Related papers: Nested sampling, statistical physics and the Potts…
Studies in atomic-scale modeling of surface phase equilibria often focus on temperatures near zero Kelvin due to the challenges in calculating the free energy of surfaces at finite temperatures. The Bayesian-inference-based nested sampling…
Nested sampling (NS) computes parameter posterior distributions and makes Bayesian model comparison computationally feasible. Its strengths are the unsupervised navigation of complex, potentially multi-modal posteriors until a well-defined…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of…
We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested…
We present an efficient sampling method for computing a partition function and accelerating configuration sampling. The method performs a random walk in the $\lambda$ space, with $\lambda$ being any thermodynamic variable that characterizes…
Nested sampling is a promising method for calculating phase diagrams of materials, however, the computational cost limits its applicability if ab-initio accuracy is required. In the present work, we report on the efficient use of a…
We present a performant, general-purpose gradient-guided nested sampling algorithm, ${\tt GGNS}$, combining the state of the art in differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
We investigate the sampling efficiency for the simulations of quantum many-body systems at finite temperatures when initial sampling states are generated by applying Trotter gates to random phase product states (RPPSs). We restrict the…
Nested Sampling is a method for computing the Bayesian evidence, also called the marginal likelihood, which is the integral of the likelihood with respect to the prior. More generally, it is a numerical probabilistic quadrature rule. The…
Tensor network (TN) methods are well established for computing partition functions in statistical mechanics, though this use has traditionally been limited to lattice models. We extend the scope of TN methodology to interacting particle…
The main idea of nested sampling is to substitute the high-dimensional likelihood integral over the parameter space $\Omega$ by an integral over the unit line $[0,1]$ by employing a push-forward with respect to a suitable transformation.…
In our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008], we developed a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities at temperature T,…
Stochastic equations play an important role in computational science, due to their ability to treat a wide variety of complex statistical problems. However, current algorithms are strongly limited by their sampling variance, which scales…
In this survey, we give a friendly introduction from a graph theory perspective to the q-state Potts model, an important statistical mechanics tool for analyzing complex systems in which nearest neighbor interactions determine the aggregate…
We introduce a novel technique within the Nested Sampling framework to enhance efficiency of the computation of Bayesian evidence, a critical component in scientific data analysis. In higher dimensions, Nested Sampling relies on Markov…
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
Microcanonical thermodynamics (MT) is analysed for phase transitions of first and second order in finite systems. The transiton temperature, the latent heat and the surface tension of first order transitions can easily be determined by MT…
All ensembles of statistical mechanics are equivalent in the sense that they give the equivalent thermodynamic functions in the thermodynamic limit. However, when investigating microscopic structures in the first-order phase transition…