Related papers: P-measures in models without P-points

Although Bayes's theorem demands a prior that is a probability distribution on the parameter space, the calculus associated with Bayes's theorem sometimes generates sensible procedures from improper priors, Pitman's estimator being a good…

A limitation on simultaneous measurement of two arbitrary positive operator valued measures is discussed. In general, simultaneous measurement of two noncommutative observables is only approximately possible. Following Werner's formulation,…

Are there fundamentally random processes in nature? Theoretical predictions, confirmed experimentally, such as the violation of Bell inequalities, point to an affirmative answer. However, these results are based on the assumption that…

With a view to quantum foundations, we define the concepts of an empirical model (a probabilistic model describing measurements and outcomes), a hidden-variable model (an empirical model augmented by unobserved variables), and various…

A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an "anomalous weak value", is generally believed to…

Point processes and, more generally, random measures are ubiquitous in modern statistics. However, they can only take positive values, which is a severe limitation in many situations. In this work, we introduce and study random signed…

We present a model where \omega_1 is inaccessible by reals, Silver measurability holds for all sets but Miller and Lebesgue measurability fail for some sets. This contributes to a line of research started by Shelah in the 1980s and more…

Diffusion models have shown their effectiveness in generation tasks by well-approximating the underlying probability distribution. However, diffusion models are known to suffer from an amplified inherent bias from the training data in terms…

The Petermann factor and the phase rigidity are convenient measures for various aspects of open quantum and wave systems, such as the sensitivity of energy eigenvalues to perturbations or the magnitude of quantum excess noise in lasers. We…

In this paper, we study the bead model: beads are threaded on a set of wires on the plane represented by parallel straight lines. We add the constraint that between two consecutive beads on a wire; there must be exactly one bead on each…

We deal with countable alphabet locally compact random subshifts of finite type (the latter merely meaning that the symbol space is generated by an incidence matrix) under the absence of Big Images Property and under the absence of uniform…

In [6], a constraint on invariant measures of bi-permutative cellular automata has been observed: fixed values at the positive indices determine almost-surely a uniform conditional probability on the subset of values of positive conditional…

Measurement involves the determination of quantitative estimates of physical quantities from experiment, along with estimates of their associated uncertainties. Herewith an experimental system model is the key to extracting information from…

We present the construction of a probability measure with compact support on R such that adding a discrete pure point results in changes in the recursion coefficients without exponential decay.

The development of mathematically complete and consistent models solving the so-called "measurement problem", strongly renewed the interest of the scientific community for the foundations of quantum mechanics, among these the Dynamical…

By forcing with $\mathbb{P}_{\rm max}$ over strong models of determinacy, we obtain models where different square principles at $\omega_2$ and $\omega_3$ fail. In particular, we obtain a model of $2^{\aleph_0}=2^{\aleph_1}=\aleph_2 +…

Deciding whether a model provides a good description of data is often based on a goodness-of-fit criterion summarized by a p-value. Although there is considerable confusion concerning the meaning of p-values, leading to their misuse, they…

One can consider $\mu$-Martin-L\"of randomness for a probability measure $\mu$ on $2^{\omega}$, such as the Bernoulli measure $\mu_p$ given $p \in (0, 1)$. We study Bernoulli randomness of sequences in $n^{\omega}$ with parameters $p_0,…

The presence of measurement error is a widespread issue which, when ignored, can render the results of an analysis unreliable. Numerous corrections for the effects of measurement error have been proposed and studied, often under the…

In many scientific and data-driven applications, machine learning models are increasingly used as measurement instruments, rather than merely as predictors of predefined labels. When the measurement function is learned from data, the…