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The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
Parameter-space regularization in neural network optimization is a fundamental tool for improving generalization. However, standard parameter-space regularization methods make it challenging to encode explicit preferences about desired…
According to Hansen, Madow and Tepping [J. Amer. Statist. Assoc. 78 (1983) 776--793], "Probability sampling designs and randomization inference are widely accepted as the standard approach in sample surveys." In this article, reasons are…
We consider the problem of maximizing a real-valued continuous function $f$ using a Bayesian approach. Since the early work of Jonas Mockus and Antanas \v{Z}ilinskas in the 70's, the problem of optimization is usually formulated by…
In this paper we address the statistical problem of testing if a stationary process is Gaussian. The observation consists in a finite sample path of the process. Using a random projection technique introduced and studied in Cuesta-Albertos…
Feature selection has remained a daunting challenge in machine learning and artificial intelligence, where increasingly complex, high-dimensional datasets demand principled strategies for isolating the most informative predictors. Despite…
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
We consider the problem of sampling from a distribution governed by a potential function. This work proposes an explicit score based MCMC method that is deterministic, resulting in a deterministic evolution for particles rather than a…
This paper offers a comprehensive introduction to Bayesian inference, combining historical context, theoretical foundations, and core analytical examples. Beginning with Bayes' theorem and the philosophical distinctions between Bayesian and…
While gravitational waves have not yet been measured directly, data analysis from detection experiments commonly includes an upper limit statement. Such upper limits may be derived via a frequentist or Bayesian approach; the theoretical…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
Iteration of randomly chosen quadratic maps defines a Markov process: X_{n+1}=\epsilon_{n+1}X_n(1-X_n), where \epsilon_n are i.i.d. with values in the parameter space [0,4] of quadratic maps F_{\theta}(x)=\theta x(1-x). Its study is of…
Bayesian filtering serves as the mainstream framework of state estimation in dynamic systems. Its standard version utilizes total probability rule and Bayes' law alternatively, where how to define and compute conditional probability is…
An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully…
Quantum-enhanced measurements exploit quantum mechanical effects to provide ultra-precise estimates of physical variables for use in advanced technologies, such as frequency calibration of atomic clocks, gravitational waves detection, and…
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…
The ideal probabilistic forecast for a random variable $Y$ based on an information set $\mathcal{F}$ is the conditional distribution of $Y$ given $\mathcal{F}$. In the context of point forecasts aiming to specify a functional $T$ such as…
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…