Related papers: Simpson's Paradox: A Singularity of Statistical an…
A double occurrence word $w$ over a finite alphabet $\Sigma$ is a word in which each alphabet letter appears exactly twice. Such words arise naturally in the study of topology, graph theory, and combinatorics. Recently, double occurrence…
The Boolean satisfiability problem (SAT) is a well-known example of monotonic reasoning, of intense practical interest due to fast solvers, complemented by rigorous fine-grained complexity results. However, for non-monotonic reasoning,…
I argue that if a special science satisfies certain key assumptions that are familiar from physicalist accounts of the special sciences and from physics, then its causal regularities have an associated notion of entropy, and that this…
Demonstrations of quantum entanglement which confirm the violation of Bell's inequality indicate that under certain conditions action at a distance is possible. This consequence seems to contradict the relativistic principle of causality,…
We argue that the notion of epistemic \emph{possible worlds} in constructivism (intuitionism) is not as the same as it is in classic view, and there are possibilities, called non-predetermined worlds, which are ignored in (classic)…
The "paradox" arises in the Two Envelopes Paradox from the incorrect formulation of the argument. The infomation given is misused and therefore the results are incorrect for the question asked. The key is to be clear on what question we are…
If the quantum mechanical description of reality is not complete and a hidden variable theory is possible, what arises is the problem to explain where the rates of the outcomes of statistical experiments come from, as already noticed by…
We present methodology for constructing exact significance tests for cross tabulated data for "difficult" composite alternative hypotheses that have no natural test statistic. We construct a test for discovering Simpson's Paradox and a…
The Jeffreys-Lindley paradox stands as the most profound divergence between frequentist and Bayesian approaches to hypothesis testing. Yet despite more than six decades of discussion, this paradox remains frequently misunderstood--even in…
Statistical mechanics determines the abundance of different arrangements of matter depending on cost-benefit balances. Its formalism and phenomenology percolate throughout biological processes and set limits to effective computation. Under…
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…
This paper investigates a statistical procedure for testing the equality of two independent estimated covariance matrices when the number of potentially dependent data vectors is large and proportional to the size of the vectors, that is,…
We study the complexity of satisfiability problems in probabilistic and causal reasoning. Given random variables $X_1, X_2,\ldots$ over finite domains, the basic terms are probabilities of propositional formulas over atomic events $X_i =…
The Sapient Paradox is the apparently unexplainable time delay of several ten thousand years following the arrival of Homo sapiens in Asia and Europe and before the introduction of impressive innovations with the agricultural revolution.…
In a recent paper published in the Journal of Causal Inference, Philip Dawid has described a graphical causal model based on decision diagrams. This article describes how single-world intervention graphs (SWIGs) relate to these diagrams. In…
This paper calls attention to the current state of the probability (P) domain which presents weak points at the mathematical level and more significant flaws at the application level. Popper notices how fundamental issues raised in quantum…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
In the last ten years, the employment of symbolic methods has substantially extended both the theory and the applications of statistics and probability. This survey reviews the development of a symbolic technique arising from classical…
We propose an abductive diagnosis theory that integrates probabilistic, causal and taxonomic knowledge. Probabilistic knowledge allows us to select the most likely explanation; causal knowledge allows us to make reasonable independence…
Quantum pre- and post-selection (PPS) paradoxes occur when counterfactual inferences are made about different measurements that might have been performed, between two measurements that are actually performed. The 3 box paradox is the…