Related papers: Infinite lattice models by expansion with a non-Ga…
It is often the case in Statistics that one needs to compute sums of infinite series, especially in marginalising over discrete latent variables. This has become more relevant with the popularization of gradient-based techniques (e.g.…
The quantum-critical properties of the transverse-field Ising model with algebraically decaying interactions are investigated by means of stochastic series expansion quantum Monte Carlo, on both the one-dimensional linear chain and the…
Lattice simulation of supersymmetric gauge theories is not straightforward. In some cases the lack of manifest supersymmetry just necessitates cumbersome fine-tuning, but in the worse cases the chiral and/or Majorana nature of fermions…
The scaling exponent and scaling function for the 1D single species coagulation model $(A+A\rightarrow A)$ are shown to be universal, i.e. they are not influenced by the value of the coagulation rate. They are independent of the initial…
Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…
Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a variable. As an example, several recent studies…
Excited states are extracted from lattice correlation functions using a non-uniform prior on the model parameters. Models for both a single exponential and a sum of exponentials are considered, as well as an alternate model for the…
Mixture models are one of the most widely used statistical tools when dealing with data from heterogeneous populations. This paper considers the long-standing debate over finite mixture and infinite mixtures and brings the two modelling…
Inverse problems are in many cases solved with optimization techniques. When the underlying model is linear, first-order gradient methods are usually sufficient. With nonlinear models, due to nonconvexity, one must often resort to…
The finite lattice method of series expansion is generalised to the $q$-state Potts model on the simple cubic lattice. It is found that the computational effort grows exponentially with the square of the number of series terms obtained,…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
In this paper we address the questions of perfectly sampling a Gibbs measure with infinite range interactions and of perfectly sampling the measure together with its finite range approximations. We solve these questions by introducing a…
Conformal field theory predicts finite-size scaling amplitudes of correlation lengths universally related to critical exponents on sphere-like, semi-finite systems $S^{d-1}\times\mathbb{R}$ of arbitrary dimensionality $d$. Numerical studies…
We provide a general methodology for unbiased estimation for intractable stochastic models. We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…
In Monte Carlo calculations of expectation values in lattice quantum field theories, the stochastic variance of the sampling procedure that is used defines the precision of the calculation for a fixed number of samples. If the variance of…
Latent Gaussian process (GP) models are flexible probabilistic non-parametric function models. Vecchia approximations are accurate approximations for GPs to overcome computational bottlenecks for large data, and the Laplace approximation is…
Martingale methods are used to study the almost everywhere convergence of general function series. Applications are given to ergodic series, which improves recent results of Fan \cite{FanETDS}, and to dilated series, including Davenport…
This paper focuses on the equivalent expression of fractional integrals/derivatives with an infinite series. A universal framework for fractional Taylor series is developed by expanding an analytic function at the initial instant or the…
Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…