Instrumentation & Measurement Magazine 24-1 - 8

probability to declare a correspondence between two profiles
when they do not correspond. The Bayes factor is calculated
as if any possibility of error in the handling of the evidence
has been conclusively excluded; it only expresses one type of
" error, " which is the possibility that one innocent person will
match the trace by chance (i.e., the random match probability).
This makes no sense from a scientific point of view, because it
is clear that if the possibility of an error were to be taken into account, the value of the Bayes factor would very often decrease
by orders of magnitude [11].

From Source to Activity
One additional problem that has emerged recently is due, paradoxically, to technological advances: the limits of detection
and the analytical capabilities have made it possible to derive
a DNA profile from a single cell. But what does it mean to find
a single cell somewhere, with regards to somebody's presence
or activity? Focusing one's attention to the analysis stage of the
life of the evidence presents the risk of blinding the court to the
real meaning of the evidence in the context of the case. This was
theorized under the concept of hierarchy of propositions, which
distinguishes the evaluation of evidence under hypotheses (or
propositions) referring (a) to the source of the recovered trace,
(b) to the activity committed by the suspect or by other people
involved and (c) to the offense under scrutiny [12].
In the last two decades, instances of wrongful convictions
have demonstrated in a dramatic manner that a person cannot
be convicted of a crime simply because a trace seemingly links
her to the offense. First, contaminations can happen. In Australia, for example, Farah Jama was exonerated in 2009 after
spending several years in prison for a rape he did not commit.
His DNA had been observed in a vaginal sample taken from
a woman who had been found passed out in the lavatories of
a nightclub. It later turned out that the rape kit had been contaminated with Mr. Jama's genetic material [13]. Second, traces
can be transferred from one person or one object to another
through one or several vectors. Many studies have now documented the possibility of indirect transfer, which renders the
interpretation of evidence very difficult in certain cases [14].
Aware of the importance of assessing evidence at the activity level, the European Network of Forensic Science Institutes
published guidelines in 2015 to encourage forensic practitioners to render conclusions under activity-level hypotheses
when there is a risk, in the case at hand, that rendering conclusions under source hypotheses could lead the fact finder to
give the evidence undue value [15].

Decision Theory in Forensic Science
As previously said, on the basis of observations, one can construct probabilistic arguments in support of hypotheses of
interest. As such, probabilistic models provide a coherent environment wherein probabilities about target propositions can
be revised upon receipt of newly acquired information. This
represents a fundamental requirement for an additional step,
that is the coherent measure of probabilities for decision-making under uncertainty.
8

One makes decisions on the basis of essentially two elements: one's beliefs about uncertain events (the hypotheses
of interest, Hp and Hd) and one's assignment of desirability of
decision consequences. The latter aspect is formalized by invoking the concept of utility. Both concepts, probability and
utility, can operate within a general decision framework that
involves the practical rule that one should select the decision
which has the highest expected utility (or, alternatively, the
lowest expected loss) [16].
To formalize a decision problem, decision theory first requires one to draw up an exclusive and exhaustive list of
available decisions (from a legal point of view, acquitting or
convicting a given suspect, for instance). Secondly, a list of exclusive and exhaustive uncertain events (i.e., the hypotheses)
is needed. The decision maker is then faced with a problem
of decision-making under uncertainty: because it cannot be
known with certainty which state of nature holds, one cannot directly tell which decision leads to a consequence that is,
in some sense, optimal. The main problem is thus to choose a
decision without knowing which state of nature holds. The
combination of a particular decision with a given state of nature will result in a foreseeable consequence: e.g., 1) acquitting
an innocent; 2) acquitting a guilty suspect; 3) convicting an innocent, and 4) convicting a guilty suspect. These consequences
have each a distinct associated utility. Further development
of this argument leads to the so-called expected utility, which
assigns a numerical value to a given decision, as a function
of the probabilities of outcomes as well as their respective
desirability. The result thus consists in a qualifier for the appropriateness of particular decisions, evaluated on the basis of the
desirability of outcomes.
The final goal that the justice system pursues is that of making decisions. Not making a decision is not an option; it is even
forbidden in most modern justice systems, as a denial of justice. Decision theory aims to define what the best decision is
for a rational agent, given the information that she has and her
personal values for the possible consequences of her decisions
[17]. This is why developing a framework for decision-making
in the forensic process is so important.

Conclusion
Judges, attorneys and forensic scientists only have incomplete knowledge as to the states of nature that make up the
cases before them. Uncertainty is thus a complication that
accompanies all actors of the justice system who face inference and decision-making as core aspects of their activities.
Probability, as a measure of uncertainty, can help them make
the best decisions on the basis of the knowledge at hand and
the preferred values of the stakeholders. The probabilistic
model, in turn, can help focus resources into appropriate
data gathering strategies and clarify the structure and mechanisms of scientific evidence assessment. Finally, as a tool
that informs the rational management of the risk of errors,
the use of a probabilistic model increases the accuracy of judicial fact-finding and thus helps materialize the right to a
fair trial.

IEEE Instrumentation & Measurement Magazine

February 2021

Instrumentation & Measurement Magazine 24-1

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 24-1