Related papers: Constriction for sets of probabilities
A stream of algorithmic advances has steadily increased the popularity of the Bayesian approach as an inference paradigm, both from the theoretical and applied perspective. Even with apparent successes in numerous application fields, a…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
There is wide support in logic, philosophy, and psychology for the hypothesis that the probability of the indicative conditional of natural language, $P(\textit{if } A \textit{ then } B)$, is the conditional probability of $B$ given $A$,…
Non-closedness of subexponentiality by the convolution operation is well-known. We go a step further and show that subexponentiality and non-subexponentiality are generally changeable by the convolution. We also give several conditions, by…
Constraint Satisfaction Problems are ubiquitous in fields ranging from the physics of solids to artificial intelligence. In many cases, such systems undergo a transition when the ratio of constraints to variables reaches some value…
We introduce a testing-by-betting framework that leverages predictions on unlabeled data to enhance the power of sequential hypothesis testing. Given limited samples from the joint distribution of $(X,Y)$, and additional unlabeled samples…
We consider a broad class of permutation invariant statistical problems by extending the standard decision theoretic definition to allow also selective inference tasks, where the target is specified only after seeing the data. For any such…
Closed testing procedures are classically used for familywise error rate (FWER) control, but they can also be used to obtain simultaneous confidence bounds for the false discovery proportion (FDP) in all subsets of the hypotheses. In this…
Regression in supervised learning often requires the enforcement of constraints to ensure that the trained models are consistent with the underlying structures of the input and output data. This paper presents an iterative procedure to…
Hypothesis tests and confidence intervals are ubiquitous in empirical research, yet their connection to subsequent decision-making is often unclear. We develop a theory of certified decisions that pairs recommended decisions with…
The probability of observing $x_t$ at time $t$, given past observations $x_1...x_{t-1}$ can be computed with Bayes' rule if the true generating distribution $\mu$ of the sequences $x_1x_2x_3...$ is known. If $\mu$ is unknown, but known to…
Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…
We consider the problem of determining feasible systems from a finite set of simulated alternatives with respect to probability constraints, where the observations from stochastic simulations are Bernoulli distributed. Most statistically…
Contextuality is usually defined as absence of a joint distribution for a set of measurements (random variables) with known joint distributions of some of its subsets. However, if these subsets of measurements are not disjoint,…
We study hypothesis testing under communication constraints, where each sample is quantized before being revealed to a statistician. Without communication constraints, it is well known that the sample complexity of simple binary hypothesis…
This paper considers a distributionally robust chance constraint model with a general ambiguity set. We show that a sample based approximation of this model converges under suitable sufficient conditions. We also show that upper and lower…
In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process…
In this paper we give an improved upper bound, as compared to the one given in [3] for the number of extreme points of the convex set of all G-invariant probability measures on X*Y with given marginals of full support.
We introduce probability estimation, a broadly applicable framework to certify randomness in a finite sequence of measurement results without assuming that these results are independent and identically distributed. Probability estimation…
Let $(X_n:n\ge 1)$ be a sequence of random observations. Let $\sigma_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the $n$-th predictive distribution and $\sigma_0(\cdot)=P(X_1\in\cdot)$ the marginal distribution of $X_1$. In…