Reconstruction and Probabilistic Reasoning

Reconstruction is not about recreating every moment of an event. The physical evidence at a scene is a sample, not a complete record. Evidence is damaged, contaminated, missed, or moved before scientists arrive. What reconstruction actually does is more limited and more honest: it produces a set of scenarios that are physically consistent with the observed evidence, and it eliminates scenarios that are not.

The method is abductive: reasoning to the best explanation. You observe a set of effects (bloodstain at this location, fracture pattern on this glass, spent cartridge here) and ask what cause or sequence of causes could have produced them. Unlike deduction, abduction does not guarantee a unique answer. Multiple causes can produce the same effects. This is the fundamental reason forensic conclusions are probabilistic and why a good forensic scientist never says 'this is the only way this could have happened'.

Sequencing deserves special mention. Locard's exchange principle tells us that contacts leave traces. Reconstruction uses those traces to order contacts in time. Blood over a disturbed surface versus a disturbed surface over dried blood. Glass fragments inside a vehicle when the window was broken from outside versus fragments on the exterior when broken from within. These physical sequences can establish what happened before what, independent of any witness account, and they are some of the most reliable outputs of reconstruction.

Reasoning from evidence to conclusion is always reasoning from effect to cause. This is the reverse of the direction in which physical processes run, and it is harder. A cause uniquely produces its effects, given the laws of physics. But an effect can have multiple causes. A bloodstain is consistent with a fall, a punch, a cut, or a spray. Each is a different cause. The forensic scientist must evaluate the relative probabilities of each cause given the observed effect and everything else known about the case.

This asymmetry is why forensic conclusions should always name the competing hypotheses they are assessing. A statement like 'this glass fracture is consistent with a blow from outside' is only meaningful when it is paired with 'it is not consistent with being broken from inside, for the following physical reasons'. The conclusion gains weight from the comparison of alternatives, not from standing alone.

Some forensic scientists describe the structure of their reasoning explicitly as comparative. They identify a prosecution hypothesis, typically the claim made by investigators or the charge, and a defence hypothesis, the most plausible alternative. They then ask: given this evidence, how much more probable is the prosecution hypothesis than the defence hypothesis? That is the likelihood ratio question, and it is a more precise version of what good forensic scientists have always done informally.

The likelihood ratio (LR) is the central tool for expressing the weight of forensic evidence in a probabilistically coherent way. It is defined as:

LR = P(Evidence | Hypothesis 1) / P(Evidence | Hypothesis 2)

P(E | H1) is the probability of observing the evidence assuming hypothesis 1 is true. P(E | H2) is the probability of observing the same evidence assuming hypothesis 2 is true. If H1 is 'this DNA comes from the suspect' and H2 is 'this DNA comes from an unrelated person from the population', then the LR is how many times more likely the DNA evidence is under H1 than under H2. An LR of 1,000,000 means the evidence is a million times more probable if it came from the suspect than if it came from a random person.

The Bayesian framework does not require a forensic scientist to assign numbers to everything. The logic of updating a prior belief with new evidence is the same whether the updating is formal and numerical or qualitative. A pathologist who says 'this injury is more consistent with a fall than a punch' is applying likelihood reasoning without writing the formula. The formal LR just makes the implicit explicit and allows the reasoning to be scrutinised and challenged.

Forensic questions operate at different levels, and evidence that is strong at one level may be weak or silent at another. This framework is called the hierarchy of propositions, and it was developed prominently in the work of Ian Evett and colleagues at the UK Forensic Science Service.

1. Source level
   The proposition concerns where a piece of evidence came from. 'This DNA originated from the suspect' versus 'this DNA originated from an unknown person'. This is the level where forensic analysis is most direct and most reliable. The examiner can measure the evidence, compare it to a known sample, and quantify the result.
2. Activity level
   'The suspect fired the weapon' versus 'the suspect was in the area but did not fire'. This asks what the person was doing, which requires reasoning about how evidence is generated by activities. Transfer and persistence data, background rates, and case-specific context all matter. More uncertainty, more inference.
3. Offence level
   'The suspect committed the crime' versus 'the suspect did not commit the crime'. This is a legal conclusion, not a scientific one. Forensic scientists should not testify at this level because it invades the function of the trier of fact and requires weighing non-scientific evidence that the expert is not in a position to assess.

The hierarchy has practical consequences. A DNA match is a source-level finding: the profile is consistent with the suspect being the donor of the sample. It says nothing, by itself, about what the suspect was doing or whether they committed an offence. If the defence proposes that the DNA arrived by secondary transfer, or by innocent prior contact, the relevant question becomes activity-level: how probable is it that the DNA was deposited by the alleged activity versus the innocent alternative? That requires different data and a different kind of reasoning than the source-level match.

Forensic science operates under several constraints that make absolute conclusions impossible in principle, not just in practice. Physical evidence degrades. Crime scenes are disturbed. Samples are contaminated. Background rates of trace materials in the population are not always known. Any one of these constraints introduces uncertainty, and the honest expert names it rather than papering over it with confident language.

• Incomplete data: the evidence at a scene is a sample of what was produced, not the complete record. What is missing is itself unknown.
• Alternative explanations: physical evidence is consistent with more than one cause. Ruling out all alternatives is impossible; ruling out the most plausible alternatives is the achievable goal.
• Measurement uncertainty: every measurement instrument has a precision limit. The result is not a single value but a range, and conclusions must reflect that range.
• Population data gaps: calculating an LR requires knowing how common a feature is in the relevant population. For many trace evidence types, those population databases are limited or unavailable.
• Transfer and persistence variability: the same activity under different conditions produces different amounts of trace. A single data point from one case cannot be extrapolated without reference to the range of outcomes documented in research.

The adoption of probabilistic language in forensic testimony reflects scientific maturity, not weakness. A DNA analyst who says 'the LR for this profile is greater than a billion, meaning the evidence is a billion times more probable if it came from the suspect than from an unrelated person' is giving the court more useful information than one who says 'the match is conclusive'. The first statement allows the court to weigh the evidence; the second preempts that weighing.

Reconstruction starts with the physical evidence, formulates the possible hypotheses that could explain it, and tests each against the full body of physical facts. Starting with a narrative and seeking evidence to support it is confirmation bias, and it has contributed to serious miscarriages of justice in forensic history.

The logical structure follows the same pattern as scientific hypothesis testing. A hypothesis makes predictions: if this scenario is true, then we should expect to see this pattern of blood, this trajectory, these footwear impressions. The reconstruction checks whether the predicted evidence matches the observed evidence. A single contradiction between prediction and observation is enough to challenge a hypothesis, though it may not be enough to eliminate it entirely if alternative explanations for the discrepancy exist.

Sequencing adds a time dimension. Physical chemistry, biology, and physics allow statements like: blood that dried before glass was broken will not appear on glass fragments, so the presence of blood on shards implies the glass broke first. Rigor mortis and body temperature give time-of-death windows. The progression of decomposition, wound aging, and trace persistence all carry temporal information that can be read as a rough clock. These physical sequences are often more reliable than witness memory because they obey known rules.