Statistical modelA statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population). A statistical model represents, often in considerably idealized form, the data-generating process. When referring specifically to probabilities, the corresponding term is probabilistic model. A statistical model is usually specified as a mathematical relationship between one or more random variables and other non-random variables.
Statistical assumptionStatistics, like all mathematical disciplines, does not infer valid conclusions from nothing. Inferring interesting conclusions about real statistical populations almost always requires some background assumptions. Those assumptions must be made carefully, because incorrect assumptions can generate wildly inaccurate conclusions. Here are some examples of statistical assumptions: Independence of observations from each other (this assumption is an especially common error). Independence of observational error from potential confounding effects.
Random variableA random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.
AsthenosphereThe asthenosphere () is the mechanically weak and ductile region of the upper mantle of Earth. It lies below the lithosphere, at a depth between ~ below the surface, and extends as deep as . However, the lower boundary of the asthenosphere is not well defined. The asthenosphere is almost solid, but a slight amount of melting (less than 0.1% of the rock) contributes to its mechanical weakness. More extensive decompression melting of the asthenosphere takes place where it wells upwards, and this is the most important source of magma on Earth.
Oceanic basinIn hydrology, an 'oceanic basin (or ocean basin') is anywhere on Earth that is covered by seawater. Geologically, most of the ocean basins are large geologic basins that are below sea level. Most commonly the ocean is divided into basins following the continents distribution: the North and South Atlantic (together approximately 75 million km2/ 29 million mi2), North and South Pacific (together approximately 155 million km2/ 59 million mi2), Indian Ocean (68 million km2/ 26 million mi2) and Arctic Ocean (14 million km2/ 5.
Picrite basaltPicrite basalt or picrobasalt is a variety of high-magnesium olivine basalt that is very rich in the mineral olivine. It is dark with yellow-green olivine phenocrysts (20-50%) and black to dark brown pyroxene, mostly augite. The olivine-rich picrite basalts that occur with the more common tholeiitic basalts of Kīlauea and other volcanoes of the Hawaiian Islands are the result of accumulation of olivine crystals either in a portion of the magma chamber or in a caldera lava lake.
Normal distributionIn statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter is its standard deviation. The variance of the distribution is . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate.
Statistical parameterIn statistics, as opposed to its general use in mathematics, a parameter is any measured quantity of a statistical population that summarises 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 completely describes the population, and can be considered to define a probability distribution for the purposes of extracting samples from this population.
GeochemistryGeochemistry is the science that uses the tools and principles of chemistry to explain the mechanisms behind major geological systems such as the Earth's crust and its oceans. The realm of geochemistry extends beyond the Earth, encompassing the entire Solar System, and has made important contributions to the understanding of a number of processes including mantle convection, the formation of planets and the origins of granite and basalt. It is an integrated field of chemistry and geology.
Stable distributionIn probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).
