24,318 research outputs found
A General Framework for Updating Belief Distributions
We propose a framework for general Bayesian inference. We argue that a valid
update of a prior belief distribution to a posterior can be made for parameters
which are connected to observations through a loss function rather than the
traditional likelihood function, which is recovered under the special case of
using self information loss. Modern application areas make it is increasingly
challenging for Bayesians to attempt to model the true data generating
mechanism. Moreover, when the object of interest is low dimensional, such as a
mean or median, it is cumbersome to have to achieve this via a complete model
for the whole data distribution. More importantly, there are settings where the
parameter of interest does not directly index a family of density functions and
thus the Bayesian approach to learning about such parameters is currently
regarded as problematic. Our proposed framework uses loss-functions to connect
information in the data to functionals of interest. The updating of beliefs
then follows from a decision theoretic approach involving cumulative loss
functions. Importantly, the procedure coincides with Bayesian updating when a
true likelihood is known, yet provides coherent subjective inference in much
more general settings. Connections to other inference frameworks are
highlighted.Comment: This is the pre-peer reviewed version of the article "A General
Framework for Updating Belief Distributions", which has been accepted for
publication in the Journal of Statistical Society - Series B. This article
may be used for non-commercial purposes in accordance with Wiley Terms and
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Neural signals encoding shifts in beliefs
Dopamine is implicated in a diverse range of cognitive functions including cognitive flexibility, task switching, signalling novel or unexpected stimuli as well as advance information. There is also longstanding line of thought that links dopamine with belief formation and, crucially, aberrant belief formation in psychosis. Integrating these strands of evidence would suggest that dopamine plays a central role in belief updating and more specifically in encoding of meaningful information content in observations. The precise nature of this relationship has remained unclear. To directly address this question we developed a paradigm that allowed us to decompose two distinct types of information content, information-theoretic surprise that reflects the unexpectedness of an observation, and epistemic value that induces shifts in beliefs or, more formally, Bayesian surprise. Using functional magnetic-resonance imaging in humans we show that dopamine-rich midbrain regions encode shifts in beliefs whereas surprise is encoded in prefrontal regions, including the pre-supplementary motor area and dorsal cingulate cortex. By linking putative dopaminergic activity to belief updating these data provide a link to false belief formation that characterises hyperdopaminergic states associated with idiopathic and drug induced psychosis
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Learning about a Moving Target in Resource Management: Optimal Bayesian Disease Control
Resource managers must often make difficult choices in the face of imperfectly observed and dynamically changing systems (e.g., livestock, fisheries, water, and invasive species). A rich set of techniques exists for identifying optimal choices when that uncertainty is assumed to be understood and irreducible. Standard optimization approaches, however, cannot address situations in which reducible uncertainty applies to either system behavior or environmental states. The adaptive management literature overcomes this limitation with tools for optimal learning, but has been limited to highly simplified models with state and action spaces that are discrete and small. We overcome this problem by using a recently developed extension of the Partially Observable Markov Decision Process (POMDP) framework to allow for learning about a continuous state. We illustrate this methodology by exploring optimal control of bovine tuberculosis in New Zealand cattle. Disease testing—the control variable—serves to identify herds for treatment and provides information on prevalence, which is both imperfectly observed and subject to change due to controllable and uncontrollable factors. We find substantial efficiency losses from both ignoring learning (standard stochastic optimization) and from simplifying system dynamics (to facilitate a typical, simple learning model), though the latter effect dominates in our setting. We also find that under an adaptive management approach, simplifying dynamics can lead to a belief trap in which information gathering ceases, beliefs become increasingly inaccurate, and losses abound
Reliable Uncertain Evidence Modeling in Bayesian Networks by Credal Networks
A reliable modeling of uncertain evidence in Bayesian networks based on a
set-valued quantification is proposed. Both soft and virtual evidences are
considered. We show that evidence propagation in this setup can be reduced to
standard updating in an augmented credal network, equivalent to a set of
consistent Bayesian networks. A characterization of the computational
complexity for this task is derived together with an efficient exact procedure
for a subclass of instances. In the case of multiple uncertain evidences over
the same variable, the proposed procedure can provide a set-valued version of
the geometric approach to opinion pooling.Comment: 19 page
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