Related papers: The Bayesian Who Knew Too Much

When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…

Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential…

The choice of priors may become an insoluble problem if priors and Bayes' rule are not seen and accepted in the framework of subjectivism. Therefore, the meaning and the role of subjectivity in science is considered and defended from the…

After experimenting with a number of non-probabilistic methods for dealing with uncertainty many researchers reaffirm a preference for probability methods [1] [2], although this remains controversial. The importance of being able to form…

Neural networks are powerful function approximators with tremendous potential in learning complex distributions. However, they are prone to overfitting on spurious patterns. Bayesian inference provides a principled way to regularize neural…

Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and…

Bayesian inference paradigms are regarded as powerful tools for solution of inverse problems. However, when applied to inverse problems in physical sciences, Bayesian formulations suffer from a number of inconsistencies that are often…

In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process…

Currently, there is renewed interest in the problem, raised by Shafer in 1985, of updating probabilities when observations are incomplete. This is a fundamental problem in general, and of particular interest for Bayesian networks. Recently,…

Could an AI have conscious experiences? Any answer to this question should conform to Evidentialism - that is, it should be based not on intuition, dogma or speculation but on solid scientific evidence. I argue that such evidence is hard to…

One difficulty faced in knowledge engineering for Bayesian Network (BN) is the quan-tification step where the Conditional Probability Tables (CPTs) are determined. The number of parameters included in CPTs increases exponentially with the…

There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Go\"edel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things…

Background: Confirmation bias is the tendency to acquire or evaluate new information in a way that is consistent with one's preexisting beliefs. It is omnipresent in psychology, economics, and even scientific practices. Prior theoretical…

The willingness to trust predictions formulated by automatic algorithms is key in a vast number of domains. However, a vast number of deep architectures are only able to formulate predictions without an associated uncertainty. In this…

Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm,…

Over time, there have hen refinements in the way that probability distributions are used for representing beliefs. Models which rely on single probability distributions depict a complete ordering among the propositions of interest, yet…

In normative models a decision-maker is usually assumed to be Bayesian rational, and so to maximize subjective expected utility, within a complete and correctly specified decision model. Following the discussion in Hammond (2007) of…

Bayesian networks provide a probabilistic semantics for qualitative assertions about likelihood. A qualitative reasoner based on an algebra over these assertions can derive further conclusions about the influence of actions. While the…

We argue that the Bayesian paradigm, of a prior which represents the beliefs of the statistician before observing the data, is not feasible in ultra-high-dimensional models. We claim that natural priors that represent the a priori beliefs…

Whether the fate of our species can be forecast from its past has been the topic of considerable controversy. One refutation of the so-called Doomsday Argument is based on the premise that we are more likely to exist in a universe…