Parameter in the context of Point estimate

Christiaan Huygens, Lord of Zeelhem, FRS (/ˈhaɪɡənz/ HY-gənz, US also /ˈhɔɪɡənz/ HOY-gənz; Dutch: [ˈkrɪstijaːn ˈɦœyɣə(n)s] ; also spelled Huyghens; Latin: Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor who is regarded as a key figure in the Scientific Revolution. In physics, Huygens made seminal contributions to optics and mechanics, while as an astronomer he studied the rings of Saturn and discovered its largest moon, Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, the most accurate timekeeper for almost 300 years. A talented mathematician and physicist, his works contain the first idealization of a physical problem by a set of mathematical parameters, and the first mathematical and mechanistic explanation of an unobservable physical phenomenon.

Huygens first identified the correct laws of elastic collision in his work De Motu Corporum ex Percussione, completed in 1656 but published posthumously in 1703. In 1659, Huygens derived geometrically the formula in classical mechanics for the centrifugal force in his work De vi Centrifuga, a decade before Isaac Newton. In optics, he is best known for his wave theory of light, which he described in his Traité de la Lumière (1690). His theory of light was initially rejected in favour of Newton's corpuscular theory of light, until Augustin-Jean Fresnel adapted Huygens's principle to give a complete explanation of the rectilinear propagation and diffraction effects of light in 1821. Today this principle is known as the Huygens–Fresnel principle.

In statistics, as opposed to its general use in mathematics, a parameter is any quantity of a statistical population that summarizes or describes an aspect of the population, such as a mean or a standard deviation. If a population exactly follows a known and defined distribution, for example the normal distribution, then a small set of parameters can be measured which provide a comprehensive description of the population and can be considered to define a probability distribution for the purposes of extracting samples from this population.

A "parameter" is to a population as a "statistic" is to a sample; that is to say, a parameter describes the true value calculated from the full population (such as the population mean), whereas a statistic is an estimated measurement of the parameter based on a sample (such as the sample mean, which is the mean of gathered data per sampling, called sample). Thus a "statistical parameter" can be more specifically referred to as a population parameter.

In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation: its two coordinates; a non-infinitesimal object on the plane might have additional degrees of freedoms related to its orientation.

In mathematics, this notion is formalized as the dimension of a manifold or an algebraic variety. When degrees of freedom is used instead of dimension, this usually means that the manifold or variety that models the system is only implicitly defined.See:

In mathematics, a linear equation is an equation that may be put in the form${\displaystyle a_{1}x_{1}+\ldots +a_{n}x_{n}+b=0,}$ where ${\displaystyle x_{1},\ldots ,x_{n}}$ are the variables (or unknowns), and ${\displaystyle b,a_{1},\ldots ,a_{n}}$ are the coefficients, which are often real numbers. The coefficients may be considered as parameters of the equation and may be arbitrary expressions, provided they do not contain any of the variables. To yield a meaningful equation, the coefficients ${\displaystyle a_{1},\ldots ,a_{n}}$ are required to not all be zero.

Alternatively, a linear equation can be obtained by equating to zero a linear polynomial over some field, from which the coefficients are taken.

Drinking water quality standards describes the quality parameters set for drinking water. Water may contain many harmful constituents, yet there are no universally recognised and accepted international standards for drinking water. Even where standards do exist, the permitted concentration of individual constituents may vary by up to ten times from one set of standards to another. Many countries specify standards to be applied in their own country. In Europe, this includes the European Drinking Water Directive and in the United States, the United States Environmental Protection Agency (EPA) establishes standards as required by the Safe Drinking Water Act. China adopted its own drinking water standard GB3838-2002 (Type II) enacted by Ministry of Environmental Protection in 2002. For countries without a legislative or administrative framework for such standards, the World Health Organization (WHO) publishes guidelines on the standards that should be achieved.

Where drinking water quality standards do exist, most are expressed as guidelines or targets rather than requirements, and very few water standards have any legal basis or, are subject to enforcement. Two exceptions are the European Drinking Water Directive and the Safe Drinking Water Act in the United States, which require legal compliance with specific standards. In Europe, this includes a requirement for member states to enact appropriate local legislation to mandate the directive in each country. Routine inspection and, where required, enforcement is enacted by means of penalties imposed by the European Commission on non-compliant nations.

In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or any other type of expression. It may be a number without units, in which case it is known as a numerical factor. It may also be a constant with units of measurement, in which it is known as a constant multiplier. In general, coefficients may be any expression (including variables such as a, b and c). When the combination of variables and constants is not necessarily involved in a product, it may be called a parameter. For example, the polynomial ${\displaystyle 2x^{2}-x+3}$ has coefficients 2, −1, and 3, and the powers of the variable ${\displaystyle x}$ in the polynomial ${\displaystyle ax^{2}+bx+c}$ have coefficient parameters ${\displaystyle a}$, ${\displaystyle b}$, and ${\displaystyle c}$.

A constant coefficient, also known as constant term or simply constant, is a quantity either implicitly attached to the zeroth power of a variable or not attached to other variables in an expression; for example, the constant coefficients of the expressions above are the number 3 and the parameter c, involved in 3=c⋅x. The coefficient attached to the highest degree of the variable in a polynomial of one variable is referred to as the leading coefficient; for example, in the example expressions above, the leading coefficients are 2 and a, respectively.

An economic model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes. Frequently, economic models posit structural parameters. A model may have various exogenous variables, and those variables may change to create various responses by economic variables. Methodological uses of models include investigation, theorizing, and fitting theories to the world.

In the context of chemistry, molecular physics, physical chemistry, and molecular modelling, a force field is a computational model that is used to describe the forces between atoms (or collections of atoms) within molecules or between molecules as well as in crystals. Force fields are a variety of interatomic potentials. More precisely, the force field refers to the functional form and parameter sets used to calculate the potential energy of a system on the atomistic level. Force fields are usually used in molecular dynamics or Monte Carlo simulations. The parameters for a chosen energy function may be derived from classical laboratory experiment data, calculations in quantum mechanics, or both. Force fields utilize the same concept as force fields in classical physics, with the main difference being that the force field parameters in chemistry describe the energy landscape on the atomistic level. From a force field, the acting forces on every particle are derived as a gradient of the potential energy with respect to the particle coordinates.

A large number of different force field types exist today (e.g. for organic molecules, ions, polymers, minerals, and metals). Depending on the material, different functional forms are usually chosen for the force fields since different types of atomistic interactions dominate the material behavior.

A large language model (LLM) is a language model trained with self-supervised machine learning on a vast amount of text, designed for natural language processing tasks, especially language generation. The largest and most capable LLMs are generative pre-trained transformers (GPTs) and provide the core capabilities of modern chatbots. LLMs can be fine-tuned for specific tasks or guided by prompt engineering. These models acquire predictive power regarding syntax, semantics, and ontologies inherent in human language corpora, but they also inherit inaccuracies and biases present in the data they are trained on.

They consist of billions to trillions of parameters and operate as general-purpose sequence models, generating, summarizing, translating, and reasoning over text. LLMs represent a significant new technology in their ability to generalize across tasks with minimal task-specific supervision, enabling capabilities like conversational agents, code generation, knowledge retrieval, and automated reasoning that previously required bespoke systems.

A microclimate (or micro-climate) is a local set of atmospheric conditions that differ from those in the surrounding areas, often slightly but sometimes substantially. The term may refer to areas as small as a few square meters or smaller (for example a garden bed, underneath a rock, or a cave) or as large as many square kilometers. Because climate is statistical, which implies spatial and temporal variation of the mean values of the describing parameters, microclimates are identified as statistically distinct conditions which occur and/or persist within a region. Microclimates can be found in most places but are most pronounced in topographically dynamic zones such as mountainous areas, islands, and coastal areas.

Microclimates exist, for example, near bodies of water which may cool the local atmosphere, or in heavy urban areas where brick, concrete, and asphalt absorb the sun's energy, heat up, and re-radiate that heat to the ambient air: the resulting urban heat island (UHI) is a kind of microclimate that is additionally driven by relative paucity of vegetation.

Total organic carbon (TOC) is an analytical parameter representing the concentration of organic carbon in a sample. TOC determinations are made in a variety of application areas. For example, TOC may be used as a non-specific indicator of water quality, or TOC of source rock may be used as one factor in evaluating a petroleum play. For marine surface sediments average TOC content is 0.5% in the deep ocean, and 2% along the eastern margins.

A typical analysis for total carbon (TC) measures both the total organic carbon (TOC) present and the complementing total inorganic carbon (TIC), the latter representing the amount of non-organic carbon, like carbon in carbonate minerals. Subtracting the inorganic carbon from the total carbon yields TOC. Another common variant of TOC analysis involves removing the TIC portion first and then measuring the leftover carbon. This method involves purging an acidified sample with carbon-free air or nitrogen prior to measurement, and so is more accurately called non-purgeable organic carbon (NPOC).

Effective descriptive set theory is the branch of descriptive set theory dealing with sets of reals having lightface definitions; that is, definitions that do not require an arbitrary real parameter (Moschovakis 1980). Thus effective descriptive set theory combines descriptive set theory with recursion theory.

In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population mean). More formally, it is the application of a point estimator to the data to obtain a point estimate.

Point estimation can be contrasted with interval estimation: such interval estimates are typically either confidence intervals, in the case of frequentist inference, or credible intervals, in the case of Bayesian inference. More generally, a point estimator can be contrasted with a set estimator. Examples are given by confidence sets or credible sets. A point estimator can also be contrasted with a distribution estimator. Examples are given by confidence distributions, randomized estimators, and Bayesian posteriors.

Biochemical oxygen demand (also known as BOD or biological oxygen demand) is an analytical parameter representing the amount of dissolved oxygen (DO) consumed by aerobic bacteria growing on the organic material present in a water sample at a specific temperature over a specific time period. The BOD value is most commonly expressed in milligrams of oxygen consumed per liter of sample during 5 days of incubation at 20 °C and is often used as a surrogate of the degree of organic water pollution.

Biochemical Oxygen Demand (BOD) reduction is used as a gauge of the effectiveness of wastewater treatment plants. BOD of wastewater effluents is used to indicate the short-term impact on the oxygen levels of the receiving water.