Related papers: Optimal Monte Carlo Updating
Using a dual representation of lattice fermion models that is based on spin-charge transformation and fermionisation of the original description, I derive an algorithm for diagrammatic Monte Carlo simulation of strongly correlated systems.…
Second order stochastic optimization methods, such as the linear method, couple the updates of different parameters and, in so doing, allow statistical uncertainty in one parameter to affect the update of other parameters. In simple tests,…
Many physical systems can be described in terms of matrix models that we often cannot solve analytically. Fortunately, they can be studied numerically in a straightforward way. Many commonly used algorithms follow the Monte Carlo method,…
A new algorithm for Monte Carlo calculation of the double exchange model is studied. The algorithm is commonly applicable to wide classes of strongly correlated electron systems which involve itinerant electrons coupled with…
We propose a method to obtain the optimal weight function of 9 paths in (3+1)D space-time whose length is less than or equal to $2\times (6+2)$ lattice units. The factor 2 comes from inclusion of opposite direction path or time reversed…
Sequential Monte Carlo techniques are useful for state estimation in non-linear, non-Gaussian dynamic models. These methods allow us to approximate the joint posterior distribution using sequential importance sampling. In this framework,…
Markov chain Monte Carlo methods are often deemed too computationally intensive to be of any practical use for big data applications, and in particular for inference on datasets containing a large number $n$ of individual data points, also…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…
Efficient quantum Monte Carlo update schemes called directed loops have recently been proposed, which improve the efficiency of simulations of quantum lattice models. We propose to generalize the detailed balance equations at the local…
Recently there have been exciting developments in Monte Carlo methods, with the development of new MCMC and sequential Monte Carlo (SMC) algorithms which are based on continuous-time, rather than discrete-time, Markov processes. This has…
We introduce a new framework for efficient sampling from complex probability distributions, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core idea is to use continuous transportation to transform…
We propose a new Markov chain Monte Carlo method in which trial configurations are generated by evolving a state, sampled from a prior distribution, using a Markov transition matrix. We present two prototypical algorithms and derive their…
We discuss modern ideas in Monte Carlo algorithms in the simplified setting of the one-dimensional anharmonic oscillator. After reviewing the connection between molecular dynamics and Monte Carlo, we introduce to the Metropolis and the…
Global optimization is an active area of research in atomistic simulations, and many algorithms have been proposed to date. A prominent example is basin hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to explore…
The main idea of this work is that the quantum-classical isomorphism is a suitable framework for a generalization of the notion of detailed balance. The quantum-classical isomorphism is used in order to develop a Monte Carlo simulation with…
Determinant Quantum Monte Carlo (DQMC) provides numerically exact solutions for strongly correlated fermionic systems but faces significant computational challenges with increasing system size. While submatrix updates were originally…
We develop a trap-size scaling theory for trapped particle systems at quantum transitions. As a theoretical laboratory, we consider a quantum XY chain in an external transverse field acting as a trap for the spinless fermions of its…
State-space models are commonly used to describe different forms of ecological data. We consider the case of count data with observation errors. For such data the system process is typically multi-dimensional consisting of coupled Markov…
In this Ph.D. thesis quantum Monte Carlo methods are applied to investigate the properties of a number of ultracold quantum systems. In Chapter 1 we discuss the analytical approaches and approximations used in the subsequent Chapters; also…
For spin rotational symmetric models with a positive-definite high-temperature expansion of the partition function, a stochastic sampling of the series expansion upon partial resummation becomes logically equivalent to sampling an…