Thursday, July 03, 2003

In Response to Popular Demand: Causality and Inference: Back to Basics

Consider conditions X, A, and B.

We have observed conditions A and B.

We suspect condition X but we have not observed or studied it.

We have observed -- but only to the extent that we have observed -- that A almost invariably follows B. We have also observed that A rarely or never occurs when B does not occur (whether before A or after A).

In the absence of further observations, can we view B as a pretty good or excellent indicator of A?

In the absence of further observations, can we presume that B is a cause of A?

Can we say "yes" to the former question if we are unwilling to say "yes" to the latter?

Now suppose that A is "motorcycle trashing"; and that B is "motorcycle tattoo on forearm."

We might well think that it would be unwise to try to do away with motorcycle trashing A by doing away with motorcycle tattoos on forearms B. We might be so inclined to think because even though we have seen (thus far) that motorcycle trashing A always or almost happens when motorcycle tattoos on forearms B (of the eventual culprits) are present, we might have strong doubts that motorcycle tattoos on forearms B cause motorcycle trashing A. We might instead suspect that some third factor (e.g., X, which happens to be "gang membership") causes both motorcycle tattoos on forearms B and motorcycle trashing A.

But, if we suspect that factor X is lurking in the background, perhaps causing both B and A, and, if we believe that X, if present, may expose B as a spurious cause of A -- we may believe this, perhaps, because we may believe that further investigation will show (we suspect) that if a potential culprit is a gang member, this factor of gang membership makes the probability of motorcycle trashing high and, furthermore, that any added information about a tattoo on the potential culprit's forearm would add nothing to the probability that the potential culprit trashed a motorcycle -- if, in short, (we strongly suspect) the following pattern of causal influence obtains



















If we suspect that this pattern of causal influence obtains -- or if we suspect that it just cannot be that motorcycle tattoos on forearms increase the frequency of motor trashing or makes motorcycle trashing more probable -- does it follow that we should forego the use of B as evidence of A -- if, for example, (i) we have not made any observations in the past to confirm our suspicion about the causal potency of X (or some other factor); or -- alternatively -- (ii) we have made such observations about X but in this case we happen not to know if X -- gang membership -- is or is not present?

  • Note: In situation #(ii) the occurrence of B may be a good indicator of the (prior) existence of X. If so, the failure to observe X directly may be immaterial. So focus on scenario #(i) in the question directly above.
  • In the absence of something like causation -- or, if you prefer, in the absence of some "natural stability" in the phenomena that we may observe --, it may turn out that the observed connection (in the past) between A and B is just an accident, a coincidence and, thus, cannot be trusted to recur. This thought is what gives the belief in the importance of causality for inference its power! But ..., again, does it follow that human beings should abandon reliance on all "mere associations" when they are bereft of an articulable causal theory (or when they have no evidence to support whatever choate or inchoate causal theory they may happen to entertain)? But, by the same token, it really is true, isn't it, that mere association is not enough? The world is full of coincidences -- and you can find them (easily! everywhere!) -- you can find meaningless coincidences all around you -- if you just look for them.

    Further Comments and Questions about Causality and Inference

    Comment 1: Even if you are a believer in causation -- even if you believe that events in the space-time continuum can and do influence later events --, you may reject the intimation in my last blog that you (as a believer in causality) must believe in some underlying mechanism, some device or process that lies in some substratum, in some stratum below the level of phenomena. You might protest that the sort of notion of causation that I seem to be peddling is both unnecessarily mechanistic and unnecessarily reductionist. You might argue that you are entitled to believe in causation even if all that you believe is that phenomena can be explained by principles that express relationships between events in space and time and that there is no need to suppose that these causal principles or explanations somehow exist in or beneath the events that they describe. It is sufficient, you might say, that the "laws" -- or, better said, principles or law-like statements -- that you embrace -- such as [F = MA] or [e = m(c-squared)]? -- predict the relationships among phenomena in a wide variety of circumstances.

    Question: If this is what you think, why is it that causal "laws" or principles often or ordinarily do seem to rest on some image of a mechanism or real process that generates or controls the phenomena that one both uses as evidence and that one wants to explain -- e.g., an image such as a spinning atom surrounded by electrons in odd orbits; an image of a double helix? Granted, these "spatial" images sometimes or often collapse -- they come be seen as inadequate -- as scientific understanding progresses -- but perhaps this merely shows that science progresses. Is it the case that the progress of science often involves, not the elimination of spatial images of (hidden) processes or mechanisms, but, rather, the modification of old images or their replacement with new and better ones? (So: Kepler posits elliptical orbits rather than circular ones.) So is it true, after all, that a belief in causality involves or requires, at least sometimes, a belief -- a provisional belief, to be sure -- in the existence of underlying mechanisms or processes; and is it true that it cannot be said that "causal mechanisms" are merely or nothing more than disguised non-spatial principles that describe observed regularities or phenomena in nature? If one is to arrive at causal explanations, is it necessary to have a kind of "persuasive local ontology," a kind of vision of how (some) things just must work? (By the way: Why should we presume that spatial representations are not "principles"? Graphs are "spatial" {at least in two dimensions, and graphs can be multi-dimensional} -- but properly-constructed graphs are rigorously logical things. If they aren't "principles," what are they?)
    Counterpoint: Would one say of a causal explanation for, say, a social phenomenon -- e.g., "gang behavior" -- that it is necessary to have or develop a spatial representation or image of the mechanism or process that causes or influences this kind of phenomenon? (Answer: probably not, which may be a reason for the persistent belief in the existence of "souls." The causal explanation {if any} in this sort of situation might be in terms of the incorporeal principles -- principles and rules that exist but that cannot be seen (even in the mind's eye) -- principles that, it might be supposed, animate or govern (to some extent) the behavior of the members of a gang and the gang itself.)
    Comment 2: Causality implies that prior events influence future events. But human beings (and perhaps other animals) peer into the future and allow their vision(s) of the future -- of future events -- to influence their actions in the present. Does this mean that the future influences the present? If you are a believer in unidirectional causality, you will reply, "Certainly not!" You will say that the future influences prior events only in this sense: people's projections at time t of future events influence their decisions or choices at time t + 1, which in turn presumably influence yet later events. Hence, there is no violation of the premise that causality runs only in one direction and -- to be sure -- from the "past" to the "future." (You say my last statement is circular? I know the past, present, and the future when I see it ["them"?], b'gosh!)

    Comment 3: [I am preparing a comment -- a question, a hypothetical problem -- involving the "variables" (1) gang membership, (2) burglaries, and (3) tattoos. And at some appropriate point I will try to confound everything by mentioning the additional variable or factor, (4) the drinking of gin. This problem, if I can construct it, will raise two basic questions: (a) Can any set of numbers (alone) establish any causal relationship(s) among these three or four variables or factors?; and (b) If not, is evidence of the existence of any one of these three or four factors necessarily bereft of any probative value for any other factor (e.g., the commission of a burglary vel non)? But I do not yet have a suitably-crafted version of this hypothetical problem in hand -- and it is possible that I won't have the time to formulate it properly. Perhaps you can do so, Gentle and Wise Reader? (One of the matters or questions I have in mind is Judea Pearl's "d-separation" criterion for inferring causes from statistical data.)]

    Tuesday, July 01, 2003

    Causality and Inference Redux: Evidence Blogfans, Your Reading Assignment!

    On the topic of the relationship between causation and inference (which was the subject of my previous blog), please see Christian Borgelt & Rudolf Kruse, Probabilistic Networks and Inferred Causation, 18 Cardozo Law Review 2001 (1997).

  • You need the hard copy version of this article -- a LEXIS or WESTLAW version will not do -- because you need to see the authors' diagrams.
  • If you are not familiar with graph theory -- and even if you are --, you might want to skim (the more difficult) portions of Part I of the article. But plow ahead! Fear not! With a bit of effort, you can get the drift of the rest of the argument. And you will reap rewards from your labor -- and, to be sure, from your labour.
  • The main point of the article is a critique -- a gentle critique -- of a proposal by Judea Pearl for inferring causation from correlation, associations, or observed regularities. This critique is in itself very interesting, illuminating, and suggestive: it raises fundamental questions about the structure of causation or causal influence. But even if that critique does not interest you or if the phrasing of the athors' critique eludes your comprehension, read on!

    While (gently) questioning a particular approach to the problem of inferring causation, the authors remain largely convinced -- but with qualifications and hedges -- , the authors remained convinced of the importance of causal explanations for inference, and they serve up some familiar but very useful reminders of the perils of drawing conclusions on the basis of correlation or association alone. (I found it particularly reassuring to be reminded that "causal correlations are fairly rare." [I found this assertion reassuring because I agree with it: the notion that experience alone is "voiceless" plays a large part in my thinking about inference.])

    I am personally ontologically attracted -- what awful language, eh?! --, I am attracted to the thesis that in many or most domains of human life something like a principle of causation holds, that prior events do, in some way, generally influence subsequent events in the space-time continuum in which we seem to exist. I am also very strongly attracted to the hypothesis that the power of inference is greatly enhanced when human actors have and use plausible accounts of the mechanisms or processes that underlie "surface" phenomena, events, and associations. (One of my favorite cliches: experience does not speak for itself.)

    But there is a great practical difficulty (and, in an important sense, a theoretical one -- because the absence of human omniscience must figure large in any "theoretical" analysis of inference), -- there is, let me simply say, a VERY BIG difficulty: In many situations human comprehension of "causes" is extraordinarily frail. In these situations, how is inference to work (ideally, but for real human beings)?

    Even when human knowledge of underlying causes or mechanisms is limited, it remains true that experience and associations do not speak for themselves. The world is replete with spurious and misleading associations! So some sort of sense of how the world works perhaps -- very probably -- remains important for the drawing of sound inferences from observed or reported regularities in the world.

    So, Gentle Reader, where does all of this leave us -- and, for example, where does it leave jurors or where should it leave them when they turn to the job of assessing evidence of, say, the past criminal behavior of a defendant on trial for a crime or the defendant's habit of "associating with criminals"? What, if anything, should we tell jurors or what evidence, if any, should be withhold from their gaze to make sure that they do not make inferential mistakes?

    Your thoughts, Gentle Reader? (Don't be bashful! ... O.k., o.k., not-so-gentle readers can chime in too.)