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We study approximation methods for a large class of mixed models with a probit link function that includes mixed versions of the binomial model, the multinomial model, and generalized survival models. The class of models is special because…

We present and study approximate notions of dimensional and margin complexity, which correspond to the minimal dimension or norm of an embedding required to approximate, rather then exactly represent, a given hypothesis class. We show that…

The goodness of fit methods for classification problems relies traditionally on confusion matrices. This paper aims to enrich these methods with a risk evaluation and stability analysis tools. For this purpose, we present a parametric PDF…

Many statistical models can be simulated forwards but have intractable likelihoods. Approximate Bayesian Computation (ABC) methods are used to infer properties of these models from data. Traditionally these methods approximate the posterior…

Gradients have been exploited in proposal distributions to accelerate the convergence of Markov chain Monte Carlo algorithms on discrete distributions. However, these methods require a natural differentiable extension of the target discrete…

Fitting PDFs requires the integration of a broad range of datasets, both from data and theory side, into a unique framework. While for data the integration mainly consists in the standardization of the data format, for the theory…

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…

The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic…

An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…

Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…

We develop a method for the evaluation of extreme event statistics associated with nonlinear dynamical systems, using a small number of samples. From an initial dataset of design points, we formulate a sequential strategy that provides the…

Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits…

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess…

We continue to explore the hypothesis that neuronal populations represent and process analog variables in terms of probability density functions (PDFs). A neural assembly encoding the joint probability density over relevant analog variables…

A probabilistic circuit (PC) succinctly expresses a function that represents a multivariate probability distribution and, given sufficient structural properties of the circuit, supports efficient probabilistic inference. Typically a PC…

The one-point probability distribution function (PDF) is a powerful summary statistic for non-Gaussian cosmological fields, such as the weak lensing (WL) convergence reconstructed from galaxy shapes or cosmic microwave background (CMB)…

I propose a method to fit the probability distribution function (hereafter PDF) of the large scale density field rho, motivated by a Lagrangian version of the continuity equation. It consists in applying the Edgeworth expansion to the…

The probability density function (PDF) plays a central role in statistical and machine learning modeling. Real-world data often deviates from Gaussian assumptions, exhibiting skewness and exponential decay. To evaluate how well different…

Scientists continue to develop increasingly complex mechanistic models to reflect their knowledge more realistically. Statistical inference using these models can be challenging since the corresponding likelihood function is often…

Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by…