Related papers: Laplace's formula: an approach by nonstandard anal…

We consider radial solutions of a general elliptic equation involving a weighted $p$-Laplace operator with a subcritical nonlinearity. By a shooting method we prove the existence of solutions with any prescribed number of nodes. The method…

We present non-asymptotic two-sided bounds to the log-marginal likelihood in Bayesian inference. The classical Laplace approximation is recovered as the leading term. Our derivation permits model misspecification and allows the parameter…

Discriminant analysis (DA) is one of the most popular methods for classification due to its conceptual simplicity, low computational cost, and often solid performance. In its standard form, DA uses the arithmetic mean and sample covariance…

The results of a series of theoretical studies are reported, examining the convergence rate for different approximate representations of $\alpha$-stable distributions. Although they play a key role in modelling random processes with jumps…

Integrated Nested Laplace Approximations (INLA) has been a successful approximate Bayesian inference framework since its proposal by Rue et al. (2009). The increased computational efficiency and accuracy when compared with sampling-based…

In a recent letter (EPL, 104 (2013) 60003) we suggested a way to avoid divergences inherent to the formulation of nonextensive statistical mechanics. They can be eliminated via the use of a q-Laplace transformation, which was illustrated…

TLA+ is a specification language based on standard set theory and temporal logic that has constructs for hierarchical proofs. We describe how to write TLA+ proofs and check them with TLAPS, the TLA+ Proof System. We use Peterson's mutual…

In the article \The State of SAT", the authors asked whether a procedure dramatically different from DPLL can be found for handling unsatisfiable instances. This study proposes a new linear programming approach to address this issue…

SAGA is a fast incremental gradient method on the finite sum problem and its effectiveness has been tested on a vast of applications. In this paper, we analyze SAGA on a class of non-strongly convex and non-convex statistical problem such…

The classical satisfiability problem (SAT) is used as a natural and general tool to express and solve combinatorial problems that are in NP. We postulate that provability for implicational intuitionistic propositional logic (IIPC) can serve…

Truncated sum rules have been used to calculate the fundamental limits of the nonlinear susceptibilities; and, the results have been consistent with all measured molecules. However, given that finite-state models result in inconsistencies…

The goal of this present manuscript is to introduce the reader to the nonstandard method and to provide an overview of its most prominent applications in Ramsey theory and combinatorial number theory.

A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…

We present a new software tool for teaching logic based on natural deduction. Its proof system is formalized in the proof assistant Isabelle such that its definition is very precise. Soundness of the formalization has been proved in…

The marginal likelihood is a well established model selection criterion in Bayesian statistics. It also allows to efficiently calculate the marginal posterior model probabilities that can be used for Bayesian model averaging of quantities…

Bayesian formulations of deep learning have been shown to have compelling theoretical properties and offer practical functional benefits, such as improved predictive uncertainty quantification and model selection. The Laplace approximation…

In this article, we analyze the SPICE method developed in [1], and establish its connections with other standard sparse estimation methods such as the Lasso and the LAD-Lasso. This result positions SPICE as a computationally efficient…

For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…

We use the Laplace transform and the Gamma function to introduce a new integral transform and name it the Laplace-type transform possessing the property of mapping a function to a functional sequence, which cannot be achieved by the Laplace…

Solving of regular equations via Arden's Lemma is folklore knowledge. We first give a concise algorithmic specification of all elementary solving steps. We then discuss a computational interpretation of solving in terms of coercions that…