M1 stats: p(r|y)= 0.5646, pxp=1
winning model | 3-level HGF
1 Freeman, Daniel. "Suspicious minds: the psychology of persecutory delusions." Clinical psychology review 27.4 (2007): 425-457.
2Stephan, Klaas Enno, and Christoph Mathys. "Computational approaches to psychiatry." Current opinion in neurobiology 25 (2014): 85-92.
3Friston, Karl. "A theory of cortical responses." Philosophical transactions of the Royal Society B: Biological sciences 360.1456 (2005): 815-836.
4 Rao, Rajesh PN, and Dana H. Ballard. "Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects." Nature neuroscience 2.1 (1999): 79.
5Lee, Tai Sing, and David Mumford. "Hierarchical Bayesian inference in the visual cortex." JOSA A 20.7 (2003): 1434-1448.
6Doya, Kenji. "Modulators of decision making." Nature neuroscience 11.4 (2008): 410.
7Fletcher, Paul C., and Chris D. Frith. "Perceiving is believing: a Bayesian approach to explaining the positive symptoms of schizophrenia." Nature Reviews Neuroscience 10.1 (2009): 48.
8Corlett, Phil R., et al. "Toward a neurobiology of delusions." Progress in neurobiology 92.3 (2010): 345-369.
9Stephan, Klaas E., Andreea O. Diaconescu, and Sandra Iglesias. "Bayesian inference, dysconnectivity and neuromodulation in schizophrenia." Brain 139.7 (2016): 1874-1876.
10 Stephan, Klaas Enno, et al. "Bayesian model selection for group studies." Neuroimage 46.4 (2009): 1004-1017.
11 Mathys, Christoph, et al. "A Bayesian foundation for individual learning under uncertainty." Frontiers in human neuroscience 5 (2011): 39.
12 Freeman, Daniel, et al. "Psychological investigation of the structure of paranoia in a non-clinical population." The British Journal of Psychiatry 186.5 (2005): 427-435.
13 Adams, Rick A., et al. "The computational anatomy of psychosis." Frontiers in psychiatry 4 (2013): 47.
analysis methods | model parameter comparison
I. Initial prior beliefs about adviser fidelity, !"
#$% &'()*+ ,-(./0
II. Tonic evolution rate at 2nd level (adviser fidelity), 1"&23'2 4567)8 45
III.Social weighting parameter,9&'()*+ :'()*+ ,-(./0
IV. Belief precision at 2nd level ,;"~'()*+ ,-(./0 ,+2.<0 (task phase
after volatility vs.before volatility, see figure 2).
2-way ANOVAs on MAP estimates for =>
3-way ANOVA on MAP estimates for E>
low PD, dispositional
low PD, situational
figure 3 | model comparison –model space and winning model
* p<0.05, ** p<0.01, *** p<0.001
social weighting parameter
winning model | equations
Mapping of level 1 (
, advice accuracy) to level 2 (
I JKJ>L M J>NOG P M?J>BKQNOLR0(S)*773 ?JKT M J>B
M J U K
KVWXY QN 
Mapping of level 2 (
, advice validity) to level 3 (
, volatility of
?@B[ ][ C>L ^ J>
?@B : C>
?@QKB[ C\L ^ J\
Belief update equation:
The trial-wise updating of beliefs at any level of the hierarchy by
PEs depends on their weighting by sensory relative to prior
precision.Thus beliefs are updated more readily the more precise
the sensory information and the less precise (certain) the prior
belief. I.e. agents who are highly confident in their predictions are
less likely to update their model of the world in the face of
analysis methods |model comparison
The model space
consisted of 6perceptual models paired with 3
response models [see figure 3] which proposed that participants’
beliefs are based on (i) both cue &advice information (integrated), (ii)
advice only (advice),or (ii) cue only, i.e. that only the given cue
probabilities (i.e., the pie chart) enter the belief-to-response mapping
We performed random effects Bayesian model selection
which treats the model as arandom variable in the population and
allows for estimating which proportion of the population is best
described by each of the models considered.
high PD, dispositional
high PD, situational
initial beliefs about adviser fidelity
tonic evolution rate
Low PD participants
exhibited higher evolution rates (1")in the
dispositional compared to the situational frame, suggesting that they
updated their beliefs about the adviser’s fidelity more rapidly in the
condition when the adviser was emphasized as the potential source of
High PD participants
exhibited lower evolution rates (1")(than low
PD participants) which were similar across the two experimental
frames.This suggests that their belief-updating process was similar
across experimental frames, and –consistent with the group-by-frame
interaction for the social weighting parameter F–that they made less
use of social context when learning from advice.
High PD participants
also showed less variable belief precision (;")
estimates across experimental frames (vs.low PD) suggesting that
they might have amodel of the adviser’s intentions that is less
susceptible to contextual information (i.e., the frame).This is
corroborated by the reduced influence of experimental framing with
regard to how much high PD participants took into account social
The results of the current study support the general idea that
delusions can be conceptualized as beliefs with overly high precision
and that belief precision might also be increased on the subclinical
belief precision at 2nd level
n.s. p > 0.24
experimental methods | procedure
We examined social inference with aprobabilistic advice-
taking task in asocial context and investigated the role of precision in
the belief updating process by manipulating (i) changes in the
association strength between advice and outcome (volatility) and (ii) the
social context by instructing participants about the task under one of
two experimental frames (experimentally-induced priors).
etween-subject factorial design with 2groups (high PD
vs.low PD)and 2conditions (dispositional vs.situational frame).
We prescreened N=1’145 individuals from the general
population, and included 151 participants who exhibited either low or
high scores on the Paranoia Checklist (PCL) 12 across 3time points
spanning over >5 weeks. All cells (group xcondition) were matched
regarding age, gender, and education in years.
Participants played an iterative probabilistic advice-taking
paradigm [see figure 2] under one of 2experimental frames,which
differentially emphasized causes of invalid advice:
(i) the adviser’s possible intentions (dispositional frame), or
(ii) the rules of the game (situational frame).
Participants had to make binary decisions (blue vs.green) based
on asocial and anon-social cue (advice &pie chart) presented
simultaneously.Players could accumulate points with every correct
prediction.After predicting what colour would ‘win’ they were informed
regarding the real outcome.
Pie chart probabilities varied between 50:50,55:45,and 65:35.Advice
validity was varied across 210 trials [see figure 2].Correct predictions
result in the accumulation of points growing aprogress-bar toward the
targets displayed.Surpassing the targets earned participants an
additional smaller bonus (silver target) or large bonus (gold target)
additional to the standard reimbursement for their time.
Hierarchical Bayesian models of social inference for probing
persecutory delusional ideation
Andreea O. Diaconescu* 1, 2, Katharina V. Wellstein* 1, Lars Kasper 1, 3, Christoph Mathys 1, 4, Klaas Enno Stephan 1, 5, 6
Translational Neuromodeling Unit (TNU), Institute for Biomedical Engineering, University of Zurich & ETH Zurich, Switzerland,
Department of Psychiatry (UPK), University of Basel, Switzerland,
Institute for Biomedical Engineering, MR Technology Group, ETH Zurich & University of Zurich, Switzerland,
Scuola Internazionale Superiore di Studi Avanzati (SISSA), Trieste, Italy,
Centre for Human Neuroimaging, University College London, UK,
Max Planck Institute for Metabolism Research, Cologne, Germany
This generative model assumes that
top-down predictions about sensory
inputs are updated by experience via
prediction errors (PEs).which are
weighted with their inverse variance
(precision) 5,6 [see figure 1].
Based on this framework delusions
have been proposed to arise from
increased sensory precision of low-
level PEs, rendering these PEs
abnormally salient and leading to a
chronic surprise about sensory inputs.
It is assumed that the subsequent
formation of highly precise high-level
beliefs may represent acompensatory
response that is required to “explain
away” the low-level PE signals 7,8.
figure 1 | illustration of
predictive coding process 9
040 80 120 160 200
task probability structure
inter-trial interval advice / cue decision outcome
3-4 sec 2 sec 5 sec 1 sec
figure 2 | social learning task and probability structure of advice validity
volatile task phase
CP Course code & behavior contact
analysis plan analysis
introduction | background
Persecutory delusions (PD)
are defined as an agent’s beliefs that others
are acting deliberately to cause them harm despite disconfirming
evidence 1.PD have been linked to fallacies of reasoning (e.g. jumping
to conclusions) and deficits in social inference.However, mechanistic
insight into the underlying processes are rare.
has been proposed as apromising approach to
understand these underlying mechanisms, i.e. how sensory inputs are
probabilistically generated by hidden states of the world 2.
Bayesian brain theories and predictive coding provide such a
generative model and propose that the brain infers on the causes of its
sensations using ahierarchically structured model of the world 3,4.
_o0730- &i+(0l3<3)S ,i
volatile phase 2nd stable
volatile phase 2nd stable