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Monte Carlo methods represent a cornerstone of computer science. They allow to sample high dimensional distribution functions in an efficient way. In this paper we consider the extension of Automatic Differentiation (AD) techniques to Monte…
We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main new ingredient we introduce the superposed…
Random samples of quantum states with specific properties are useful for various applications, such as Monte Carlo integration over the state space. In the high-dimensional situations that one encounters already for a few qubits, the…
We propose a flat-histogram Monte Carlo method to efficiently sample fractal landscapes such as escape time functions of open chaotic systems. This is achieved by using a random-walk step which depends on the height of the landscape via the…
Bayesian Neural Networks (BNNs) provide a promising framework for modeling predictive uncertainty and enhancing out-of-distribution robustness (OOD) by estimating the posterior distribution of network parameters. Stochastic Gradient Markov…
As a widely used method in metabolic network studies, Monte-Carlo sampling in the steady state flux space is known for its flexibility and convenience of carrying out different purposes, simply by alternating constraints or objective…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
Markov Chain Monte Carlo (MCMC) proves to be powerful for Bayesian inference and in particular for exoplanet radial velocity fitting because MCMC provides more statistical information and makes better use of data than common approaches like…
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…
Modern macroeconometrics often relies on time series models for which it is time-consuming to evaluate the likelihood function. We demonstrate how Bayesian computations for such models can be drastically accelerated by reweighting and…
Sequential Monte Carlo Squared (SMC$^2$) is a Bayesian method which can infer the states and parameters of non-linear, non-Gaussian state-space models. The standard random-walk proposal in SMC$^2$ faces challenges, particularly with…
We model a set of point-to-point transports on a network as a system of polydisperse interacting self-avoiding walks (SAWs) over a finite square lattice. The ends of each SAW may be located both at random, uniformly distributed, positions…
Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…
The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-ergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for…
A class of Monte Carlo algorithms which incorporate absorbing Markov chains is presented. In a particular limit, the lowest-order of these algorithms reduces to the $n$-fold way algorithm. These algorithms are applied to study the escape…
A wide class of Bayesian models involve unidentifiable random matrices that display rotational ambiguity, with the Gaussian factor model being a typical example. A rich variety of Markov chain Monte Carlo (MCMC) algorithms have been…
A Monte Carlo method to sample the classical configurational canonical ensemble is introduced. In contrast to the Metropolis algorithm, where trial moves can be rejected, in this approach collisions take place. The implementation is…
Hamiltonian Monte Carlo (HMC) is a powerful Markov chain Monte Carlo (MCMC) algorithm for estimating expectations with respect to continuous un-normalized probability distributions. MCMC estimators typically have higher variance than…
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
We present here two irreversible Markov chain Monte Carlo algorithms for general discrete state systems, one of the algorithms is based on the random-scan Gibbs sampler for discrete states and the other on its improved version, the…