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The cerebellum and decision making under uncertainty
Cognitive Brain Research 20 (2004) 46 – 53 www.elsevier.com/locate/cogbrainres
Research report
The cerebellum and decision making under uncertainty Nigel Blackwood a,*, Dominic ffytche a, Andrew Simmons b, Richard Bentall c, Robin Murray a, Robert Howard a a
Division of Psychological Medicine, Institute of Psychiatry, PO Box 70, De Crespigny Park, London SE5 8AZ, UK b Neuroimaging Research, Institute of Psychiatry, London, UK c Department of Clinical Psychology, University of Manchester, London, UK Accepted 12 December 2003 Available online 4 March 2004
Abstract This study aimed to identify the neural basis of probabilistic reasoning, a type of inductive inference that aids decision making under conditions of uncertainty. Eight normal subjects performed two separate two-alternative-choice tasks (the balls in a bottle and personality survey tasks) while undergoing functional magnetic resonance imaging (fMRI). The experimental conditions within each task were chosen so that they differed only in their requirement to make a decision under conditions of uncertainty (probabilistic reasoning and frequency determination required) or under conditions of certainty (frequency determination required). The same visual stimuli and motor responses were used in the experimental conditions. We provide evidence that the neo-cerebellum, in conjunction with the premotor cortex, inferior parietal lobule and medial occipital cortex, mediates the probabilistic inferences that guide decision making under uncertainty. We hypothesise that the neo-cerebellum constructs internal working models of uncertain events in the external world, and that such probabilistic models subserve the predictive capacity central to induction. D 2004 Elsevier B.V. All rights reserved. Theme: Neural basis of behaviour Topic: Cognition Keywords: Probabilistic reasoning; Inductive reasoning; Cerebellum
1. Introduction Inductive inferences enable decision making under conditions of uncertainty. They expand knowledge in the face of uncertainty by building a plausible (but not necessarily true) model of the world from a set of ambiguous observations. Induction employs judgements of probability. For example, if I attempt to understand the hostile demeanour of a passenger in my train carriage, I may infer that of all possible causes, the most probable is my irritating presence. This is plausible but not necessarily true: the fact that his favourite seat has been taken by another inconsiderate passenger may in truth be the principal cause. Nevertheless, the inference is ecologically useful because it enables a quick decision in a
* Corresponding author. Tel.: +44-0207-848-0637; fax: +44-0207-8480632. E-mail address: [email protected] (N. Blackwood). 0926-6410/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cogbrainres.2003.12.009
complex situation (his hostility is directed toward me), which in turn allows adaptive action to be taken (moving carriages). There is, however, little consensus about how we make inductive inferences. Classical, or normative, models [43] suggest that we employ the laws of probability and statistics. Bayes rule, for example, operationalises the processes involved in updating an existing belief when presented with new evidence. Future events can therefore be predicted on the basis of a limited data set. The classic paradigm examining such probabilistic reasoning is the balls in a bottle task [44]. Subjects are asked to imagine two bottles containing balls of two different colours in varying proportions (for example, bottle A contains 60 red balls and 40 blue balls; bottle B contains 40 red balls and 60 blue balls). They are then asked to guess from which bottle a particular sequence of balls is likely to have been drawn (for example, the sequence red, blue, red, blue, red is likely to have been drawn from bottle A). In Bayesian terms, humans appear to be conservative reasoners, extracting less certainty from a
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situation than the evidence warrants [44]. The heuristics-andbiases research program [30] took a dimmer view of human induction, suggesting that our inferential judgements are systematically biased and error-prone because they are based upon quick-and-dirty heuristic rules rather than the laws of probability. A third approach noted that inductive inferences occur under conditions of limited time, information and computational capacity. Such ‘boundedly rational’ [18,54] inductive inferences may make Bayesian inferences by employing an innate frequency processing module associated with natural sampling [10,24], which appears to be computationally simpler and therefore evolutionarily more likely than the calculation of probabilities. Nevertheless, while psychologists disagree about the processes involved, humans are able to reason about probabilities and often reach approximately correct conclusions. Neuroimaging studies of inductive reasoning to date have contrasted inductive and deductive reasoning [21,40, 41] (where the inductive task consisted of category based inductions, and probabilistic inductions using syllogisms or propositional logic) and have sought to determine the neuroanatomical substrate of hypothesis selection in inductive inferences concerning novel animal categorisation [19]. While contrasting inductive and deductive reasoning using is of particular interest to those engaged in the ongoing mental logic vs. mental model debate [7,29], the results of such studies employing logical brain-teasers may, in fact, tell us little about ecological rationality, that is, a view of rationality that takes account of an organism’s adaptive goals, natural environments and cognitive constraints. We therefore used functional magnetic resonance imaging (fMRI) to examine probabilistic reasoning by adapting the balls in a bottle task and a structurally identical, but more ecologically realistic, variant of the same task (where participants have to reason about two possible personality surveys) [59]. The experimental conditions within the balls in a bottle and personality survey tasks required either decision making under condi-
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tions of uncertainty (probabilistic inferences and frequency determination required) or decision making under conditions of certainty (frequency determination required). Since the tasks were identical in all other aspects, the contrast between these two experimental conditions enabled us to determine the neuroanatomical substrate of probabilistic inferences. We hypothesised that such inferences would be subserved by those brain areas representing the problem to be solved in visuospatial working memory (left prefrontal cortex, left inferior parietal lobe) [37] together with areas previously implicated in tasks requiring prediction (ventromedial prefrontal cortex and lateral cerebellum) [2,13,38].
2. Materials and methods 2.1. Subjects Eight neurologically healthy male volunteers participated (mean age 38; range 18– 53 years; all right handed). The group was of above average intelligence (mean IQ estimated using the National Adult Reading Test 116; range 98– 124). Participants were informed that they were involved in a study investigating decision making. After receiving written and oral explanations of the procedures, participants gave written informed consent. The study design was approved by the Bethlem and Maudsley ethics committee. 2.2. Experimental design The main purpose of the experiment was to compare brain activity associated with decision making under conditions of uncertainty and decision making under conditions of certainty. We used abstract (experiment 1, Fig. 1) and more ecologically realistic (experiment 2, Fig. 2) paradigms. The tasks were visually presented and consisted of alternating 45s conditions in an A(probabilistic reasoning and frequency
Fig. 1. The balls in a bottle task.
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Fig. 2. The personality survey task.
determination enabling decision making under conditions of uncertainty) B(frequency determination enabling decision making under conditions of certainty) design, repeated five times, giving a total scan time of 7.5 min. The abstract design used coloured balls to isolate the problem from a participant’s everyday knowledge [44], while the more ecologically realistic design [59] used personality survey character descriptions [1], where individual judgements may be guided by schematic knowledge of others’ attributes. All stimuli were displayed on a monitor and presented to the participant via a 45j angled mirror positioned above the headcoil. The mirror was adjusted to be within the participant’s field of vision without having to tilt the head. A test image was presented on the screen prior to scanning to ensure that the image was in focus and the participant could comfortably see the balls and read the text. The experiment used a 2 2 factorial design. The first factor referred to the type of decision making required by the subject (decision making under conditions of uncertainty vs. decision making under conditions of certainty). The second factor referred to the stimuli employed (abstract [balls] vs. more ecologically realistic [words]). Thus, for the tasks which required decision making under conditions of uncertainty, participants were informed that the experimental computer ‘contained’ two bottles containing 100 balls each (experiment 1, the balls in a bottle task) and two surveys of 100 people in which each person had been asked to give a one word personality description of a person who was very similar to the trial participant (experiment 2, the personality survey descriptions task). In experiment 1, bottle A contained 60 red and 40 blue balls; bottle B contained 40 red and 60 blue balls. In experiment 2, the person was generally liked in survey A (60 people had made positive comments about the person, while 40 people had
made negative comments), but generally disliked in survey B (40 people had made positive comments while 60 people had made negative comments). During scanning, the decision making under uncertainty tasks were preceded by the question ‘Which bottle?’ or ‘Which survey?’, presented for 1.5 s. A pseudo-randomised sequence of 15 balls or personality descriptions (in a 60:40 or 40:60 red/blue or positive/negative ratio) were then presented in turn for 2.7 s each with a 0.2-s interstimulus interval. The subject’s task was to indicate by a button press when they were satisified that they knew which bottle or survey (A or B) the computer was working from. Subjects indicated their decision by selecting one of two button presses on a two-button box using their right index finger. For the tasks which required decision making under conditions of certainty, participants were informed that they had to monitor a sequence of 15 coloured balls or personality descriptions to determine whether there were greater than or less than seven red balls or seven positive comments in the presented sequence. During scanning, the decision making under conditions of certainty tasks were preceded by the command ‘Count’, presented for 1.5 s. Again, a pseudorandomised sequence of 15 balls or personality descriptions (in a 60:40 or 40:60 red/blue or positive/negative ratio) were then presented in turn for 2.7 s each with a 0.2-s interstimulus interval. The subject’s task was to indicate by a button press using their right index finger, when certain, whether there were greater (B) or less (A) than seven red balls or seven positive comments in the presented sequence of 15. The subjects were explicitly told not to guess but to wait until the answer to the question was completely specified by the presented sequence. Monitoring of the relative frequency of both red and blue balls (or positive and negative comments) was required to ensure that decision making occurred in the
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given time period (for example, if six red balls were in the sequence, subjects had to know that nine blue balls had also been presented to make a ‘less than seven’ decision by ball 15). 2.3. fMRI scan acquisition For each participant, fMRI data were acquired in a single session lasting 45 min. The two experiments were presented in a randomised order. Gradient echo echoplanar (EPI) data was acquired on a 1.5-T GE NV/i Signa LX Horizon system (General Electric, Milwaukee, WI, USA) in the Department of Neuroimaging at the Maudsley Hospital. 150 T2*weighted images depicting blood oxygenation level dependent (BOLD) contrast were acquired with an in-plane resolution of 3.75 mm (TR = 3 s; TE = 40 ms) at each of 16 near-axial non-contiguous 7-mm-thick slices to include the whole brain (slice gap = 0.7 mm). During the same imaging session, a high-contrast, high-resolution inversion recovery prepared SPGR data set (TE = 73 ms; TI = 180 ms; TR = 11 s; flip angle 90j ) with an in-plane resolution of 1.8 and 3.3 mm slice thickness was acquired.
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of the experimental material (balls or words) on this activity (interaction effect). Rigorous statistical testing in the fixed-effects models was performed at the voxel level, corrected for multiple comparisons, at p < 0.05. Fixed effects models have the disadvantage that they may be biased by responses from individual subjects and therefore may not reflect the true activation pattern of the population as a whole [16]. Our subject numbers were too small to permit additional analyses using random effects models. We therefore additionally examined single subject data for the significant findings in the analyses, to ensure that the activations were truly representative of the group and did not reflect bias from individual subjects. Coordinates of the local maxima provided by SPM were converted from MNI space to Talaraich and Tournoux space using a non-linear transform [8,9] (http://www.mrc-cbu.cam.ac.uk/Imaging/mnispace.html). Anatomical localisation of the local maxima were then assessed with reference to the standard stereotaxic atlas [55] together with superimposition of the SPM maps on the group mean structural MRI data set. Cerebellar activations were further assessed with reference to the stereotaxic cerebellar atlas [53].
2.4. fMRI data analysis Image processing was performed using statistical parametric mapping (SPM99: http://www.fil.ion.ucl.ac.uk/spm). All volumes were realigned to the first volume to correct for inter-scan and intra-scan movement and then resliced using a sinc interpolation in space [15]. Each volume was normalised [15] to a standard EPI template volume, based on the Montreal Neurological Institute reference brain [14], in the space of Talaraich and Tournoux [55] using non-linear basis functions. Finally, the data were smoothed with a Gaussian kernel of 10 mm full width at halfmaximum to compensate for residual variability after spatial normalisation and to permit application of Gaussian random field theory to provide for corrected statistical inferences. Statistical analyses were performed using SPM99. Data from all 16 experiments (8 subjects balls in a bottle and personality survey conditions) were included in a single matrix allowing a factorial analysis of main and interaction effects. Fixed-effects models were composed of the 16 subject-specific models of target conditions (decision making under conditions of uncertainty) with reference conditions (decision making under conditions of certainty) modelled as an implicit baseline. The periods between making a decision (indicated by a key press) and the end of the 45-s block were modelled as effects of no interest and excluded from further analysis. While the factorial design allows us to test for a number of effects, we restrict ourselves here to those that have direct relevance to decision making under uncertainty. t-statistic contrasts were realised for the comparisons of interest: (i) the main effect of decision making under uncertainty, and (ii) the influence
3. Results 3.1. Behavioural data Performance of the probabilistic and counting tasks did not differ in mean response times (balls probabilistic task mean = 35.83 s, balls counting task mean = 38.56 s: paired t test, df = 7, t = 2.05, p>0.05; personality probabilistic task mean = 35.45 s, personality counting task mean = 37.37 s: paired t test, df = 7, t = 1.01, p>0.05) or error rates (balls probabilistic task mean error rate = 25%, balls counting task mean error rate = 25% paired t test, df = 7, t = 0.00, p>0.05; personality probabilistic task mean error rate = 15%, personality counting task mean error rate = 30%: paired t test, df = 7, t = 1.27, p>0.05). Activations cannot therefore be attributed to task performance artefacts because the probabilistic and counting tasks were matched in difficulty and in stimulus and response characteristics. The behavioural data indicates that the participants made probabilistic decisions under conditions of limited time and knowledge (for example, taking an average of 12 words before reaching a decision about which personality survey had been used), rather than surveying all possible information before making a decision: the search amongst alternatives terminated when a certain critical confidence threshold was exceeded. 3.2. Brain activations during task performance The brain areas showing significantly increased BOLD signal in the fixed-effects analysis of the main effect of decision making under uncertainty and the interaction
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N. Blackwood et al. / Cognitive Brain Research 20 (2004) 46–53 Table 1 Brain areas activated during decision making under conditions of uncertainty compared to decision making under conditions of certainty Talairach coordinates (x, y, z) and selection of foci are according to the conventions of SPM99 Brain region
Coordinates
Z Cluster score size
Uncertain decisions>Certain decisions, Balls in a bottle + Personality survey tasks Left lateral cerebellum (Lobule VI) 32, 62, 28 5.56 87 Left medial cerebellum (Lobule VI) 10, 73, 28 5.10 30 Left premotor cortex (BA 6) 46, 2, 42 4.91 8 Left inferior parietal lobe (BA 40) 51, 35, 42 4.63 4 Left medial occipital cortex (BA 17) 10, 95, 3 5.16 57 Left medial occipital cortex (BA 17) 6, 85, 4 4.56 2
Fig. 3. Significant activations associated with decision making under conditions of uncertainty compared to decision making under conditions of certainty ( p < 0.05 corrected for multiple comparisons) for the balls in a bottle and personality survey tasks overlaid on a standardised brain volume in a left lateral view.
effects (influence of balls vs. words on decision making under uncertainty) are shown in Figs. 3 and 4 and Table 1. The areas of activation common to both probabilistic reasoning tasks included left medial and lateral cerebellum,
Certain decisions>Uncertain decisions, Balls in a bottle + Personality survey tasks Left middle frontal gyrus (BA 9) 28, 38, 28 5.52 66 Right precuneus (BA 7) 10, 44, 43 5.14 16 Left uncus (BA 34) 24, 5, 18 4.79 7 Uncertain decisions>Certain decisions, Balls in a bottle>Personality survey task Left inferior temporal gyrus (BA 37) 38, 58, 0 5.44 376 Left inferior parietal lobe (BA 40) 52, 26, 32 5.42 123 Right inferior parietal lobe (BA 40) 34, 42, 48 5.02 34 40, 30, 40 4.88 37 Right middle occipital gyrus (BA 19) 40, 72, 6 5.05 51 Right precentral gyrus (BA 6) 48, 2, 34 4.79 11 Right precentral gyrus (BA 4) 26, 10, 56 4.76 17 Uncertain decisions>Certain decisions, Personality survey>Balls in a bottle task Left temporal pole (BA 38) 44, 20, 16 5.36 98 Left posterior inferior 36, 66, 48 5.37 75 parietal lobe (BA 40) Left middle temporal gyrus (BA 21) 64, 30, 8 4.74 2 Right cuneus (BA 17) 16, 96, 6 5.39 39 The table shows all regions significant in the fixed-effects models at p < 0.05 corrected for multiple comparisons at the voxel level.
Fig. 4. (A) Cerebellar activations subserving decision making under uncertainty. The fixed-effects SPM thresholded at p < 0.05, corrected for multiple comparisons, superimposed on a transverse section of the group mean structural T1 image, shows the activations in the left lateral cerebellum (x = 32, y = 62, z = 28), Z = 5.56, and the left medial cerebellum (x = 10, y = 73, z = 28), Z = 5.10. (B) Individual subject responses (averaged between the balls in a bottle and personality survey experiments) at the left lateral cerebellar focus ( 32, 62, 28) demonstrating significantly greater activity during decision making under conditions of uncertainty than under conditions of certainty.
premotor cortex, inferior parietal lobule and medial occipital cortex. The areas of activation common to both counting tasks included dorsolateral prefrontal cortex (left middle frontal gyrus), right precuneus and left medial temporal lobe (left uncus). The areas of greater activation when decision making under uncertainty involved balls rather than words included left inferior temporal gyrus, bilateral inferior parietal lobe, right precentral gyrus and right middle occipital gyrus. The areas of greater activation when decision making under uncertainty involved words rather than balls included left temporal pole, left posterior inferior parietal lobe, left middle temporal gyrus and right cuneus.
4. Discussion Decision making under conditions of uncertainty in these experiments required the construction of two competing hypothetical models and the resolution of conflict through
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inferring which of the two best accounted for the presented data. Components of the neural network subserving such processing (left lateral and medial cerebellar cortex, inferior parietal lobe, premotor cortex and medial occipital cortex) will be considered in turn. Phylogenetically ancient regions of the cerebellum (e.g., the vermis) are capable of acquiring the internal models of the body required for movement control through motor learning [27,34]. Newer regions (e.g., the lateral cerebellar hemispheres) are capable of forming and maintaining internal working models of objects in the external world such as new tools [26,27], and of monitoring the consequences of actions [6]. The ‘forward internal’ models which subserve these activities act as predictive devices so that actions correctly anticipate changes in the external world [38,57,58]. It is possible that the computational process used by such forward models to predict the sensory consequences of one’s own movements could also be used to predict the outcome of ambiguous events in the external world through a process of simulation. Thus, the usual direction of prediction in the forward model is from self-generated intentions and motor commands to the consequences of actions. When we are attempting to resolve ambiguity in an uncertain situation, a related mechanism could operate in the reverse direction, from consequences to cause. Such models have been also proposed to be involved in higher order social cognition such as the discernment of other’s intentions [5]. Alternatively, forward models could be used to make multiple predictions, and based on the correspondence between the predictions and the observed events we could infer which of the models best accounted for the data [58]. The lateral cerebellar activations we observed are consistent with the findings from previous problem solving imaging studies. In a pegboard task [33] and a conceptual reasoning task derived from the Wisconsin Card Sort test [48], dentate nucleus and left lateral cerebellar activations (lobule VI), respectively, were associated with the inference of underlying structural solutions in incompletely specified circumstances. Judgements of probability or likelihood are central to such inferences. Left-sided lateral cerebellar activations (lobule VI) were also observed in the study examining both the formation and application of an inductive categorisation rule [19]. The lateral cerebellar activations (lobule VI) in the present study encompassed the ventral dentate nucleus, which projects via the medial thalamus to the dorsolateral prefrontal cortex [39]. It is hypothesised that this network co-ordinates and sequences human thought [49 – 51]. Certainly, lesions in posterior areas of the cerebellar cortex (which includes lobule VI and crus I/ II) result in marked impairments of abstract reasoning [52]. The cerebellar activations in these experiments support such hypotheses by suggesting that the neo-cerebellum constructs internal working models of uncertain events in the external world. Such models subserve the predictive capacity central to induction. Error rate accounts of the cerebellar activations are ruled out by the behavioural data and there is no obvious reason to suppose that eye movements subserving visual
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monitoring of the data would be greater in the probabilistic than in the counting tasks. Cerebellar contributions to attentional and working memory processing [28] also represent a potential confound. However, the attentional and working memory loads were similar in the probabilistic and counting tasks because frequency monitoring of both types of ball or personality descriptions were required in each task. Moreover, there was no statistically significant difference between the probabilistic reasoning and counting tasks in the time taken to reach a decision. Most of the cortical activations we observed were leftsided. This accords with data from split-brain patients suggesting that the left hemisphere is dominant for the formation of inferential hypotheses which assimilate information into a comprehensible whole [17,56]. The inferior parietal lobule and pre-motor cortex contribute to the visuospatial representation of the problem in working memory: these areas encode motor-sequence specific information [23,25] and contribute to the processing of comparative magnitudes in humans, particularly when this involves approximate calculations [11,42,45]. Primate research investigating categorical inferences in perceptual tasks [46] such as direction discrimination tasks also implicates these parietal and frontal areas. In such tasks, the underlying neural computations may involve the calculation of the likelihood ratio favouring one inferential hypothesis over an alternative [22]. This would involve the incorporation of accumulated sensory information with psychological factors such as the knowledge of the prior probability that a particular hypothesis is correct and the anticipated value of the response. Such computations involve parietal and frontal association cortices in the sustained representation of accumulated sensory evidence, thereby encoding the inferential decision in an abstract sense. Other neurons within these structures prepare and initiate overt responses. The pre-motor and posterior parietal cortices have topographically organised feedforward projections (via corticopontine and pontocerebellar projections) to the cerebellum as well as feedback projections (via the thalamus) from the cerebellum. Taking these findings together suggests that the parietal and pre-motor activations are ideally suited to contribute to the network encoding the ‘leading’ probabilistic hypothesis. However, we must be cautious at this stage in attributing ‘network’ status to these joint activations, given that the connections between the cerebral and cerebellar hemispheres are crossed. Finally, we suggest that the activation observed in medial occipital cortex (area 17) [36] may represent the greater degree of visual imagery involved in the formation, maintenance and comparison of two competing probabilistic hypotheses compared to that involved in the comparison of two completely specified data types. However, subjects did not spontaneously report an increased use of visual imagery in the probabilistic reasoning conditions in post-scanning debriefing and this account of the medial occipital activation is clearly speculative at this stage.
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We were surprised by the marked absence of ventromedial prefrontal cortex activation in the probabilistic reasoning tasks. Activity in this area might have been expected given its suggested role in guessing [13] and in adaptive decision making informed by the representation of prior beliefs or past experience [3,4,20]. However, there were no direct consequences for the subjects of opting for one decision rather than the other in direct contrast to the feedback obtained in the Bechara gambling task [2], nor were the uncertain decisions informed by prior beliefs or past experience [20,41]. The lack of these features may explain the failure to activate this area. During decision making, we consider the value of the options before us and their practical outcomes (based on past experience) in addition to the chances of their happening. By removing a reward or prior belief component, we believe that we have been able to isolate a network subserving probabilistic reasoning which in turn may interact with the ventromedial prefrontal cortex in considering the respective utilities of competing decisions based on past experience. The interaction effects are unsurprisingly accounted for by the contrasting material employed in the two experiments (words or balls). Thus, areas activated to a greater extent when decision making under uncertainty employed words are implicated in the semantic processing of words (Wernike’s area, BA 21, temporal pole, BA 38 and left posterior inferior parietal cortex, BA40) [47]. Areas activated to a greater extent when decision making under uncertainty employed balls are implicated in object episodic memory encoding and object working memory (inferior parietal lobe, BA 40, left inferior temporal gyrus, BA37) [12,32] object imagery (middle occipital gyrus, BA 19) [35] and sequence learning (right precentral gyrus) [25]. In conclusion, it has been speculated that internal cerebellar models might have a role not only in motor control but also in cognition [57], and that they might form the basis of cognitive processes in which predictive functions are important [31]. Prediction under conditions of uncertainty is the central feature of induction examined in this study. We suggest that forms of representation within the cerebellum that evolved as part of a limited task domain such as motor control (the monitoring of the uncertain consequences of motor commands) have become accessible for other tasks which can exploit this specialisation including inferential thought (the monitoring of the uncertain meaning of ambiguous external events).
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Research report
The cerebellum and decision making under uncertainty Nigel Blackwood a,*, Dominic ffytche a, Andrew Simmons b, Richard Bentall c, Robin Murray a, Robert Howard a a
Division of Psychological Medicine, Institute of Psychiatry, PO Box 70, De Crespigny Park, London SE5 8AZ, UK b Neuroimaging Research, Institute of Psychiatry, London, UK c Department of Clinical Psychology, University of Manchester, London, UK Accepted 12 December 2003 Available online 4 March 2004
Abstract This study aimed to identify the neural basis of probabilistic reasoning, a type of inductive inference that aids decision making under conditions of uncertainty. Eight normal subjects performed two separate two-alternative-choice tasks (the balls in a bottle and personality survey tasks) while undergoing functional magnetic resonance imaging (fMRI). The experimental conditions within each task were chosen so that they differed only in their requirement to make a decision under conditions of uncertainty (probabilistic reasoning and frequency determination required) or under conditions of certainty (frequency determination required). The same visual stimuli and motor responses were used in the experimental conditions. We provide evidence that the neo-cerebellum, in conjunction with the premotor cortex, inferior parietal lobule and medial occipital cortex, mediates the probabilistic inferences that guide decision making under uncertainty. We hypothesise that the neo-cerebellum constructs internal working models of uncertain events in the external world, and that such probabilistic models subserve the predictive capacity central to induction. D 2004 Elsevier B.V. All rights reserved. Theme: Neural basis of behaviour Topic: Cognition Keywords: Probabilistic reasoning; Inductive reasoning; Cerebellum
1. Introduction Inductive inferences enable decision making under conditions of uncertainty. They expand knowledge in the face of uncertainty by building a plausible (but not necessarily true) model of the world from a set of ambiguous observations. Induction employs judgements of probability. For example, if I attempt to understand the hostile demeanour of a passenger in my train carriage, I may infer that of all possible causes, the most probable is my irritating presence. This is plausible but not necessarily true: the fact that his favourite seat has been taken by another inconsiderate passenger may in truth be the principal cause. Nevertheless, the inference is ecologically useful because it enables a quick decision in a
* Corresponding author. Tel.: +44-0207-848-0637; fax: +44-0207-8480632. E-mail address: [email protected] (N. Blackwood). 0926-6410/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cogbrainres.2003.12.009
complex situation (his hostility is directed toward me), which in turn allows adaptive action to be taken (moving carriages). There is, however, little consensus about how we make inductive inferences. Classical, or normative, models [43] suggest that we employ the laws of probability and statistics. Bayes rule, for example, operationalises the processes involved in updating an existing belief when presented with new evidence. Future events can therefore be predicted on the basis of a limited data set. The classic paradigm examining such probabilistic reasoning is the balls in a bottle task [44]. Subjects are asked to imagine two bottles containing balls of two different colours in varying proportions (for example, bottle A contains 60 red balls and 40 blue balls; bottle B contains 40 red balls and 60 blue balls). They are then asked to guess from which bottle a particular sequence of balls is likely to have been drawn (for example, the sequence red, blue, red, blue, red is likely to have been drawn from bottle A). In Bayesian terms, humans appear to be conservative reasoners, extracting less certainty from a
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situation than the evidence warrants [44]. The heuristics-andbiases research program [30] took a dimmer view of human induction, suggesting that our inferential judgements are systematically biased and error-prone because they are based upon quick-and-dirty heuristic rules rather than the laws of probability. A third approach noted that inductive inferences occur under conditions of limited time, information and computational capacity. Such ‘boundedly rational’ [18,54] inductive inferences may make Bayesian inferences by employing an innate frequency processing module associated with natural sampling [10,24], which appears to be computationally simpler and therefore evolutionarily more likely than the calculation of probabilities. Nevertheless, while psychologists disagree about the processes involved, humans are able to reason about probabilities and often reach approximately correct conclusions. Neuroimaging studies of inductive reasoning to date have contrasted inductive and deductive reasoning [21,40, 41] (where the inductive task consisted of category based inductions, and probabilistic inductions using syllogisms or propositional logic) and have sought to determine the neuroanatomical substrate of hypothesis selection in inductive inferences concerning novel animal categorisation [19]. While contrasting inductive and deductive reasoning using is of particular interest to those engaged in the ongoing mental logic vs. mental model debate [7,29], the results of such studies employing logical brain-teasers may, in fact, tell us little about ecological rationality, that is, a view of rationality that takes account of an organism’s adaptive goals, natural environments and cognitive constraints. We therefore used functional magnetic resonance imaging (fMRI) to examine probabilistic reasoning by adapting the balls in a bottle task and a structurally identical, but more ecologically realistic, variant of the same task (where participants have to reason about two possible personality surveys) [59]. The experimental conditions within the balls in a bottle and personality survey tasks required either decision making under condi-
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tions of uncertainty (probabilistic inferences and frequency determination required) or decision making under conditions of certainty (frequency determination required). Since the tasks were identical in all other aspects, the contrast between these two experimental conditions enabled us to determine the neuroanatomical substrate of probabilistic inferences. We hypothesised that such inferences would be subserved by those brain areas representing the problem to be solved in visuospatial working memory (left prefrontal cortex, left inferior parietal lobe) [37] together with areas previously implicated in tasks requiring prediction (ventromedial prefrontal cortex and lateral cerebellum) [2,13,38].
2. Materials and methods 2.1. Subjects Eight neurologically healthy male volunteers participated (mean age 38; range 18– 53 years; all right handed). The group was of above average intelligence (mean IQ estimated using the National Adult Reading Test 116; range 98– 124). Participants were informed that they were involved in a study investigating decision making. After receiving written and oral explanations of the procedures, participants gave written informed consent. The study design was approved by the Bethlem and Maudsley ethics committee. 2.2. Experimental design The main purpose of the experiment was to compare brain activity associated with decision making under conditions of uncertainty and decision making under conditions of certainty. We used abstract (experiment 1, Fig. 1) and more ecologically realistic (experiment 2, Fig. 2) paradigms. The tasks were visually presented and consisted of alternating 45s conditions in an A(probabilistic reasoning and frequency
Fig. 1. The balls in a bottle task.
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Fig. 2. The personality survey task.
determination enabling decision making under conditions of uncertainty) B(frequency determination enabling decision making under conditions of certainty) design, repeated five times, giving a total scan time of 7.5 min. The abstract design used coloured balls to isolate the problem from a participant’s everyday knowledge [44], while the more ecologically realistic design [59] used personality survey character descriptions [1], where individual judgements may be guided by schematic knowledge of others’ attributes. All stimuli were displayed on a monitor and presented to the participant via a 45j angled mirror positioned above the headcoil. The mirror was adjusted to be within the participant’s field of vision without having to tilt the head. A test image was presented on the screen prior to scanning to ensure that the image was in focus and the participant could comfortably see the balls and read the text. The experiment used a 2 2 factorial design. The first factor referred to the type of decision making required by the subject (decision making under conditions of uncertainty vs. decision making under conditions of certainty). The second factor referred to the stimuli employed (abstract [balls] vs. more ecologically realistic [words]). Thus, for the tasks which required decision making under conditions of uncertainty, participants were informed that the experimental computer ‘contained’ two bottles containing 100 balls each (experiment 1, the balls in a bottle task) and two surveys of 100 people in which each person had been asked to give a one word personality description of a person who was very similar to the trial participant (experiment 2, the personality survey descriptions task). In experiment 1, bottle A contained 60 red and 40 blue balls; bottle B contained 40 red and 60 blue balls. In experiment 2, the person was generally liked in survey A (60 people had made positive comments about the person, while 40 people had
made negative comments), but generally disliked in survey B (40 people had made positive comments while 60 people had made negative comments). During scanning, the decision making under uncertainty tasks were preceded by the question ‘Which bottle?’ or ‘Which survey?’, presented for 1.5 s. A pseudo-randomised sequence of 15 balls or personality descriptions (in a 60:40 or 40:60 red/blue or positive/negative ratio) were then presented in turn for 2.7 s each with a 0.2-s interstimulus interval. The subject’s task was to indicate by a button press when they were satisified that they knew which bottle or survey (A or B) the computer was working from. Subjects indicated their decision by selecting one of two button presses on a two-button box using their right index finger. For the tasks which required decision making under conditions of certainty, participants were informed that they had to monitor a sequence of 15 coloured balls or personality descriptions to determine whether there were greater than or less than seven red balls or seven positive comments in the presented sequence. During scanning, the decision making under conditions of certainty tasks were preceded by the command ‘Count’, presented for 1.5 s. Again, a pseudorandomised sequence of 15 balls or personality descriptions (in a 60:40 or 40:60 red/blue or positive/negative ratio) were then presented in turn for 2.7 s each with a 0.2-s interstimulus interval. The subject’s task was to indicate by a button press using their right index finger, when certain, whether there were greater (B) or less (A) than seven red balls or seven positive comments in the presented sequence of 15. The subjects were explicitly told not to guess but to wait until the answer to the question was completely specified by the presented sequence. Monitoring of the relative frequency of both red and blue balls (or positive and negative comments) was required to ensure that decision making occurred in the
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given time period (for example, if six red balls were in the sequence, subjects had to know that nine blue balls had also been presented to make a ‘less than seven’ decision by ball 15). 2.3. fMRI scan acquisition For each participant, fMRI data were acquired in a single session lasting 45 min. The two experiments were presented in a randomised order. Gradient echo echoplanar (EPI) data was acquired on a 1.5-T GE NV/i Signa LX Horizon system (General Electric, Milwaukee, WI, USA) in the Department of Neuroimaging at the Maudsley Hospital. 150 T2*weighted images depicting blood oxygenation level dependent (BOLD) contrast were acquired with an in-plane resolution of 3.75 mm (TR = 3 s; TE = 40 ms) at each of 16 near-axial non-contiguous 7-mm-thick slices to include the whole brain (slice gap = 0.7 mm). During the same imaging session, a high-contrast, high-resolution inversion recovery prepared SPGR data set (TE = 73 ms; TI = 180 ms; TR = 11 s; flip angle 90j ) with an in-plane resolution of 1.8 and 3.3 mm slice thickness was acquired.
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of the experimental material (balls or words) on this activity (interaction effect). Rigorous statistical testing in the fixed-effects models was performed at the voxel level, corrected for multiple comparisons, at p < 0.05. Fixed effects models have the disadvantage that they may be biased by responses from individual subjects and therefore may not reflect the true activation pattern of the population as a whole [16]. Our subject numbers were too small to permit additional analyses using random effects models. We therefore additionally examined single subject data for the significant findings in the analyses, to ensure that the activations were truly representative of the group and did not reflect bias from individual subjects. Coordinates of the local maxima provided by SPM were converted from MNI space to Talaraich and Tournoux space using a non-linear transform [8,9] (http://www.mrc-cbu.cam.ac.uk/Imaging/mnispace.html). Anatomical localisation of the local maxima were then assessed with reference to the standard stereotaxic atlas [55] together with superimposition of the SPM maps on the group mean structural MRI data set. Cerebellar activations were further assessed with reference to the stereotaxic cerebellar atlas [53].
2.4. fMRI data analysis Image processing was performed using statistical parametric mapping (SPM99: http://www.fil.ion.ucl.ac.uk/spm). All volumes were realigned to the first volume to correct for inter-scan and intra-scan movement and then resliced using a sinc interpolation in space [15]. Each volume was normalised [15] to a standard EPI template volume, based on the Montreal Neurological Institute reference brain [14], in the space of Talaraich and Tournoux [55] using non-linear basis functions. Finally, the data were smoothed with a Gaussian kernel of 10 mm full width at halfmaximum to compensate for residual variability after spatial normalisation and to permit application of Gaussian random field theory to provide for corrected statistical inferences. Statistical analyses were performed using SPM99. Data from all 16 experiments (8 subjects balls in a bottle and personality survey conditions) were included in a single matrix allowing a factorial analysis of main and interaction effects. Fixed-effects models were composed of the 16 subject-specific models of target conditions (decision making under conditions of uncertainty) with reference conditions (decision making under conditions of certainty) modelled as an implicit baseline. The periods between making a decision (indicated by a key press) and the end of the 45-s block were modelled as effects of no interest and excluded from further analysis. While the factorial design allows us to test for a number of effects, we restrict ourselves here to those that have direct relevance to decision making under uncertainty. t-statistic contrasts were realised for the comparisons of interest: (i) the main effect of decision making under uncertainty, and (ii) the influence
3. Results 3.1. Behavioural data Performance of the probabilistic and counting tasks did not differ in mean response times (balls probabilistic task mean = 35.83 s, balls counting task mean = 38.56 s: paired t test, df = 7, t = 2.05, p>0.05; personality probabilistic task mean = 35.45 s, personality counting task mean = 37.37 s: paired t test, df = 7, t = 1.01, p>0.05) or error rates (balls probabilistic task mean error rate = 25%, balls counting task mean error rate = 25% paired t test, df = 7, t = 0.00, p>0.05; personality probabilistic task mean error rate = 15%, personality counting task mean error rate = 30%: paired t test, df = 7, t = 1.27, p>0.05). Activations cannot therefore be attributed to task performance artefacts because the probabilistic and counting tasks were matched in difficulty and in stimulus and response characteristics. The behavioural data indicates that the participants made probabilistic decisions under conditions of limited time and knowledge (for example, taking an average of 12 words before reaching a decision about which personality survey had been used), rather than surveying all possible information before making a decision: the search amongst alternatives terminated when a certain critical confidence threshold was exceeded. 3.2. Brain activations during task performance The brain areas showing significantly increased BOLD signal in the fixed-effects analysis of the main effect of decision making under uncertainty and the interaction
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N. Blackwood et al. / Cognitive Brain Research 20 (2004) 46–53 Table 1 Brain areas activated during decision making under conditions of uncertainty compared to decision making under conditions of certainty Talairach coordinates (x, y, z) and selection of foci are according to the conventions of SPM99 Brain region
Coordinates
Z Cluster score size
Uncertain decisions>Certain decisions, Balls in a bottle + Personality survey tasks Left lateral cerebellum (Lobule VI) 32, 62, 28 5.56 87 Left medial cerebellum (Lobule VI) 10, 73, 28 5.10 30 Left premotor cortex (BA 6) 46, 2, 42 4.91 8 Left inferior parietal lobe (BA 40) 51, 35, 42 4.63 4 Left medial occipital cortex (BA 17) 10, 95, 3 5.16 57 Left medial occipital cortex (BA 17) 6, 85, 4 4.56 2
Fig. 3. Significant activations associated with decision making under conditions of uncertainty compared to decision making under conditions of certainty ( p < 0.05 corrected for multiple comparisons) for the balls in a bottle and personality survey tasks overlaid on a standardised brain volume in a left lateral view.
effects (influence of balls vs. words on decision making under uncertainty) are shown in Figs. 3 and 4 and Table 1. The areas of activation common to both probabilistic reasoning tasks included left medial and lateral cerebellum,
Certain decisions>Uncertain decisions, Balls in a bottle + Personality survey tasks Left middle frontal gyrus (BA 9) 28, 38, 28 5.52 66 Right precuneus (BA 7) 10, 44, 43 5.14 16 Left uncus (BA 34) 24, 5, 18 4.79 7 Uncertain decisions>Certain decisions, Balls in a bottle>Personality survey task Left inferior temporal gyrus (BA 37) 38, 58, 0 5.44 376 Left inferior parietal lobe (BA 40) 52, 26, 32 5.42 123 Right inferior parietal lobe (BA 40) 34, 42, 48 5.02 34 40, 30, 40 4.88 37 Right middle occipital gyrus (BA 19) 40, 72, 6 5.05 51 Right precentral gyrus (BA 6) 48, 2, 34 4.79 11 Right precentral gyrus (BA 4) 26, 10, 56 4.76 17 Uncertain decisions>Certain decisions, Personality survey>Balls in a bottle task Left temporal pole (BA 38) 44, 20, 16 5.36 98 Left posterior inferior 36, 66, 48 5.37 75 parietal lobe (BA 40) Left middle temporal gyrus (BA 21) 64, 30, 8 4.74 2 Right cuneus (BA 17) 16, 96, 6 5.39 39 The table shows all regions significant in the fixed-effects models at p < 0.05 corrected for multiple comparisons at the voxel level.
Fig. 4. (A) Cerebellar activations subserving decision making under uncertainty. The fixed-effects SPM thresholded at p < 0.05, corrected for multiple comparisons, superimposed on a transverse section of the group mean structural T1 image, shows the activations in the left lateral cerebellum (x = 32, y = 62, z = 28), Z = 5.56, and the left medial cerebellum (x = 10, y = 73, z = 28), Z = 5.10. (B) Individual subject responses (averaged between the balls in a bottle and personality survey experiments) at the left lateral cerebellar focus ( 32, 62, 28) demonstrating significantly greater activity during decision making under conditions of uncertainty than under conditions of certainty.
premotor cortex, inferior parietal lobule and medial occipital cortex. The areas of activation common to both counting tasks included dorsolateral prefrontal cortex (left middle frontal gyrus), right precuneus and left medial temporal lobe (left uncus). The areas of greater activation when decision making under uncertainty involved balls rather than words included left inferior temporal gyrus, bilateral inferior parietal lobe, right precentral gyrus and right middle occipital gyrus. The areas of greater activation when decision making under uncertainty involved words rather than balls included left temporal pole, left posterior inferior parietal lobe, left middle temporal gyrus and right cuneus.
4. Discussion Decision making under conditions of uncertainty in these experiments required the construction of two competing hypothetical models and the resolution of conflict through
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inferring which of the two best accounted for the presented data. Components of the neural network subserving such processing (left lateral and medial cerebellar cortex, inferior parietal lobe, premotor cortex and medial occipital cortex) will be considered in turn. Phylogenetically ancient regions of the cerebellum (e.g., the vermis) are capable of acquiring the internal models of the body required for movement control through motor learning [27,34]. Newer regions (e.g., the lateral cerebellar hemispheres) are capable of forming and maintaining internal working models of objects in the external world such as new tools [26,27], and of monitoring the consequences of actions [6]. The ‘forward internal’ models which subserve these activities act as predictive devices so that actions correctly anticipate changes in the external world [38,57,58]. It is possible that the computational process used by such forward models to predict the sensory consequences of one’s own movements could also be used to predict the outcome of ambiguous events in the external world through a process of simulation. Thus, the usual direction of prediction in the forward model is from self-generated intentions and motor commands to the consequences of actions. When we are attempting to resolve ambiguity in an uncertain situation, a related mechanism could operate in the reverse direction, from consequences to cause. Such models have been also proposed to be involved in higher order social cognition such as the discernment of other’s intentions [5]. Alternatively, forward models could be used to make multiple predictions, and based on the correspondence between the predictions and the observed events we could infer which of the models best accounted for the data [58]. The lateral cerebellar activations we observed are consistent with the findings from previous problem solving imaging studies. In a pegboard task [33] and a conceptual reasoning task derived from the Wisconsin Card Sort test [48], dentate nucleus and left lateral cerebellar activations (lobule VI), respectively, were associated with the inference of underlying structural solutions in incompletely specified circumstances. Judgements of probability or likelihood are central to such inferences. Left-sided lateral cerebellar activations (lobule VI) were also observed in the study examining both the formation and application of an inductive categorisation rule [19]. The lateral cerebellar activations (lobule VI) in the present study encompassed the ventral dentate nucleus, which projects via the medial thalamus to the dorsolateral prefrontal cortex [39]. It is hypothesised that this network co-ordinates and sequences human thought [49 – 51]. Certainly, lesions in posterior areas of the cerebellar cortex (which includes lobule VI and crus I/ II) result in marked impairments of abstract reasoning [52]. The cerebellar activations in these experiments support such hypotheses by suggesting that the neo-cerebellum constructs internal working models of uncertain events in the external world. Such models subserve the predictive capacity central to induction. Error rate accounts of the cerebellar activations are ruled out by the behavioural data and there is no obvious reason to suppose that eye movements subserving visual
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monitoring of the data would be greater in the probabilistic than in the counting tasks. Cerebellar contributions to attentional and working memory processing [28] also represent a potential confound. However, the attentional and working memory loads were similar in the probabilistic and counting tasks because frequency monitoring of both types of ball or personality descriptions were required in each task. Moreover, there was no statistically significant difference between the probabilistic reasoning and counting tasks in the time taken to reach a decision. Most of the cortical activations we observed were leftsided. This accords with data from split-brain patients suggesting that the left hemisphere is dominant for the formation of inferential hypotheses which assimilate information into a comprehensible whole [17,56]. The inferior parietal lobule and pre-motor cortex contribute to the visuospatial representation of the problem in working memory: these areas encode motor-sequence specific information [23,25] and contribute to the processing of comparative magnitudes in humans, particularly when this involves approximate calculations [11,42,45]. Primate research investigating categorical inferences in perceptual tasks [46] such as direction discrimination tasks also implicates these parietal and frontal areas. In such tasks, the underlying neural computations may involve the calculation of the likelihood ratio favouring one inferential hypothesis over an alternative [22]. This would involve the incorporation of accumulated sensory information with psychological factors such as the knowledge of the prior probability that a particular hypothesis is correct and the anticipated value of the response. Such computations involve parietal and frontal association cortices in the sustained representation of accumulated sensory evidence, thereby encoding the inferential decision in an abstract sense. Other neurons within these structures prepare and initiate overt responses. The pre-motor and posterior parietal cortices have topographically organised feedforward projections (via corticopontine and pontocerebellar projections) to the cerebellum as well as feedback projections (via the thalamus) from the cerebellum. Taking these findings together suggests that the parietal and pre-motor activations are ideally suited to contribute to the network encoding the ‘leading’ probabilistic hypothesis. However, we must be cautious at this stage in attributing ‘network’ status to these joint activations, given that the connections between the cerebral and cerebellar hemispheres are crossed. Finally, we suggest that the activation observed in medial occipital cortex (area 17) [36] may represent the greater degree of visual imagery involved in the formation, maintenance and comparison of two competing probabilistic hypotheses compared to that involved in the comparison of two completely specified data types. However, subjects did not spontaneously report an increased use of visual imagery in the probabilistic reasoning conditions in post-scanning debriefing and this account of the medial occipital activation is clearly speculative at this stage.
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We were surprised by the marked absence of ventromedial prefrontal cortex activation in the probabilistic reasoning tasks. Activity in this area might have been expected given its suggested role in guessing [13] and in adaptive decision making informed by the representation of prior beliefs or past experience [3,4,20]. However, there were no direct consequences for the subjects of opting for one decision rather than the other in direct contrast to the feedback obtained in the Bechara gambling task [2], nor were the uncertain decisions informed by prior beliefs or past experience [20,41]. The lack of these features may explain the failure to activate this area. During decision making, we consider the value of the options before us and their practical outcomes (based on past experience) in addition to the chances of their happening. By removing a reward or prior belief component, we believe that we have been able to isolate a network subserving probabilistic reasoning which in turn may interact with the ventromedial prefrontal cortex in considering the respective utilities of competing decisions based on past experience. The interaction effects are unsurprisingly accounted for by the contrasting material employed in the two experiments (words or balls). Thus, areas activated to a greater extent when decision making under uncertainty employed words are implicated in the semantic processing of words (Wernike’s area, BA 21, temporal pole, BA 38 and left posterior inferior parietal cortex, BA40) [47]. Areas activated to a greater extent when decision making under uncertainty employed balls are implicated in object episodic memory encoding and object working memory (inferior parietal lobe, BA 40, left inferior temporal gyrus, BA37) [12,32] object imagery (middle occipital gyrus, BA 19) [35] and sequence learning (right precentral gyrus) [25]. In conclusion, it has been speculated that internal cerebellar models might have a role not only in motor control but also in cognition [57], and that they might form the basis of cognitive processes in which predictive functions are important [31]. Prediction under conditions of uncertainty is the central feature of induction examined in this study. We suggest that forms of representation within the cerebellum that evolved as part of a limited task domain such as motor control (the monitoring of the uncertain consequences of motor commands) have become accessible for other tasks which can exploit this specialisation including inferential thought (the monitoring of the uncertain meaning of ambiguous external events).
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