Related papers: Pointwise defined version of conditional expectati…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
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 $A$,…
A known property of conditional expectation is extended to the framework of Markov kernels. Its meaning in terms of densities is provided. Some examples located in the field of clinical diagnosis are presented to delimit the main result of…
There is a growing interest in the so-called Bayesian Predictive Inference approach, which allows to perform Bayesian inference without specifying the likelihood and prior of the model, or the need of any MCMC. Instead, only a sequence of…
In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on $\mathbb{R}^k,$ considering both constrained and unconstrained frameworks. For each setting, we define the associated…
We consider a class of conditional forward-backward diffusion models for conditional generative modeling, that is, generating new data given a covariate (or control variable). To formally study the theoretical properties of these…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
Many important statistical models fall outside classical moment-based methods due to the non-existence of moments or moment generating functions. We propose a generalised probabilistic framework in which densities are replaced by pairs…
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…
The Papangelou intensities of determinantal (or fermion) point processes are investigated. These exhibit a monotonicity property expressing the repulsive nature of the interaction, and satisfy a bound implying stochastic domination by a…
In this article, we review selective inference, a set of techniques for inference when the statistical question asked is a function of the data. This setting often arises in contemporary scientific workflows, where hypotheses and parameters…
The new estimates of the conditional Shannon entropy are introduced in the framework of the model describing a discrete response variable depending on a vector of d factors having a density w.r.t. the Lebesgue measure in R^d. Namely, the…
We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the…
Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some…
Deriving exact density functions for Gibbs point processes has been challenging due to their general intractability, stemming from the intractability of their normalising constants/partition functions. This paper offers a solution to this…
We propose an estimation method for the conditional mode when the conditioning variable is high-dimensional. In the proposed method, we first estimate the conditional density by solving quantile regressions multiple times. We then estimate…
We propose a general new method, the conditional permutation test, for testing the conditional independence of variables $X$ and $Y$ given a potentially high-dimensional random vector $Z$ that may contain confounding factors. The proposed…
Conditionals play a key role in different areas of logic and probabilistic reasoning, and they have been studied and formalized from different angles. In this paper we focus on the de Finetti's notion of conditional as a three-valued…
Conditionally specified models are often used to describe complex multivariate data. Such models assume implicit structures on the extremes. So far, no methodology exists for calculating extremal characteristics of conditional models since…
We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known…