Brit. J. Phil. Sci. 65 (2014), 251–267
In Defense of Reverse Inference
Edouard Machery
ABSTRACT
Reverse inference is the most commonly used inferential strategy for bringing images of
brain activation to bear on psychological hypotheses, but its inductive validity has recently been questioned. In this article, I show that, when it is analyzed in likelihoodist
terms, reverse inference does not suffer from the problems highlighted in the recent literature, and I defend the appropriateness of treating reverse inference in these terms.
1
2
3
4
5
Introduction
Reverse Inference
Reverse Inference Defended
3.1 Typical reverse inferences are fallacious
3.2 No quick and easy fix
3.3 A likelihoodist defense of reverse inference
3.4 An example
Appropriateness of the Likelihoodist Approach
4.1 Likelihoodist reverse inference is not applicable
4.2 Cognitive neuroscientists are not interested in comparative conclusions
4.3 Reverse inference and negative hypotheses
4.4 Likelihoodist reverse inference may confuse cognitive neuroscientists
4.5 Bayesian reverse inferences should be preferred to likelihoodist reverse
inferences
Conclusion
1 Introduction
Cognitive neuroscientists hold that neuroscientific data, particularly images of
brain activation obtained by means of fMRI, PET, or other technologies, can
be used to support or undermine psychological hypotheses about the processes and events underlying the capacity to read, recognize faces, ascribe
beliefs, or make moral judgments. To fulfill this goal, cognitive neuroscientists
and cognitive scientists have examined various inferential strategies for
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bringing neuroimages to bear on psychological hypotheses (Sternberg [2001],
[2011]; Shallice [2003]; Poldrack and Wagner [2004]; Henson [2005], [2006],
[2011]; Poldrack [2006], [2010]). In this article, I will discuss the most influential of these inferential strategies1: reverse inference.2 Despite its popularity,
the inductive validity of reverse inference has recently been questioned
(Henson [2005]; Poldrack [2006]), and an increasing number of cognitive
neuroscientists now view this inferential pattern with skepticism. In this article, I defend reverse inference: I argue that when reverse inference is recast in
likelihoodist terms, patterns of brain activation provide genuine evidence for
and against psychological hypotheses.
Here is how I will proceed: In Section 2, I describe reverse inference and I
illustrate its use in cognitive neuroscience. In Section 3, I show that when it is
cast in likelihoodist terms, reverse inference is immune to the main objections
against it. In Section 4, I defend the appropriateness of treating reverse inference in likelihoodist terms.3
2 Reverse Inference
When cognitive neuroscientists reverse infer, they conclude that a particular
psychological process or event (be it a cognitive process, an emotion, a mood,
etc.) is recruited by an experimental task from the fact that a particular pattern
of brain activation is elicited during this task. As it is typically used in cognitive neuroscience, reverse inference rests on two premises and has the following structure:
Argument structure of typical reverse inferences:
(A) When psychological process, p, is recruited by a task, pattern of brain
activation, E, is likely to be found.
(B) In task T, pattern of brain activation, E, was found.
(C) Hence, psychological process p was recruited by task T.
The conclusion, (C), does not, and is not meant to, follow deductively from
premises (A) and (B). Rather, reverse inferences are, and are meant to be,
inductive: Premises (A) and (B) are meant to provide a non-conclusive reason
to hold (C). Premise (A) is typically supported by surveying, often informally,
the existing literature in neuroimagery. Such literature reviews examine
whether tasks that are believed to recruit psychological process p are likely
1
2
3
For instance, Anderson ([2010a]) notes the frequency of reverse inferences in Neuroeconomics:
Decision Making and the Brain.
For a discussion of another influential strategy—Henson’s ([2005], [2006]) function-to-structure
inference or forward inference—see (Machery [2012]).
In this article, ‘likely’ does not have the technical sense that it has in the likelihoodist literature.
Rather, ‘likely’ will be used in its everyday sense as a synonym of ‘probable’.
In Defense of Reverse Inference
253
to elicit pattern E. Premise (B) describes the experimental data to which
reverse inference is applied.
Consider, for instance, Greene et al.’s ([2001]) article on moral judgements.
While undergoing brain scanning, participants were presented with sixty dilemmas that were classified as non-moral, moral-impersonal, or moralpersonal. The footbridge trolley dilemma (in which participants judge whether
it is permissible to push someone from a footbridge in order to stop a runaway
trolley that is about to kill five people) illustrates the class of moral-personal
dilemmas, while the bystander trolley dilemma (in which participants judge
whether it is permissible for a bystander to push a lever that will divert a
runaway trolley that is about to kill five people onto a sidetrack where the
trolley will kill a single person) illustrates the class of moral-impersonal dilemmas. Greene and colleagues singled out the brain areas that responded
more to moral-personal dilemmas than to moral-impersonal and non-moral
dilemmas—BA 9 and 10 in the medial frontal gyrus, BA 31 in the posterior
cingulate gyrus, and BA 39 in the angular gyrus (bilateral)—as well as those
areas that responded less to the former class of dilemmas than to the latter
class of dilemmas—BA 46 in the middle frontal gyrus (right) and BA 7/40 in
the parietal lobe (bilateral). The second premise of Greene et al.’s reverse
inference describes this pattern of brain activation. Furthermore, Greene
and colleagues review the empirical literature showing that BA 9 and 10,
BA 31, and BA 39 are activated in tasks recruiting emotional processing: citing
four cognitive-neuroscientific studies, they write that ‘[r]ecent functional imaging studies have associated each of these areas with emotion’ ([2001], p.
2107). Citing two studies, they also assert that BA 46 and BA 7/40 are
‘both associated with working memory’. This informal, succinct literature
review provides evidence for the first premise of their reverse inference. On
the basis of the pattern of brain activation found in their experiments and of
their succinct literature review, Greene et al. ([2001], p. 2106) conclude that
[. . .] from a psychological point of view, the crucial difference between
the trolley dilemma and the footbridge dilemma lies in the latter’s
tendency to engage people’s emotions in a way that the former does not.
The thought of pushing someone to his death is, we propose, more
emotionally salient than the thought of hitting a switch that will cause a
trolley to produce similar consequences, and it is this emotional response
that accounts for people’s tendency to treat these cases differently.
Greene and colleagues’ use of brain imagery data is a crystal-clear instance
of reverse inference, and it can be easily recast along the lines of the argument
structure presented above:
(A) When emotional processing is elicited by a task, BA 9 and 10, BA 31,
and BA 39 are likely to be activated.
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(B) Reading moral-personal dilemmas resulted in greater activation of BA
9 and 10, BA 31, and BA 39 than reading moral-impersonal and
non-moral dilemmas.
(C) Hence, moral-personal dilemmas (e.g. the footbridge trolley dilemma)
elicit greater emotional processing than moral-impersonal (e.g. the
bystander trolley dilemma) or non-moral dilemmas.
Consider, more briefly, an additional example. Richeson et al.’s ([2003])
experiment was meant to test the hypothesis that interracial interactions
weaken people’s executive resources (as shown by, for example, Richeson
and Shelton [2003]) because executive function is a finite resource that can
be temporarily depleted. White participants were given an implicit association
test (IAT), interacted with a black participant, then completed a Stroop task4;
in a distinct experiment, they were presented with black faces while undergoing brain scanning. For present purposes, let’s focus on this latter experiment,
which involves a reverse inference. Richeson and colleagues found that, while
viewing black faces, activation in the right dorsolateral prefrontal cortex
(DLPFC) correlated with people’s implicit bias toward Blacks, as measured
by the IAT. This provides the content of the second premise of their reverse
inference. Based on the cognitive-neuroscientific literature, they assume that
reliance on executive function activates the right DLPFC: as they put it
([2003], p. 1323), citing about twenty studies, ‘we based the present investigation on emerging literature in cognitive neuroscience that has identified a
complex circuit of brain structures—consisting, in part of dorsolateral prefrontal cortex (DLPFC) and anterior cingulated cortex (ACC)—that supports
executive control’. This literature provides empirical support for the first
premise of their reverse inference. The conclusion of their reverse inference
is that, the greater one’s implicit bias is, the more one attempts to control it,
and thus the more one’s executive function is taxed (which contributes to the
explanation of why more biased individuals tend to do worse on the Stroop
task after having met a black experimenter). This reverse inference can also be
recast along the lines of the argument structure presented earlier:
(A) When executive function is recruited, the DLPFC is likely to be
activated.
(B) When presented with black faces, the greater a participant’s implicit
bias, the more the DLPFC was activated.
(C) Hence, when presented with black faces, the greater a participant’s
implicit bias, the more people’s executive function was recruited.
4
In a Stroop task, participants are asked to read the names of colors that are printed in a color
different from the colors named (for example, participants are asked to read ‘yellow’ when it is
written in red).
In Defense of Reverse Inference
255
In these two cases, as well as in many other cases, cognitive neuroscientists
conclude that a task recruits a particular psychological process or elicits a
particular mental state on the grounds that the brain areas activated in the
task are known to be activated when this process is recruited or when this
mental state is elicited. But are they justified in so doing? Under which conditions are cognitive neuroscientists justified in treating patterns of brain
activation as evidence for the conclusions of reverse inferences? In the remainder of this article, I will attempt to delineate these conditions.5
3 Reverse Inference Defended
3.1 Typical reverse inferences are fallacious
When they reverse infer, cognitive neuroscientists typically treat patterns of
brain activation as evidence that particular psychological processes are recruited by particular tasks on the grounds that these patterns of brain activation are likely to be found when these processes are recruited. The problem is
that, for a pattern of activation, E, to be evidence for the conclusion that a
psychological process, p, is recruited by a task, T, it is not sufficient that E be
likely to occur when p is recruited, because E could be even more likely to
occur when psychological processes other than p are recruited. So, a particular
pattern of brain activation constitutes evidence for the conclusion of a reverse
inference if and only if it is more likely to occur when the psychological process under consideration is recruited by an experimental task than when it is
not recruited.
This observation is the gist of Poldrack’s ([2006]) influential critique of
reverse inference as it is typically applied in cognitive neuroscience (see also
Henson [2005]; Harrison [2008]): it is fallacious to infer from a particular
pattern of brain activation and from the fact that tasks recruiting a particular
psychological process, p, are likely to elicit this pattern that the task under
consideration recruits p because one then does not take into account the probability of obtaining this pattern of brain activation when p is not recruited.
Poldrack puts this point in simple Bayesian terms. According to Bayesians
(for example, Earman [1992]; Howson and Urbach [1993]), a piece of evidence,
E, supports a hypothesis, H, if and only if the posterior probability of H
conditional of E is larger than its prior probability. In turn, as H and H
are mutually exclusive and jointly exhaustive,6 this inequality holds if and only
E is more likely if H is true than if H is false. Thus, a particular pattern of brain
5
6
In the terminology of Bandyopadhyay and Brittan ([2006]), I will focus on ‘the evidence question’—under which conditions do patterns of brain activation provide evidence for the conclusions of reverse inferences?—rather than ‘the belief question’—under which conditions are
cognitive neuroscientists justified in believing the conclusion of a reverse inference?
I am grateful to a reviewer for highlighting this assumption.
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activation supports the hypothesis that psychological process p is recruited by
T if and only if the probability of the occurrence of this pattern of brain
activation if p is recruited, is higher than the probability of its occurrence if
p is not recruited.
3.2 No quick and easy fix
One may think that a small fix is all that is needed to remedy the invalidity of
reverse inferences (e.g. Harrison [2008], pp. 536–7). Cognitive neuroscientists
should compare the probability of the occurrence of the pattern of brain activation observed during T if p is recruited and the probability of its occurrence if p is not recruited, instead of just taking into account the former
probability. A pattern of activation provides evidence for the conclusion
that p is recruited by T if and only if the former probability is larger than
the latter.
While cognitive neuroscientists would be justified in treating patterns of
brain activation as evidence for the conclusions of reverse inferences if this
necessary and sufficient condition were met, this Bayesian characterization of
reverse inference is not very useful for two distinct reasons. First, in many
cases, cognitive neuroscientists have no sense of the probability of obtaining a
particular pattern of brain activation if psychological process p is not recruited
by experimental tasks and, as a result, they do not know whether the observed
pattern of activation gives them a reason to conclude that the psychological
process of interest was involved during the task under consideration. Second,
as meta-analyses and systematic literature reviews of the activation of particular brain areas across experimental tasks show (for example, for the precuneus, see Cavanna and Trimble [2006]; for the posterior cingulate cortex, see
Vann et al. [2009]; see also Anderson [2010b]; Yarkoni et al. [2010]), many
brain areas are such that they are activated when many different psychological
processes are recruited. As a result, the probability of obtaining a particular
pattern of brain activation when the psychological process of interest is not
recruited is likely to be high. In this case, observing the relevant pattern of
brain activation can only provide at best weak evidence, if any evidence at all,
for the psychological hypothesis under consideration.
At this point, it may be tempting to simply reject every inference that a
particular psychological process is recruited by an experimental task on the
basis of the activation of the brain during this task. Influenced by Poldrack,
many cognitive neuroscientists and cognitive scientists now regard reverse
inference with skepticism,7 and some recommend that it be completely
7
See, for example, (McCabe and Castel [2008], p. 345; Young and Saxe [2008], p. 1404; Greene
and Paxton [2009], p. 2 of the supporting information; Gonsalves and Cohen, [2010], p. 746).
In Defense of Reverse Inference
257
discarded. For instance, Anderson ([2010a], p. 152) writes that ‘[t]he solution
to the problems exemplified by neural correlate work and reverse inference is
not to use the techniques with caution, but to stop doing it’. However, this
rejection would deprive cognitive neuroscientists of the most commonly used
inferential strategy for bringing neuroscientific evidence to bear on psychological hypotheses, and one should only discard reverse inference altogether if
there is no alternative formulation of the conditions under which cognitive
neuroscientists are justified to treat patterns of brain activation as evidence for
the conclusions of reverse inferences.
3.3 A likelihoodist defense of reverse inference
The first step for developing this alternative formulation involves distinguishing two conceptions of evidence. According to the first conception (endorsed
by Bayesians), the evidential relationship is a relation between an empirical
result and a particular hypothesis: an empirical result supports (undermines,
or neither supports nor undermines) a particular hypothesis. When evidence is
understood this way, an empirical result supports a hypothesis if and only if it
is more likely if the hypothesis is true than if it is false. According to a second
conception (embraced by likelihoodists such as, for example, Edwards [1972];
Royall [1997]; Forster and Sober [2004]; Sober [2008]; Blume [2011]; Taper
and Lele [2011]), the evidential relationship is a relation between an empirical
result and two competing hypotheses8: an empirical result supports a particular hypothesis more than (or less than or to the same degree as) another hypothesis. In this case, evidence is comparative. When evidence is understood
this way, an empirical result supports a hypothesis over another one if and
only if it is more likely if the former hypothesis is true than if the latter is true.
Reverse inference can thus be recast in likelihoodist terms: cognitive neuroscientists are justified in treating a pattern of brain activation, E, as providing
evidence for the hypothesis that a task, T, recruits a first psychological process, p1, over the hypothesis that it recruits another psychological process, p2,
if and only if E is more likely to be found when p1 is recruited than when p2 is
recruited.9
So recast, reverse inference does not suffer from the problems highlighted
earlier in this section. First, there is now nothing fallacious in overlooking the
probability that a pattern of brain activation occurs when a particular psychological process is not recruited. Second, it is not of limited utility: neither
cognitive neuroscientists’ ignorance of this probability nor its possible high
value stand in the way of using patterns of brain activation as evidence for
8
9
Or more than three if more than two hypotheses are competing.
As noted by an anonymous reviewer, this is reminiscent of Lipton’s inference to the best explanation (Lipton [1991]).
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particular psychological hypotheses. Cognitive neuroscientists only need to
take into account the probability that the pattern of brain activation under
consideration occurs when the specific psychological processes, which are
mentioned in the competing hypotheses, are recruited by experimental tasks.
3.4 An example
If one views reverse inference in Bayesian terms, one is forced to conclude that
Greene and colleagues invalidly inferred that moral-personal dilemmas elicit
more emotional processing than moral-impersonal and non-moral dilemmas.
They did not take into account the probability that the medial frontal gyrus,
the posterior cingulate gyrus, and the angular gyrus are activated when psychological processes other than emotional processing are recruited by experimental tasks. Furthermore, it is unclear whether taking into account this
probability so as to counter the invalidity charge would have helped Greene
and colleagues. Because, as Klein ([2011]) argues, the neuroscientific literature
suggests that the medial frontal gyrus, the posterior cingulate gyrus, and the
angular gyrus are activated when processes other than emotional processing
are involved in a task. Greene et al.’s findings could have provided at best
weak evidence for their hypothesis.
In contrast, when Greene and colleagues’ reverse inference is recast in likelihoodist terms, it becomes irrelevant that the medial frontal gyrus, the posterior cingulate gyrus, and the angular gyrus are activated when a variety of
psychological processes other than emotional processing are recruited by experimental tasks. Let’s see in detail how this works.
In a likelihoodist framework, one always compares several particular
hypotheses, and one examines the probability of the evidence in light of
these hypotheses. The relevant hypotheses for Greene and colleagues are the
following ones:
H1: People respond differently to moral-personal and moralimpersonal dilemmas because the former elicit more emotional processing than the latter.
H2: People respond differently to moral-personal and moralimpersonal dilemmas because the single moral rule that is applied to
both kinds of dilemmas (for example, the doctrine of double effect)
yields different permissibility judgments.
Greene and colleagues favour H1, whereas other authors (for example,
Nichols and Mallon [2006]) favour H2. Greene and colleagues correctly treated the observed pattern of activation as evidence for the hypothesis they
favour if the probability that the medial frontal gyrus, the posterior cingulate
gyrus, and the angular gyrus are activated during emotional processing is
In Defense of Reverse Inference
259
larger than the probability that they are activated when a moral rule or a
moral principle such as the doctrine of double effect is applied to a case. As
this inequality holds, evidence does support the hypothesis that
moral-personal dilemmas elicit more emotional processing than
moral-impersonal and non-moral dilemmas over the hypothesis that a single
moral rule was applied to both kinds of dilemmas (for another example, see
Section 4.2).
4 Appropriateness of the Likelihoodist Approach
In this final section, I examine five objections that could be raised against the
likelihoodist treatment of reverse inference presented in this article. These
objections assert successively that likelihoodist reverse inference is not applicable; that, even if it is applicable, it is not useful for cognitive neuroscientists;
that, in any case, it often does not differ from Bayesian reverse inference; that,
even if it is applicable, useful, and differs from Bayesian reverse inference; it is
confusing; and finally that, even if it is applicable, useful, differs from
Bayesian reverse inference, and is not distinctively confusing, it is not needed.
4.1 Likelihoodist reverse inference is not applicable
According to the likelihoodist framework developed here, reverse inference
can only be useful if cognitive neuroscientists have some sense of how likely it
is that some pattern of activation will be observed if two distinct psychological
processes, p1 and p2, are recruited by experimental tasks. However, one could
object that this knowledge is often lacking.10
This objection rightly notes that likelihoodist reverse inference can only be
used when two competing psychological hypotheses, H1 and H2, are available
and when, based on the existing literature, cognitive neuroscientists expect
two different patterns of brain activation if p1 is recruited and if p2 is recruited.
In some research contexts, this knowledge will be missing, and likelihoodist
reverse inference won’t be applicable there. On the other hand, in some contexts, this knowledge is available, and conceiving reverse inference in likelihoodist terms allows cognitive neuroscientists to apply reverse inference
there.
One may wonder how in practice one determines the probabilities that a
particular pattern of brain activation occurs if p1 is recruited and if p2 is
recruited, and whether determining these probabilities relies on past reverse
inferences.11 While past reverse inferences may play a role, they do not seem
necessary. To determine whether it is likely that one would observe a
10
11
I owe this objection to Matt Bateman.
I owe this question to Rik Henson.
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Edouard Machery
particular pattern of brain activation if, say, the hypothesis that psychological
process p1 is involved, one can look at other tasks (tasks different from T) that
are known to recruit p1 based on behavioural data, neuropsychological data
such as dissociations, self-reports, and so on. To illustrate, consider Greene
et al. ([2001]). Many tasks are known to recruit emotions on the basis of
behavioural data, physiological data, and self-reports. One can examine
which brain areas tend to be activated in these tasks in order to get a sense
of how likely it is that a particular pattern of activation is found if emotional
processing is elicited. Importantly, this procedure assumes that the neural
correlate of a particular psychological process or of a particular psychological
state (for example, fear) does not vary from one task to the other.
4.2 Cognitive neuroscientists are not interested in comparative
conclusions
If reverse inference is understood in likelihoodist terms, it is intrinsically comparative: reverse inference can only show that evidence supports a particular
psychological hypothesis more than a competing one. One may thus object
that cognitive neuroscientists are not merely (if at all) interested in comparative claims; rather, they want to provide evidence for their hypothesis, understood in non-comparative terms. For instance, Greene and colleagues’ goal
was to provide evidence for the hypothesis that moral-personal dilemmas elicit
more emotional processing than moral-impersonal dilemmas and non-moral
dilemmas, not merely to provide evidence supporting this hypothesis over a
competing hypothesis (for example, that a single moral rule was applied to
both kinds of dilemmas). Understood in likelihoodist terms, reverse inference
is thus unable to fulfill cognitive neuroscientists’ goals.12
There are two mutually-consistent responses to this objection: first, appearances notwithstanding, cognitive neuroscientists who use reverse inference are
in fact sometimes, and perhaps often, interested in comparative claims;
second, when they are not, they are typically mistaken to use reverse inference.
I briefly elaborate on these two responses.
First, when cognitive neuroscientists use brain images to support a psychological hypothesis, they are sometimes weighing on a controversy between two
competing psychological hypotheses that disagree about the nature of the
processes involved in some task. Typically, one of these two hypotheses entails
that a first psychological process is recruited by this task, while the other
hypothesis entails that a distinct process is recruited. In these cases, cognitive
neuroscientists’ goal is, at least implicitly, comparative, and reverse inference
conceived in likelihoodist terms is well suited to this goal.
12
I owe this objection to Michael Anderson, Felipe de Brigard, and Russ Poldrack.
In Defense of Reverse Inference
261
Indeed, it is easy to recast some uses of reverse inference in cognitive neuroscience in comparative terms, even when reverse inference was not originally
presented to support a comparative conclusion. The discussion of Greene
et al. ([2001]) in Section 3.4 illustrates this claim.
More important, some existing cognitive–neuroscientific studies are explicitly comparing two psychological hypotheses, and such comparisons amount
to applying implicitly the likelihoodist reverse inference described in this article. Fernandes et al.’s ([2005]) goal was to test two alternative hypotheses that
had been put forth to explain the effect of divided attention during episodic
recollection.13 According to the first hypothesis, H1, episodic retrieval is disrupted by a concurrent task because retrieval and this task compete for general
attentional resources. According to the second hypothesis, H2, this disruption
is due to the fact that retrieval and the concurrent task ‘compete for specific
structural representations’ (p. 1115), viz. to the fact that the concurrent task
involves retrieving some information (for example, phonological and word
representations) that is related to what one tries to remember. While undergoing brain scanning, participants were asked to perform a word-recognition
task either without a competing task (full-attention condition) or with either a
word-related or a digit-related concurrent task (divided-attention condition).
Based on the existing literature about the neural correlates of verbal processing, the use of domain-general attentional resources, and memory retrieval,
Fernandes and colleagues held that, if H1 were true—if memory retrieval taps
into general attentional resources—then a particular pattern of brain activation would be observed: more activation in the DLPFC for the word-related
task than for the digit-related task and no difference between the word-related
and digit-related task in the neural correlates of verbal processing and memory
retrieval (left inferior frontal, left temporal, and left supramarginal cortex), as
well as no difference between these two tasks in the areas related to memory
retrieval (hippocampus, parietal lobe, precuneus). They also held that, if H2 is
true, this pattern of brain activation should not be observed. Rather, a different pattern should be found, involving a difference between the word-related
and digit-related tasks in the neural correlates of verbal processing and
memory retrieval. The latter pattern having been observed, they drew the
following comparative conclusion ([2005], p. 1115): ‘Results also support a
component-process model of retrieval which posits that MTL-mediated
(medial temporal lobe) retrieval does not compete for general cognitive resources but does compete for specific structural representations’. This is a
clear (albeit implicit) likelihoodist use of reverse inference.
However, it is also true that some other uses of reverse inference cannot be
so recast because reverse inference is then not used (even implicitly) to weigh
13
I am grateful to Felipe de Brigard for this example.
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Edouard Machery
on a controversy between two psychological hypotheses. In these cases, reverse inference will typically not be applicable. The reason is that reverse
inference cannot be put in likelihoodist terms, and has to be recast in
Bayesian terms. Then, on pain of committing a fallacy, cognitive neuroscientists have to take into account the probability of observing the pattern of
activation obtained in the task under consideration if the psychological hypothesis is false. But, this probability is often unknown, and, when it is known,
it often turns out to be high (because many psychological processes produce
this pattern of activation).
It is unclear how often reverse inference can be recast in likelihoodist terms,
but one can be confident that this is often possible when brain imagery data
are used for psychological purposes—to better understand which cognitive
processes or psychological states are involved in a particular task—because
cognitive neuroscientists then start with existing psychological hypotheses
about these processes or states. They bring a new form of data to bear on a
few competing hypotheses.
A philosophically-minded reader could perhaps push the objection under
consideration one step further and ask whether the interpretation of reverse
inference in likelihoodist, comparative terms is committed to the controversial
claim that evidential support is necessarily comparative.14 However, this interpretation is compatible with the view that there are two distinct notions of
evidential support: a comparative and a non-comparative notion. But then,
our reader could object, if I do not reject the notion of non-comparative
evidential support, why do I think that cognitive neuroscientists should be
aiming for contrastive evidential support rather than non-comparative evidential support? The reason is that, in many inferential contexts in cognitive
neuroscience (Section 3), it is dubious that non-comparative evidential support can be obtained, while contrastive evidential support is available. In these
contexts, cognitive neuroscientists should aim for the latter.
4.3 Reverse inference and negative hypotheses
The third objection follows up on the second objection. Some psychological
controversies do not pit a first hypothesis, H1—that a particular psychological
process, p1, is recruited by a task—against a competing hypothesis, H2—that
another particular psychological process, p2, is recruited by this task. Rather,
they pit H1 against its negation, namely, the hypothesis that it is not the case
that p1 is recruited by this task. For this kind of controversy, showing that
14
I owe this objection to a reviewer.
In Defense of Reverse Inference
263
P(EjH1) > P(EjH2) amounts to showing that P(EjH1) > P(EjH1), and likelihoodist and Bayesian reverse inferences are identical.15
My response can be brief as it is similar to the response provided above.
When a psychological controversy has this form, reverse inference will often
not be applicable.
4.4 Likelihoodist reverse inference may confuse cognitive
neuroscientists
The fourth objection is also connected to the comparative nature of likelihoodist reverse inference. One could concede that reverse inference can be put in
likelihoodist terms, but object that putting it in these terms would be dangerous because cognitive neuroscientists are likely to forget its comparative
nature. They are thus likely to interpret the conclusions of likelihoodist reverse
inferences in non-comparative terms.16 For instance, cognitive neuroscientists
may be prone to conclude from Greene et al. ([2001]) that evidence suggests
that moral-personal dilemmas elicit more emotional processing than
moral-impersonal dilemmas and non-moral dilemmas. This conclusion is
not comparative and it is not supported by the likelihoodist reverse inference.
This objection should be resisted. That a particular form of inference can be
misused or misunderstood is no argument against it; it merely shows that
cognitive neuroscientists and psychologists should be cautious. Indeed,
every form of inference carries some risks of misunderstanding and misapplication, and, if carrying such a risk were a ground for rejecting a form of
inference, scientists would be left with no way to draw conclusions from
data. For instance, statisticians and methodologists have often noted that
null hypothesis significance testing prompts psychologists to mistake significance values for the posterior probability that the null hypothesis is true (for
example, Morrison and Henkel [1970]; Oakes [1986]; for discussion, see
Machery [unpublished]). Closer to home, reverse inference conceived in
Bayesian terms can also lead to misuses or misunderstandings because cognitive neuroscientists may overlook that the validity of a Bayesian reverse inference depends on the probability of obtaining the pattern of activation
under consideration if the psychological hypothesis is false, or they may confuse the claim that evidence supports a particular hypothesis for the claim that
the posterior probability of this hypothesis is high.
15
16
Mazviita Chirimuuta and Michael Anderson raised an objection along these lines.
I owe this objection to Russ Poldrack.
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Edouard Machery
4.5 Bayesian reverse inferences should be preferred to likelihoodist
reverse inferences
Finally, one could object that I have given short shrift to the quick fix of
reverse inference presented in Section 3.2. When cognitive neuroscientists
are able to estimate the probability of obtaining the pattern of activation
under consideration if the psychological hypothesis is false, and if this probability is smaller than the probability of observing the pattern of activation
under consideration if the psychological hypothesis is true, they are justified in
treating the relevant pattern of brain activation as providing non-comparative
evidence for the conclusion of the relevant reverse inference.17
The problem, however, is that for many areas we do not have such estimates. Fortunately, when reverse inference is recast in likelihoodist terms,
cognitive neuroscientists can do without these estimates. In other cases, because the probability of obtaining the pattern of activation under consideration if the psychological hypothesis is false is high, the probability of a
pattern of activation if process p is recruited and if it is not recruited are
similar, and the pattern of activation under consideration does not provide
evidence for the psychological hypothesis of interest. For instance, Yarkoni
et al. ([2011]) showed that the anterior cingulate and anterior insula are active
in many different tasks. Fortunately, the similarity of the probability of a
pattern of activation if process p is recruited and if it is not recruited is not
relevant when reverse inference is recast in likelihoodist terms.
Finally, it is important to see that our capacity to predict with a surprising
accuracy which of a number of tasks, a participant is engaged in on the basis of
brain imagery data (for example, Poldrack et al. [2009]; Yarkoni et al. [2011])
does not justify relying on Bayesian reverse inference. These studies are only
able to provide an estimate of P(EjH) and to compute P(HjE) because they
restrict the space of possible hypotheses to a group of known, mutually-exclusive hypotheses. In effect, they are comparing P(EjH1) to P(EjH2) to
P(EjH3), and so on. If anything, this is in the spirit of likelihoodist reverse
inference.
5 Conclusion
Reverse inference is a common inferential strategy in cognitive neuroscience.
It allows cognitive neuroscientists to mend the bridge between the brain and
the mind by turning brain images into data that bear on psychological hypotheses. From a Bayesian point of view, typical reverse inferences are invalid
because they do not take into account the probability that the pattern of
brain activation would have been obtained if the psychological hypothesis
17
I owe this objection to Russ Poldrack.
In Defense of Reverse Inference
265
were false. Reformulated in Bayesian terms, reverse inference seems often of
little use as too often either we do not know the relevant probabilities or the
pattern of brain activation would probably have been obtained if the psychological hypothesis were false. By and large, cognitive neuroscientists have
concluded from this analysis that reverse inference is at best a suspect form
of inference, while persisting in using it to draw conclusions about the mind.
However, these problems are avoided if reverse inference is recast in likelihoodist terms. So recast, reverse inference allows cognitive neuroscientists to
use brain images to determine which of two competing psychological hypotheses is best supported. A likelihoodist approach to reverse inference is partly
restrictive: the range of its correct application is narrower than the range of its
typical applications. Cognitive neuroscientists must be comparing two distinct
psychological hypotheses: task T recruits psychological process p1 versus task
T recruits psychological process p2 (Sections 4.2 and 4.3); they must have a
good sense of how likely it is that a pattern of activation would be observed if
p1 and if p2 were recruited (Section 4.1); and they must keep in mind that, so
understood, reverse inference can only lead to comparative conclusions
(Sections 4.4). When these conditions are not met, reverse inference is typically
not applicable. On the other hand, a likelihoodist approach is only partly
restrictive: It allows reverse inference to be used when these conditions are
met (see, e.g. Fernandes et al. [2005]); it does not recommend getting rid of
reverse inference entirely (as, for example, Anderson [2010a] does); and it does
not depend on obtaining the kind of information that is needed to apply a
Bayesian reverse inference.
Acknowledgements
Many thanks to Michael Anderson, Felipe de Brigard, Mazviita Chirimuuta,
Clark Glymour, Rik Henson, Alexa Morcom, Russ Poldrack, Mark Sprevak,
and two anonymous reviewers for comments on previous versions of this
article.
Department of History and Philosophy of Science
University of Pittsburgh
1017CL, Pittsburgh, 15260 PA, USA
[email protected]
References
Anderson, M. L. [2010a]: ‘Review of Neuroeconomics: Decision Making and the
Brain’, Journal of Economic Psychology, 31, pp. 151–4.
Anderson, M. L. [2010b]: ‘Neural Reuse: A Fundamental Organizational Principle of
the Brain’, Behavioral and Brain Sciences, 33, pp. 245–313.
266
Edouard Machery
Bandyopadhyay, P. S. and Brittan, G. C. [2006]: ‘Acceptibility, Evidence, and Severity’,
Synthese, 148, pp. 259–93.
Blume, J. D. [2011]: ‘Likelihood and Its Evidential Framework’, in P. S.
Bandyopadhyay and M. Forster (eds), Hanbook of Philosophy of Statistics,
Oxford: Elsevier, pp. 493–512.
Cavanna, A. E. and Trimble, M. R. [2006]: ‘The Precuneus: A Review of its Functional
Anatomy and Behavioural Correlates’, Brain, 129, pp. 564–83.
Earman, J. [1992]: Bayes or Bust: A Critical Examination of Bayesian Confirmation
Theory, Cambridge, MA: MIT Press.
Edwards, A. W. F. [1972]: Likelihood: An Account of the Statistical Concept of
Likelihood and Its Application to Scientific Inference, Cambridge: Cambridge
University Press.
Fernandes, M. A., Moscovitch, M., Ziegler, M. and Grady, C. [2005]: ‘Brain Regions
Associated with Successful and Unsuccessful Retrieval of Verbal Episodic Memory
as Revealed by Divided Attention’, Neuropsychologia, 43, pp. 1115–27.
Forster, M. and Sober, E. [2004]: ‘Why Likelihood’, in M. Taper and S. Lele (eds),
Likelihood and Evidence, Chicago: University of Chicago Press, pp. 153–65.
Gonsalves, B. D. and Cohen, N. J. [2010]: ‘Brain Imaging, Cognitive Processes, and
Brain Networks’, Perspectives on Psychological Science, 5, pp. 744–52.
Greene, J. D. and Paxton, J. M. [2009]: ‘Patterns of Neural Activity Associated with
Honest and Dishonest Moral Decisions’, Proceedings of the National Academy of
Science, 106, pp. 12506–11.
Greene, J. D., Sommerville, R. B., Nystrom, L. E., Darley, J. M. and Cohen, J. D.
[2001]: ‘An fMRI Investigation of Emotional Engagement in Moral Judgment’,
Science, 293, pp. 2105–8.
Harrison, G. [2008]: ‘Neuroeconomics: A Rejoinder’, Economics and Philosophy, 24,
pp. 533–44.
Henson, R. [2005]: ‘What Can Functional Neuroimaging Tell the Experimental
Psychologist?’, The Quaterly Journal of Experimental Psychology, 58A, pp. 193–233.
Henson, R. [2006]: ‘Forward Inference Using Functional Neuroimaging: Dissociations
versus Associations’, Trends in Cognitive Sciences, 10, pp. 64–9.
Henson, R. [2011]: ‘How to Discover Modules in Mind and Brain: The Curse of
Nonlinearity, and Blessing of Neuroimaging. A Comment on Sternberg’,
Cognitive Neuropsychology, 28, pp. 209–23.
Howson, C. and Urbach, P. [1993]: Scientific Reasoning: The Bayesian Approach,
Chicago: Open Court.
Klein, C. [2011]: ‘The Dual Track Theory of Moral Decision-Making: A Critique of the
Neuroimaging Evidence’, Neuroethics, 4, pp. 143–62.
Lipton, P. [1991]: Inference to the Best Explanation, London: Routledge.
Machery, E. [2012]: ‘Dissociations in Cognitive Neuroscience and in
Neuropsychology’, Philosophy of Science, 79, pp. 490–518.
McCabe, D. P. and Castel, A. D. [2008]: ‘Seeing Is Believing: The Effect of Brain
Images on Judgments of Scientific Reasoning’, Cognition, 107, pp. 343–52.
Morrison, D. E. and Henkel, R. E. [1970]: The Significance Test Controversy: A Reader,
New Brunswick, NJ: Transaction Publishers.
In Defense of Reverse Inference
267
Nichols, S. and Mallon, R. [2006]: ‘Moral Dilemmas and Moral Rules’, Cognition, 100,
pp. 530–42.
Oakes, M. [1986]: Statistical Inference: A Commentary for the Social and Behavioural
Sciences, Chichester: John Wiley and Sons.
Poldrack, R. A. [2006]: ‘Can Cognitive Processes be Inferred from Neuroimaging
Data?’, Trends in Cognitive Sciences, 10, pp. 59–63.
Poldrack, R. A. [2010]: ‘Mapping Mental Function to Brain Structure: How Can
Cognitive Neuroimaging Succeed?’, Perspectives on Psychological Science, 5,
pp. 753–61.
Poldrack, R. A., Halchenko, Y. and Hanson, S. J. [2009]: ‘Decoding the Large-Scale
Structure of Brain Function by Classifying Mental States across Individuals’,
Psychological Science, 20, pp. 1364–72.
Poldrack, R. A. and Wagner, A. D. [2004]: ‘What Can Neuroimaging Tell us about the
Mind?’ Current Directions in Psychological Science, 13, pp. 177–81.
Richeson, J. A. and Shelton, J. N. [2003]: ‘When Prejudice Does Not Pay: Effects of
Interracial Contact on Executive Function’, Psychological Science, 14, pp. 287–90.
Richeson, J. A., Baird, A. A., Gordon, H. L., Heatherton, T. F., Wyland, C. L.,
Trawalter, S. and Shelton, J. N. [2003]: ‘An fMRI Investigation of the Impact of
Interracial Context on Executive Function’, Nature Neuroscience, 6, pp. 1323–8.
Royall, R. M. [1997]: Statistical Evidence: A Likelihood Paradigm, London: Chapman
and Hall.
Shallice, T. [2003]: ‘Functional Imaging and Neuropsychology Findings: How Can
They Be Linked?’, NeuroImage, 20, pp. S146–54.
Sober, E. [2008]: Evidence and Evolution: The Logic behind the Science, Cambridge:
Cambridge University Press.
Sternberg, S. [2001]: ‘Separate ModiEability, Mental Modules, and the Use of Pure and
Composite Measures to Reveal Them’, Acta Psychologica, 106, pp. 147–246.
Sternberg, S. [2011]: ‘Modular Processes in Mind and Brain’, Cognitive
Neuropsychology, 28, pp. 156–208.
Taper, M. L. and Lele, S. R. [2011]: ‘Evidence, Evidence Functions, and Error
Probabilities’, in P. S. Bandyopadhyay and M. Forster (eds), Handbook of
Philosophy of Statistics, Oxford: Elsevier, pp. 513–34.
Vann, S. D., Aggleton, J. P. and Maguire, E A. [2009]: ‘What Does the Retrosplenial
Cortex Do?’, Nature Reviews Neuroscience, 10, pp. 792–802.
Yarkoni, T., Poldrack, R. A., Nichols, T. E., Van Essen, D. C. and Wager, T. D. [2011]:
‘Large-Scale Automated Synthesis of Human Functional Neuroimaging Data’,
Nature Methods, 8, pp. 665–70.
Yarkoni, T., Poldrack, R. A., Van Essen, D. C. and Wager, T. D. [2010]: ‘Cognitive
Neuroscience 2.0: Building a Cumulative Science of Human Brain Function’, Trends
in Cognitive Sciences, 14, pp. 489–96.
Young, L. and Saxe, R. [2008]: ‘The Neural Basis of Belief Encoding and Integration in
Moral Judgement’, NeuroImage, 40, pp. 1912–20.