Related papers: Kepler versus Akaike
The Akaike information criterion (AIC) is a common tool for model selection. It is frequently used in violation of regularity conditions at parameter space singularities and boundaries. The expected AIC is generally not asymptotically…
The concept of sphere of influence of a planet is useful in both the context of impact monitoring of asteroids with the Earth and of the design of interplanetary trajectories for spacecrafts. After reviewing the classical results, we…
This article is a brief guide to the field of algorithmic information theory (AIT), its underlying philosophy, and the most important concepts. AIT arises by mixing information theory and computation theory to obtain an objective and…
AIC is commonly used for model selection but the precise value of AIC has no direct interpretation. We are interested in quantifying a difference of risks between two models. This may be useful for both an explanatory point of view or for…
We argue that Anton Zeilinger's "foundational conceptual principle" for quantum mechanics according to which an elementary system carries one bit of information is an idealistic principle, which should be replaced by a realistic principle…
We present a new framework to characterize the occurrence rates of planet candidates identified by Kepler based on hierarchical Bayesian modeling, Approximate Bayesian Computing (ABC), and sequential importance sampling. For this study we…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
For the multivariate linear regression model with unknown covariance, the corrected Akaike information criterion is the minimum variance unbiased estimator of the expected Kullback--Leibler discrepancy. In this study, based on the loss…
A brief explanation of the meaning of the anthropic principle - as a prescription for the attribution of a priori probability weighting - is illustrated by various cosmological and local applications, in which the relevant conclusions are…
The model of the Universe in this paper uses equations of the unperturbed Keplerian motion. They have been updated, complementied and generalized when the solution of these equations is the characteristic function of a random value from the…
Interpretation of cosmological data to determine the number and values of parameters describing the universe must not rely solely on statistics but involve physical insight. When statistical techniques such as "model selection" or…
In an era when we are charting multiple planets per system, one might wonder the extent to which "missing" (or failing to detect) a planet can skew our interpretation of the system architecture. We address this question with a simple…
We introduce and investigate a simple model of conditional quantum dynamics. It allows for a discussion of the information-theoretic aspects of quantum measurements, decoherence, and environment-induced superselection (einselection).
All natural things process and transform information. They receive environmental information as input, and transform it into appropriate output responses. Much of science is dedicated to building models of such systems -- algorithmic…
A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points.…
The Akaike information criterion (AIC) has been used as a statistical criterion to compare the appropriateness of different dark energy candidate models underlying a particular data set. Under suitable conditions, the AIC is an indirect…
In this contribution to FQXi's essay contest 2018, I suggest that it is sometimes a step forward to reverse our intuition on "what is fundamental", a move that is somewhat reminiscent of the idea of noncommutative geometry. I argue that…
Recent work on interpretability in machine learning and AI has focused on the building of simplified models that approximate the true criteria used to make decisions. These models are a useful pedagogical device for teaching trained…
We investigated the underlying architecture of planetary systems by deriving the distribution of planet multiplicity (number of planets) and the distribution of orbital inclinations based on the sample of planet candidates discovered by the…
We examine counterfactual explanations for explaining the decisions made by model-based AI systems. The counterfactual approach we consider defines an explanation as a set of the system's data inputs that causally drives the decision (i.e.,…