Coefficient of determinationIn statistics, the coefficient of determination, denoted R2 or r2 and pronounced "R squared", is the proportion of the variation in the dependent variable that is predictable from the independent variable(s). It is a statistic used in the context of statistical models whose main purpose is either the prediction of future outcomes or the testing of hypotheses, on the basis of other related information. It provides a measure of how well observed outcomes are replicated by the model, based on the proportion of total variation of outcomes explained by the model.
Mean absolute percentage errorThe mean absolute percentage error (MAPE), also known as mean absolute percentage deviation (MAPD), is a measure of prediction accuracy of a forecasting method in statistics. It usually expresses the accuracy as a ratio defined by the formula: where At is the actual value and Ft is the forecast value. Their difference is divided by the actual value At. The absolute value of this ratio is summed for every forecasted point in time and divided by the number of fitted points n.
Weighted least squaresWeighted least squares (WLS), also known as weighted linear regression, is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance of observations (heteroscedasticity) is incorporated into the regression. WLS is also a specialization of generalized least squares, when all the off-diagonal entries of the covariance matrix of the errors, are null.
Reduced chi-squared statisticIn statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating and variance of unit weight in the context of weighted least squares. Its square root is called regression standard error, standard error of the regression, or standard error of the equation (see ) It is defined as chi-square per degree of freedom: where the chi-squared is a weighted sum of squared deviations: with inputs: variance , observations O, and calculated data C.
EstimatorIn statistics, an estimator is a rule for calculating an estimate of a given quantity based on observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values.
Supervised learningSupervised learning (SL) is a paradigm in machine learning where input objects (for example, a vector of predictor variables) and a desired output value (also known as human-labeled supervisory signal) train a model. The training data is processed, building a function that maps new data on expected output values. An optimal scenario will allow for the algorithm to correctly determine output values for unseen instances. This requires the learning algorithm to generalize from the training data to unseen situations in a "reasonable" way (see inductive bias).
OverfittingIn mathematical modeling, overfitting is "the production of an analysis that corresponds too closely or exactly to a particular set of data, and may therefore fail to fit to additional data or predict future observations reliably". An overfitted model is a mathematical model that contains more parameters than can be justified by the data. In a mathematical sense, these parameters represent the degree of a polynomial. The essence of overfitting is to have unknowingly extracted some of the residual variation (i.
PlutoniumPlutonium is a radioactive chemical element with the symbol Pu and atomic number 94. It is an actinide metal of silvery-gray appearance that tarnishes when exposed to air, and forms a dull coating when oxidized. The element normally exhibits six allotropes and four oxidation states. It reacts with carbon, halogens, nitrogen, silicon, and hydrogen. When exposed to moist air, it forms oxides and hydrides that can expand the sample up to 70% in volume, which in turn flake off as a powder that is pyrophoric.
NeptuniumNeptunium is a chemical element with the symbol Np and atomic number 93. A radioactive actinide metal, neptunium is the first transuranic element. Its position in the periodic table just after uranium, named after the planet Uranus, led to it being named after Neptune, the next planet beyond Uranus. A neptunium atom has 93 protons and 93 electrons, of which seven are valence electrons. Neptunium metal is silvery and tarnishes when exposed to air. The element occurs in three allotropic forms and it normally exhibits five oxidation states, ranging from +3 to +7.
Plutonium-239Plutonium-239 (239Pu or Pu-239) is an isotope of plutonium. Plutonium-239 is the primary fissile isotope used for the production of nuclear weapons, although uranium-235 is also used for that purpose. Plutonium-239 is also one of the three main isotopes demonstrated usable as fuel in thermal spectrum nuclear reactors, along with uranium-235 and uranium-233. Plutonium-239 has a half-life of 24,110 years.
Plutonium-241Plutonium-241 (241Pu or Pu-241) is an isotope of plutonium formed when plutonium-240 captures a neutron. Like some other plutonium isotopes (especially 239Pu), 241Pu is fissile, with a neutron absorption cross section about one-third greater than that of 239Pu, and a similar probability of fissioning on neutron absorption, around 73%. In the non-fission case, neutron capture produces plutonium-242. In general, isotopes with an odd number of neutrons are both more likely to absorb a neutron, and more likely to undergo fission on neutron absorption, than isotopes with an even number of neutrons.
Plutonium-244Plutonium-244 (244Pu) is an isotope of plutonium that has a half-life of 80 million years. This is longer than any of the other isotopes of plutonium and longer than any other actinide isotope except for the three naturally abundant ones: uranium-235 (704 million years), uranium-238 (4.468 billion years), and thorium-232 (14.05 billion years). Although studies are in conflict, given the mathematics of the decay of plutonium-244, an exceedingly small amount should still be present in the Earth's composition, making plutonium a likely although unproven candidate as the shortest lived primordial element.
