* and

*e*have been sampled under Hq

_{s}_{ss}; the right column reports the results under H]

_{ss}. Rows: (a) the source of the control impression is common; (b) the source of the control impression is rare; (c) the source of the control impression is common, but it has virtually no variance.

have the same weight. Both scenarios converge only when the variability of the evidence is negligible (e.g., single source DNA profile, finger impression taken under controlled con- ditions). In all other circumstances, misspecifying the interpretation framework can lead to dramatic results.

- [1] The first hypothesis, denoted Hq below, is commonly called the prosecution hypothesis. The alternative hypoth-esis, denoted is commonly called the defense hypothesis. This often represents an abuse of language since, inmost cases, neither the prosecutor nor the defense attorney explicitly states these propositions.
- [2] Note that the hypotheses are stated as a function of the donor(s) of the impressions, since they are the ones ofinterest to the criminal justice system. In practice, fingerprint examiners may consider specific fingers or areasof friction ridge skin. Most of the models and data discussed in this chapter focus on finger-related hypothe-ses. Neumann et al. (2011) discuss some of the assumptions and implications of moving from finger-basedhypotheses to person-based hypotheses.
- [3] In terms of fingerprints, u is the mean of the distribution of the characteristics of all friction ridge skin in apopulation; d represents the distance between the characteristics of the friction ridge skin on various randomindividuals and the mean of the population; and wj and «2 are random effects that affect the final appearance(after development, transfer, photography, etc.) of fingerprints resulting from different impressions of the fingersrepresented by d on various surfaces. Note that uj and u2 may be different as two different impressions may beaffected by different sets of factors.
- [4] A similar analogy to the one made in the previous footnote can be made here, with ad representing the char-acteristics of the friction ridge skin of a specific finger on a known individual (e.g., a suspect); a representingthe mean of the distribution of the characteristics of all friction ridge skin in a population; d representing thedistance between the characteristics of the friction ridge skin of a specific finger from an unknown individual(e.g., the true donor of the latent print) and the mean of the population; and u and s representing random effectsthat affect the final appearance (after development, transfer, photography, etc.) of fingerprints resulting fromdifferent impressions of the fingers represented by ad an
*[5] It can be argued that finger impressions collected from a known donor under controlled conditions have virtu-ally no variability. This argument is reasonable. For example, control prints have more variability than forensicDNA profiles; however, they have much less variability than trace impressions. + This can also be seen directly from the analytical forms of the joint distributions of cui and cH2, and eu and es, as’«2 = ff2 °' t This is typically the case for forensic DNA analysis when single full DNA profiles are considered. Since theallelic designation of a full DNA profile is extremely reproducible, the inference of the identity of source of apair of full DNA profiles will be the same under both common and specific source scenarios. This may explainwhy the distinction between common and specific source scenarios was not discussed until recently by Ommenet al. (2017).*