20 papers · ranked by Valyu relevance
Ryan Martin
An inferential model (IM) is a model describing the construction of provably reliable, data-driven uncertainty quantification and inference about relevant unknowns. IMs and Fisher's fiducial argument have similar objectives, but a fundamental distinction between the two is that the former doesn't require that…
Christian Fröhlich, Robert C. Williamson
What does it mean to say that, for example, the probability for rain tomorrow is between 20% and 30%? The theory for the evaluation of precise probabilistic forecasts is well-developed and is grounded in the key concepts of proper scoring rules and calibration. For the case of imprecise probabilistic forecasts (sets of…
Gernot D. Kleiter
The contribution proposes to model imprecise and uncertain reasoning by a mental probability logic that is based on probability distributions. It shows how distributions are combined with logical operators and how distributions propagate in inference rules. It discusses a series of examples like the Linda task, the…
Justus Hibshman, Tim Weninger
We generalize standard credal set models for imprecise probabilities to include higher order credal sets – confidences about confidences. In doing so, we specify how an agent's higher order confidences (credal sets) update upon observing an event. Our model begins to address standard issues with imprecise probability…
A. E. Allahverdyan, Arshag Danageozian
Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g. via quasi-probabilities or via hidden-variable theories. After…
Rabanus Derr, Robert C. Williamson, Andrei Khrennikov, Karl Svozil
In the literature on imprecise probability, little attention is paid to the fact that imprecise probabilities are precise on a set of events. We call these sets systems of precision. We show that, under mild assumptions, the system of precision of a lower and upper probability form a so-called (pre-)Dynkin system.…
Ruobin Gong, Xiao‐Li Meng
Statistical learning using imprecise probabilities is gaining more attention because it presents an alternative strategy for reducing irreplicable findings by freeing the user from the task of making up unwarranted high-resolution assumptions. However, model updating as a mathematical operation is inherently exact…
Karl Halvor Teigen
The paper reviews two strands of research on communication of uncertainty that usually have been investigated separately: (1) Probabilities attached to specific outcomes, and (2) Range judgments. Probabilities are sometimes expressed by verbal phrases (“rain is likely”) and at other times in a numeric format (“70%…
Serafín Moral-García, María D. Benítez, Joaquín Abellán, Carlos Alberto De Bragança Pereira
'Carlos Alberto De Bragança Pereira'] Imprecise classification is a relatively new task within Machine Learning. The difference with standard classification is that not only is one state of the variable under study determined, a set of states that do not have enough information against them and cannot be ruled out is…
Charles Findling, Nicolas Chopin, Etienne Koechlin
Everyday life features uncertain and ever-changing situations. In such environments, optimal adaptive behavior requires higher-order inferential capabilities to grasp the volatility of external contingencies. These capabilities however involve complex and rapidly intractable computations, so that we poorly understand…
Sangeet S. Khemlani, Max Lotstein, Phil Johnson-Laird, Kevin Paterson
'Kevin Paterson'] Many theorists argue that the probabilities of unique events, even real possibilities such as President Obama's re-election, are meaningless. As a consequence, psychologists have seldom investigated them. We propose a new theory (implemented in a computer program) in which such estimates depend on an…
David Colquhoun
We wish to answer this question If you observe a “significant” P value after doing a single unbiased experiment, what is the probability that your result is a false positive?. The weak evidence provided by P values between 0.01 and 0.05 is explored by exact calculations of false positive rates. When you observe P =…
Adam B. Smith, Stephen J. Murphy, David Henderson, Kelley D. Erickson
Museum and herbarium specimen records are frequently used to assess species’ conservation status and responses to climate change. Typically, records of occurrence with imprecise geolocality information are discarded because they cannot be matched confidently to environmental conditions, and are thus expected to…
Junseok K. Lee, Marion Rouault, Valentin Wyart
Human value-based decisions are strikingly variable under uncertainty. This variability is known to arise from two distinct sources: variable choices aimed at exploring available options, and imprecise learning of option values due to limited cognitive resources. However, whether these two sources of decision…
Nicolas Gauvrit, Kinga Morsanyi
Perspective Authors: ['Nicolas Gauvrit' 'Kinga Morsanyi'] The equiprobability bias (EB) is a tendency to believe that every process in which randomness is involved corresponds to a fair distribution, with equal probabilities for any possible outcome. The EB is known to affect both children and adults, and to increase…
Authors not listed
Traditional electron-configuration notation (e.g. 1s^2 2s^2 2p^6) compresses multi-electron quantum information into integer occupancies that convey allowed maxima and most-probable arrangements but obscure the underlying probabilistic distribution and the spread of possible measurement outcomes. We present a…
Mattias Forsgren, Peter Juslin, Ronald van den Berg
Extensive research in the behavioural sciences has addressed people’s ability to learn stationary probabilities, which stay constant over time, but only recently have there been attempts to model the cognitive processes whereby people learn – and track – non-stationary probabilities. In this context, the old debate on…
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The rapid growth of worldwide computing power has transformed in silico chemistry into a discipline that is integrated into the daily work of many chemists. Nowadays, researchers find it increasingly straightforward to predict a wide range of molecular properties and chemi- cal processes at reasonable computational…
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Machine learning (ML) models are increasingly used in quantum chemistry, but their reliability hinges on uncertainty quantification (UQ). In this study, we compare two prominent UQ paradigms—Deep Evidential Regression (DER) and Deep Ensembles—on the QM9 and WS22 datasets, with a specific emphasis on the role of post…
Maria H. Rasmussen, Chenru Duan, Heather J. Kulik, Jan Halborg Jensen
With the increasingly more important role of machine learning (ML) models in chemical research, the need for putting a level of confidence to the model predictions naturally arises. Several methods for obtaining uncertainty estimates have been proposed in recent years but consensus on the evaluation of these have yet…