When does absence of evidence imply evidence of absence?

Question

There is a well known maxim that absence of evidence is not evidence of absence. In his book "The Black Swan", Nassim Taleb advocates this using a medical example - something along the lines of no evidence of disease is not the same as evidence of no disease.

However, I have seen multiple sources that refute this, and this does seem logical to me; if A is expected to be observed when B is present and A is not observed, that would surly constitute strong evidence of B's absence? For example, the fact that a Dodo has not been seen for hundreds of years is strong evidence of the Dodo's extinction. Or to go back to the medical example, assuming the test can accurately detect the disease then no evidence of the disease would surly imply evidence of no disease (but not necessarily proof of no disease)?

Could someone clarify when absence of evidence is evidence of absence, and when it is not?

Answer 1

Absence of evidence is almost always evidence of absence, actually. The problem is that it is often really poor evidence.

The standard way to quantify this is through Bayesian inference. In brief, you consider a set of possible models of the (relevant part of the) universe, and use evidence to sensibly adjust the probability you assign to each of the possible models.

If the true model is "absence", looking for something and not finding it is what you would always have. With any other model, there may be some (perhaps slim) chance that you would find it. Since the other models will not always give the observation ("found nothing"), you reduce your estimate of their probability.

This can be made precise and quantitative, but the bottom line is that it is correct mathematical reasoning. However, just because it is some evidence, it doesn't mean that it is conclusive or that it is sufficient to warrant changing your beliefs very much.

Answer 2

This question is related to the classical Raven Paradox (Theory of confirmation)

Answer 3

Consider the following valid propositions:

A implies B

A implies C

A implies D

Suppose than B, C, and D are all false. That's the absence of evidence of A. It does not imply A.

Consider now the following valid proposition:

(A implies B) and (B implies A)

Suppose that B is false. That implies falsehood of A, therefore it is evidence of absence.

Your example includes "assuming the test can accurately detect the disease", which seems to be equivalent to the latter proposition:

(disease implies positive test) and (positive test implies disease)

This conjunction is what turns the negative test into the evidence of absence.

Without the assumption of accuracy, if the proposition would be limited to only the (disease implies positive test) part, the negative test would be only an absence of evidence, and wouldn't imply that there was no disease.

Answer 4

First of all, we need to clarify the meanings of evidence. There are two main types of evidence to be considered: evidence of facts, and evidence of cause.

Absence of evidence of a fact:

Absence of evidence of the fact "that black swans exist" is not evidence that "black swans exist". Absence of evidence of the fact "that black swans exist" is not evidence that "black swans do not exist". Absence of evidence of the fact "that black swans do not exist" is not evidence that "black swans exist or do not exist". It is not possible to provide evidence that "X does not exist".

Absence of Evidence of Cause

Evidence of cause is much more complex. Causes are simply not simple. Every cause has a cause. Every cause of a cause has a cause. Every cause, and every consequence has a long chain of causes, as long as our imagination can create. We can often split causes into component causes, creating even longer lists of cause.

Proof of cause is subjective, not objective. Causes can be measured individually, in individual cases - or statistically - in general situations. Specific causes are subject to judgement in the individual case. Statistical causes are statistics: "lies, damn lies, and statisitcs". It is possible to demonstrate many impossible things before breakfast, using statistics.

Evidence of cause is always subjective, always subject to challenges, to appeals, to more and more complex decision processes. Lawyers thrive by creating evidence of cause and challenging evidence of cause.

Absence of evidence of cause is meaningless. It might mean there has been no search for evidence. It might mean that there has been a search for evidence of cause, or search for cause. It might refer to a trivial or cursory search for cause, or a long complex search for cause, or for evidence of cause.

But no evidence of cause has been found. That's a simple reality.

The problem we often encounter is the leap from absence of evidence to "evidence of absence".

The leap from "no evidence of cause by X has been found" to "x did not cause" is simply not logical. Innocent until proven guilty is not logical, it is moral.

Causes are not "presumed innocent until proven guilty". There is no need for a moral assumption of innocence. There is no such thing as "proof of cause" and no such thing as "proof of not cause" in the laws of science, only in courts of law.

Summary:

With regards to facts, claims of an absence of evidence is nothing, proves nothing. It might be supported by evidence of a search, but does not contain evidence of a finding.

With regards to cause, claims of absence of evidence is generally an absence of imagination, or a suspension of belief.

re: Claims of Evidence

Every claim is a fact. Every fact can be evidence. All claims of evidence and all claims of absence of evidence are facts in themselves, even when the claim is false.

Any claim of evidence is "evidence" that the fact is true.

However, a claim of "there is no evidence that" is not based on evidence. It is simply a claim. In many cases, it is simply building a wall, an attempt to ignore evidence, that must be supported by denial, or renounced, if or when evidence is produced.

Answer 5

The key word is expected. The other answers cover this pretty well. What they do not cover is motivation. People who have an interest in showing something can be expected to provide certain evidence. When you ask them for it, they should be happy and provide it because it makes it so much easier to show you the something.

Let's take your example: "the fact that a Dodo has not been seen for hundreds of years is strong evidence of the Dodo's extinction." Assume that I want to show that this is wrong. "I have evidence!" I claim. When you ask me for it, it seems that I stonewall, or speak vaguely, or get distracted. There's always something that prevents me from providing you with my evidence. What does this tell you? If my expressed interest in showing that the Dodo is not extinct is honest, then you can conclude from my failure to provide the evidence that I don't have the evidence.

Vaccines provide a controversial example:

If a vaccine works, then a graph of the disease's prevalence for a few decades before and after the introduction of the vaccine would show this. If you find a vaccine for which no such graph has been produced, that strongly suggests the vaccine isn't as effective as advertised. The graph would break a powerful engine of profit, so it is prevented from coming into existence.

APOPHATIC REASONING

I call this "apophatic reasoning": When you know a claimant has the motivation to produce evidence and they do not produce it, it is likely that such evidence counters the claim they are motivated to make. The strength of the argument grows in proportion to whatever value the claimant sees in proving the claim. If you know that the claim implies the evidence (rather than only suggesting it), then you can place the claimant into a kind of crucible by offering to help compile the evidence. If they are cooperative, it weakens the argument but the truth gets closer as the evidence is compiled. If they are uncooperative, it is likely because they know the evidence will defeat their claim.

Answer 6

Absence of evidence becomes evidence of absence when it is inconsistent with theories of existence. If the data are consistent with the entity existing, but not being found due to random chance, then it wouldn't be appropriate to conclude the entity does not exist. However, if the random chance is very small, then the data do support the conclusion of absence.

For example: the theory "Dodos still live on island X, where dodos were historically last sighted." If the island has been scoured and no evidence of living dodos has been found, then that is strong evidence of absence.

On the other hand, the theory "Dodos still live somewhere in the world" requires a much more thorough search for absence of evidence to be considered evidence of absence.

Answer 7

The first question is: If X was present, how likely is it that we would have evidence for it?

I claim: There is an elephant in your kitchen. If this claim was true, it would be impossible to not have evidence of it. If there is no evidence of elephants in your kitchen, that's quite strong evidence for the absence of elephants in your kitchen.

I claim: There is a tiny and extremely well hidden camera in your kitchen. Here it is quite plausible that evidence is absent, even if the camera is there. So absence of evidence is relatively week evidence for the absence of the camera.

The second question is: How likely is it that X is present in the first place (before we started looking for evidence)? That might be difficult to say in some cases, easier in others. If the presence of X is a priori very likely, then the best explanation for absence of evidence is that we didn't look well enough for evidence, or it is hard to find. If the presence of X is a priori very unlikely, then the explanation for lack of evidence is that X is just not present.

I claim: "Yesterday, I threw a dice, and the number six came up 12 times in a row". Without evidence, you won't believe it. I claim: "Yesterday, I saw a black car in my street". Even without evidence, you'd probably believe me.