We show: (1) It is possible to produce the three familiar statistics without referring to the problem of distinguishability; (2) what really distinguishes elementary particles is the correlation existing among them; (3) correlations existing among quantum particles, positive for bosons and negative form fermions, are completely different in character.

A generalization of Ehrenfest''s urn model is suggested. This will allow usto treat a wide class of stochastic processes describing the changes ofmicroscopic objects. These processes are homogeneous Markov chains. Thegeneralization proposed is presented as an abstract conditional (relative)probability theory. The probability axioms of such a theory and some simpleadditional conditions, yield both transition probabilities and equilibriumdistributions. The resulting theory interpreted in terms of particles andsingle-particle states, leads to the usual formulae of quantum and classicalstatistical mechanics; in terms of chromosomes (...) and allelic types, it allowsthe deduction of many genetical models including the Ewens sampling formula;in terms of agents'' strategies, it gives a justification of the ``herdbehaviour'''' typical of a population of heterogeneous economic agents. (shrink)

The aim of the present paper is to give a purely probabilistic account for the approach to equilibrium of classical and quantum gas. The probability function used is classical. The probabilistic dynamics describes the evolution of the state of the gas due to unary and binary collisions. A state change amounts to a destruction in a state and the creation in another state. Transitions probabilities are splittled into destructions terms, denoting the random choice of the colliding particle(s), and creation terms, (...) describing the allocation of the same particle(s) on the final state(s). While the destruction term is the same for all types of particles, the creation one depends upon a parameter bound to the interpraticle correlation. The transition probabilities give rise to a homogeneous Markov chain. The equilibrium distributions satisfy the principle of detailed balance. Relaxation times depend upon the interparticle correlation. Relationships with the Ehrenfest urn model, Brillouin unified method, ensemble interpretation, and quantum H-theorem are considered too. (shrink)

A pure probabilistic approach to Gibbs' distributions is given, starting from the notion of “finite exchangeable random process.” The differences between bosons, fermions, and classical particles are ascribed to different values of correlation. The relationship between exchangeability and constraints on the energy distribution is investigated.

In the present paper we face the problem of estimating cell probabilities in the case of a two-dimensional contingency table from a predictive point of view. The solution is given by a double stochastic process. The first subprocess, the unobservable one, is supposed to be exchangeable and invariant. For the second subprocess, the observable one, we suppose it is independent conditional on the first one.

The proceedings of a June 1995 conference in Luino, Italy. One poem and 16 papers explore various issues in the philosophy of science with an emphasis on the foundations of probability and statistics and quantum mechanics. The topics include subjective probability, Bayesian statistics, probability kinematics, causal decision making, and probability and realism in quantum mechanics. The problem of collecting new evidence and updating probability judgements are addressed in reference to different applications. No index. Reprinted from Erkenntnis vol. 45, nos. 2-3 (...) (1996). Annotation copyrighted by Book News, Inc., Portland, OR. (shrink)