Related papers: What is the question that MaxEnt answers? A probab…
In the many-worlds interpretations (MWIs) of Everett and others, if I am the observer, there are several versions of me but no version is singled out as the one corresponding to my perceptions. However, it can be shown that the probability…
In the following we revisit the frequency interpretation of probability of Richard von Mises, in order to bring the essential implicit notions in focus. Following von Mises, we argue that probability can only be defined for events that can…
We revisit the maximum-entropy inference of the state of a finite-level quantum system under linear constraints. The constraints are specified by the expected values of a set of fixed observables. We point out the existence of…
The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased"…
This paper presents an approach for developing the explanation capabilities of rule-based expert systems managing imprecise and uncertain knowledge. The treatment of uncertainty takes place in the framework of possibility theory where the…
A classical longstanding open problem in statistics is finding an explicit expression for the probability measure which maximizes entropy with respect to given constraints. In this paper a solution to this problem is found, using…
Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac)…
Frequentist inference typically is described in terms of hypothetical repeated sampling but there are advantages to an interpretation that uses a single random sample. Contemporary examples are given that indicate probabilities for random…
We derive asymptotic formulas for the number of integer partitions with given sums of $j$th powers of the parts for $j$ belonging to a finite, non-empty set $J \subset \mathbb N$. The method we use is based on the `principle of maximum…
Jaynes invented the Brandeis Dice Problem as a simple illustration of the MaxEnt (Maximum Entropy) procedure that he had demonstrated to work so well in Statistical Mechanics. I construct here two alternative solutions to his toy problem.…
The new interpretation of Quantum Mechanics is based on a complex probability theory. An interpretation postulate specifies events which can be observed and it follows that the complex probability of such event is, in fact, a real positive…
Finding the underlying probability distributions of a set of observed sequences under the constraint that each sequence is generated i.i.d by a distinct distribution is considered. The number of distributions, and hence the number of…
In this paper, we derive new properties of the Mertens function and discuss a likely upper bound of the absolute value of the Mertens function $\sqrt{\log{x!}}>|M(x)|$ when $x>1$. Using this likely bound we show that we have a sufficient…
We review the Consistent Amplitude approach to Quantum Theory and argue that quantum probabilities are explicitly Bayesian. In this approach amplitudes are tools for inference. They codify objective information about how complicated…
Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…
We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic…
A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that characterize the…
Difficulties over probability have often been considered fatal to the Everett interpretation of quantum mechanics. Here I argue that the Everettian can have everything she needs from `probability' without recourse to indeterminism,…
In "Recognizing the Maximum of a Sequence", Gilbert and Mosteller analyze a full information game where n measurements from an uniform distribution are drawn and a player (knowing n) must decide at each draw whether or not to choose that…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…