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Forecast Skill
In the fields of forecasting and prediction, forecast skill or prediction skill is any measure of the accuracy and/or degree of association of prediction to an observation or estimate of the actual value of what is being predicted (formally, the predictand); it may be quantified as a skill score. In meteorology, more specifically in weather forecasting, skill measures the superiority of a forecast over a simple historical baseline of past observations. The same forecast methodology can result in different skill scores at different places, or even in the same place for different seasons (e.g., spring weather might be driven by erratic local conditions, whereas winter cold snaps might correlate with observable polar winds). Weather forecast skill is often presented in the form of seasonal geographical maps. Forecast skill for single-value forecasts (i.e., time series of a scalar quantity) is commonly represented in terms of metrics such as correlation, root mean squared error, mean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forecasting
Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual results. Prediction is a similar but more general term. Forecasting might refer to specific formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods or the process of prediction and resolution itself. Usage can vary between areas of application: for example, in hydrology the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific future times, while the term "prediction" is used for more general estimates, such as the number of times floods will occur over a long period. Risk and uncertainty are central to forecasting and prediction; it is generally considered a good practice to indicate the degree of uncertainty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bias (statistics)
Statistical bias is a systematic tendency which causes differences between results and facts. The bias exists in numbers of the process of data analysis, including the source of the data, the estimator chosen, and the ways the data was analyzed. Bias may have a serious impact on results, for example, to investigate people's buying habits. If the sample size is not large enough, the results may not be representative of the buying habits of all the people. That is, there may be discrepancies between the survey results and the actual results. Therefore, understanding the source of statistical bias can help to assess whether the observed results are close to the real results. Bias can be differentiated from other mistakes such as accuracy (instrument failure/inadequacy), lack of data, or mistakes in transcription (typos). Bias implies that the data selection may have been skewed by the collection criteria. Bias does not preclude the existence of any other mistakes. One may have a po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Forecasting
Forecasting is the process of making predictions based on past and present data. Later these can be compared (resolved) against what happens. For example, a company might estimate their revenue in the next year, then compare it against the actual results. Prediction is a similar but more general term. Forecasting might refer to specific formal statistical methods employing time series, cross-sectional or longitudinal data, or alternatively to less formal judgmental methods or the process of prediction and resolution itself. Usage can vary between areas of application: for example, in hydrology the terms "forecast" and "forecasting" are sometimes reserved for estimates of values at certain specific future times, while the term "prediction" is used for more general estimates, such as the number of times floods will occur over a long period. Risk and uncertainty are central to forecasting and prediction; it is generally considered a good practice to indicate the degree of uncertainty ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Diagram
Taylor diagrams are mathematical diagrams designed to graphically indicate which of several approximate representations (or models) of a system, process, or phenomenon is most realistic. This diagram, invented by Karl E. Taylor in 1994 (published in 2001) facilitates the comparative assessment of different models. It is used to quantify the degree of correspondence between the modeled and observed behavior in terms of three statistics: the Pearson correlation coefficient, the root-mean-square error (RMSE) error, and the standard deviation. Although Taylor diagrams have primarily been used to evaluate models designed to study climate and other aspects of Earth's environment, they can be used for purposes unrelated to environmental science (e.g., to quantify and visually display how well fusion energy models represent reality). Taylor diagrams can be constructed with a number of different open source and commercial software packages, including: GrADS, IDL, MATLAB, NCL, Python, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brier Score
The Brier Score is a ''strictly proper score function'' or ''strictly proper scoring rule'' that measures the accuracy of probabilistic predictions. For unidimensional predictions, it is strictly equivalent to the mean squared error as applied to predicted probabilities. The Brier score is applicable to tasks in which predictions must assign probabilities to a set of mutually exclusive discrete outcomes or classes. The set of possible outcomes can be either binary or categorical in nature, and the probabilities assigned to this set of outcomes must sum to one (where each individual probability is in the range of 0 to 1). It was proposed by Glenn W. Brier in 1950. The Brier score can be thought of as a cost function. More precisely, across all items i\in in a set of ''N'' predictions, the Brier score measures the mean squared difference between: * The predicted probability assigned to the possible outcomes for item ''i'' * The actual outcome o_i Therefore, the ''lower'' the Bri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calibration (statistics)
There are two main uses of the term calibration in statistics that denote special types of statistical inference problems. "Calibration" can mean :*a reverse process to regression, where instead of a future dependent variable being predicted from known explanatory variables, a known observation of the dependent variables is used to predict a corresponding explanatory variable; :*procedures in statistical classification to determine class membership probabilities which assess the uncertainty of a given new observation belonging to each of the already established classes. In addition, "calibration" is used in statistics with the usual general meaning of calibration. For example, model calibration can be also used to refer to Bayesian inference about the value of a model's parameters, given some data set, or more generally to any type of fitting of a statistical model. As Philip Dawid puts it, "a forecaster is ''well calibrated'' if, for example, of those events to which he assigns a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mean Squared Error
In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate. In machine learning, specifically empirical risk minimization, MSE may refer to the ''empirical'' risk (the average loss on an observed data set), as an estimate of the true MSE (the true risk: the average loss on the actual population distribution). The MSE is a measure of the quality of an estimator. As it is derived from the square of Euclidean distance, it is always a positive value that decreases as the error ap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Detection Theory
Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information (called noise, consisting of background stimuli and random activity of the detection machine and of the nervous system of the operator). In the field of electronics, signal recovery is the separation of such patterns from a disguising background. According to the theory, there are a number of determiners of how a detecting system will detect a signal, and where its threshold levels will be. The theory can explain how changing the threshold will affect the ability to discern, often exposing how adapted the system is to the task, purpose or goal at which it is aimed. When the detecting system is a human being, characteristics such as experience, expectations, physiological state (e.g., fatigue) and other factors can affect the threshold a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Entropy (information Theory)
In information theory, the entropy of a random variable is the average level of "information", "surprise", or "uncertainty" inherent to the variable's possible outcomes. Given a discrete random variable X, which takes values in the alphabet \mathcal and is distributed according to p: \mathcal\to , 1/math>: \Eta(X) := -\sum_ p(x) \log p(x) = \mathbb \log p(X), where \Sigma denotes the sum over the variable's possible values. The choice of base for \log, the logarithm, varies for different applications. Base 2 gives the unit of bits (or " shannons"), while base ''e'' gives "natural units" nat, and base 10 gives units of "dits", "bans", or " hartleys". An equivalent definition of entropy is the expected value of the self-information of a variable. The concept of information entropy was introduced by Claude Shannon in his 1948 paper " A Mathematical Theory of Communication",PDF archived froherePDF archived frohere and is also referred to as Shannon entropy. Shannon's theory d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brier Score
The Brier Score is a ''strictly proper score function'' or ''strictly proper scoring rule'' that measures the accuracy of probabilistic predictions. For unidimensional predictions, it is strictly equivalent to the mean squared error as applied to predicted probabilities. The Brier score is applicable to tasks in which predictions must assign probabilities to a set of mutually exclusive discrete outcomes or classes. The set of possible outcomes can be either binary or categorical in nature, and the probabilities assigned to this set of outcomes must sum to one (where each individual probability is in the range of 0 to 1). It was proposed by Glenn W. Brier in 1950. The Brier score can be thought of as a cost function. More precisely, across all items i\in in a set of ''N'' predictions, the Brier score measures the mean squared difference between: * The predicted probability assigned to the possible outcomes for item ''i'' * The actual outcome o_i Therefore, the ''lower'' the Bri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relative Mean Absolute Error
Relative may refer to: General use *Kinship and family, the principle binding the most basic social units society. If two people are connected by circumstances of birth, they are said to be ''relatives'' Philosophy *Relativism, the concept that points of view have no absolute truth or validity, having only relative, subjective value according to differences in perception and consideration, or relatively, as in the relative value of an object to a person * Relative value (philosophy) Economics *Relative value (economics) Popular culture Film and television * ''Relatively Speaking'' (1965 play), 1965 British play * ''Relatively Speaking'' (game show), late 1980s television game show * ''Everything's Relative'' (episode)#Yu-Gi-Oh! (Yu-Gi-Oh! Duel Monsters), 2000 Japanese anime ''Yu-Gi-Oh! Duel Monsters'' episode *'' Relative Values'', 2000 film based on the play of the same name. *''It's All Relative'', 2003-4 comedy television series *''Intelligence is Relative'', tag line for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prediction
A prediction (Latin ''præ-'', "before," and ''dicere'', "to say"), or forecast, is a statement about a future event or data. They are often, but not always, based upon experience or knowledge. There is no universal agreement about the exact difference from " estimation"; different authors and disciplines ascribe different connotations. Future events are necessarily uncertain, so guaranteed accurate information about the future is impossible. Prediction can be useful to assist in making plans about possible developments. Opinion In a non-statistical sense, the term "prediction" is often used to refer to an informed guess or opinion. A prediction of this kind might be informed by a predicting person's abductive reasoning, inductive reasoning, deductive reasoning, and experience; and may be useful—if the predicting person is a knowledgeable person in the field. The Delphi method is a technique for eliciting such expert-judgement-based predictions in a controlled way ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
