Importance samplingImportance sampling is a Monte Carlo method for evaluating properties of a particular distribution, while only having samples generated from a different distribution than the distribution of interest. Its introduction in statistics is generally attributed to a paper by Teun Kloek and Herman K. van Dijk in 1978, but its precursors can be found in statistical physics as early as 1949. Importance sampling is also related to umbrella sampling in computational physics.Thermodynamic free energy
Potential energy surfaceA potential energy surface (PES) or energy landscape describes the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms. The surface might define the energy as a function of one or more coordinates; if there is only one coordinate, the surface is called a potential energy curve or energy profile. An example is the Morse/Long-range potential.
Activation energyIn the Arrhenius model of reaction rates, activation energy is the minimum amount of energy that must be available to reactants for a chemical reaction to occur. The activation energy (Ea) of a reaction is measured in kilojoules per mole (kJ/mol) or kilocalories per mole (kcal/mol). Simplified: Activation energy is the minimum energy barrier that reactant molecules must overcome to transform into products.
Sampling (statistics)In statistics, quality assurance, and survey methodology, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. The subset, called a statistical sample (or sample, for short), is meant to reflect the whole population, and statisticians attempt to collect samples that are representative of the population.
Computational physicsComputational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science.
Markov chainIn probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC).
ErgodicityProperty of measure-preserving dynamical systemsIn mathematics, especially in ergodic theory, ergodicity is a way of saying that a dynamical system behaves as one indivisible statistical system, rather than being composed of statistically distinguishable subsystems. More precisely, a measure-preserving dynamical system is ergodic if every invariant measurable set has either measure zero or full measure.
ChemistryChemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies matter: composition, structure, properties, behavior and the changes they undergo during reactions with other substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology.
Phase transitionIn physics, chemistry and biology, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties.
Metropolis–Hastings algorithmIn statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult.
Maximum likelihood estimationMethod of estimating the parameters of a statistical model, given observationsIn statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.*As an Amazon Associate I earn from qualifying purchases.