Inference

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Inference
/ˈɪnfərəns/ (n.)
A conclusion derived from existing information by acceptable reasoning. Such as by:

1. Deduction, the application of formal logic to valid premises to reach a necessary conclusion: “all cats are mammals; this is a cat; therefore this is a mammal.”
2. Induction, which argues from many past instances to a general predictive forward statement: the sun has risen everyday in recorded history; therefore it will rise tomorrow.”
3. Probability, which passes from frequencies within a known domain to conclusions of stated likelihood, making an outcome more or less likely: “the first suspect has criminal propensities; the second does not; therefore all other things being equal, the first is more likely than the second to have committed the crime”
4. Statistics, which concludes that, on the average, a certain percentage of a set of entities will satisfy the stated conditions.).

Inference from circumstantial evidence is rarely a matter of straightforward deduction: that is generally the domain of direct evidence.

Where there are only circumstances which may make more or less likely the scenario at issue, other forms of inference come into play such as induction (e.g.: “David Bain set out on his paper run at 5.45 every morning in the last year, so we may infer he also did so on the morning of June 20 1994, on which date the rest of his family was shot dead at 6 a.m.”), or matters of probability (“incidences of extubation at Liverpool Women’s Hospital increased by from 1% to 40% while Lucy Letby was on duty there, so we may infer that she was somehow responsible for the rise in extubations.”)

But in each case we can see these are imaginative acts that do not necessarily follow from their premises the way a deduction does. They requires us to construct a narrative around facts that are by themselves neutral to the matter at issue? David Bain was an independent moral agent who could vary his departure time: without independent corroborating evidence that he did leave at that time, induction from his self-reported history of departure times has little value. Likewise, an increased incidents in extubation data may instead be evidence of Ms. Letby’s diligence in reporting them.

Inference is “imaginative” not in the sense of being made up, but that some narrative construction was required to select one inference from the range of “available inferences” one could draw from a given set of facts. There is an element of subjectivity to which ones you select.

In many cases, the “range of possible inferences” includes scenarios beyond the experience or imagination of the inferrer and is potentially infinite.

Whence the subjectivity, then?

1. Personal experience and subject matter expertise
2. Cultural and social context
3. Cognitive biases and heuristics
4. Personal stakes in the situation
5. The underlying philosophy or goal of the system requiring or driving the inference process.

Rationality in decision-making (and by extension, in drawing inferences) is bounded by the information we have, our cognitive limitations, and the time available to make decisions.

Our prior beliefs and probabilities influence our interpretation of new evidence and the inferences we draw or find convincing.

Narrative attraction: Some inferences might be more appealing because they form more coherent, satisfying, or familiar narratives. In a criminal investigation a narrative that suggests a coherent pattern of intentional offending will be more satisfying and coherent then one which suggests an unusual cluster of random events.

This subjectivity doesn’t necessarily invalidate the inferential process, but it prays caution, transparency about our reasoning processes, and openness to revising our conclusions as new information becomes available.

See also

• Circumstantial evidence
• Prosecutors tunnel vision