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Statistical Model Validation
In statistics, model validation is the task of evaluating whether a chosen statistical model is appropriate or not. Oftentimes in statistical inference, inferences from models that appear to fit their data may be flukes, resulting in a misunderstanding by researchers of the actual relevance of their model. To combat this, model validation is used to test whether a statistical model can hold up to permutations in the data. This topic is not to be confused with the closely related task of model selection, the process of discriminating between multiple candidate models: model validation does not concern so much the conceptual design of models as it tests only the consistency between a chosen model and its stated outputs. There are many ways to validate a model. Residual plots plot the difference between the actual data and the model's predictions: correlations in the residual plots may indicate a flaw in the model. Cross validation is a method of model validation that iteratively ref ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ecological Modelling
''Ecological Modelling'' is a monthly peer-reviewed scientific journal covering the use of ecosystem models in the field of ecology. It was founded in 1975 by Sven Erik Jørgensen and is published by Elsevier. The current editor-in-chief is Brian D. Fath (Towson University). According to the ''Journal Citation Reports'', the journal has a 2016 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... of 2.363. References External links * Ecology journals Elsevier academic journals Monthly journals Publications established in 1975 English-language journals {{Ecology-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sensitivity Analysis
Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system (numerical or otherwise) can be divided and allocated to different sources of uncertainty in its inputs. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty; ideally, uncertainty and sensitivity analysis should be run in tandem. The process of recalculating outcomes under alternative assumptions to determine the impact of a variable under sensitivity analysis can be useful for a range of purposes, including: * Testing the robustness of the results of a model or system in the presence of uncertainty. * Increased understanding of the relationships between input and output variables in a system or model. * Uncertainty reduction, through the identification of model input that cause significant uncertainty in the output and should therefore be the focus of attention in order to increase robustness (perhap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predictive Model
Predictive modelling uses statistics to predict outcomes. Most often the event one wants to predict is in the future, but predictive modelling can be applied to any type of unknown event, regardless of when it occurred. For example, predictive models are often used to detect crimes and identify suspects, after the crime has taken place. In many cases the model is chosen on the basis of detection theory to try to guess the probability of an outcome given a set amount of input data, for example given an email determining how likely that it is spam. Models can use one or more classifiers in trying to determine the probability of a set of data belonging to another set. For example, a model might be used to determine whether an email is spam or "ham" (non-spam). Depending on definitional boundaries, predictive modelling is synonymous with, or largely overlapping with, the field of machine learning, as it is more commonly referred to in academic or research and development contexts. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perplexity
In information theory, perplexity is a measurement of how well a probability distribution or probability model predicts a sample. It may be used to compare probability models. A low perplexity indicates the probability distribution is good at predicting the sample. Perplexity of a probability distribution The perplexity ''PP'' of a discrete probability distribution ''p'' is defined as :\mathit(p) := 2^=2^=\prod_x p(x)^ where ''H''(''p'') is the entropy (in bits) of the distribution and ''x'' ranges over events. (The base need not be 2: The perplexity is independent of the base, provided that the entropy and the exponentiation use the ''same'' base.) This measure is also known in some domains as the '' (order-1 true) diversity''. Perplexity of a random variable ''X'' may be defined as the perplexity of the distribution over its possible values ''x''. In the special case where ''p'' models a fair ''k''-sided die (a uniform distribution over ''k'' discrete events), i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overfitting
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. The essence of overfitting is to have unknowingly extracted some of the residual variation (i.e., the noise) as if that variation represented underlying model structure. Underfitting occurs when a mathematical model cannot adequately capture the underlying structure of the data. An under-fitted model is a model where some parameters or terms that would appear in a correctly specified model are missing. Under-fitting would occur, for example, when fitting a linear model to non-linear data. Such a model will tend to have poor predictive performance. The possibility of over-fitting exists because the criterion used for selecting the model is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Identification
In statistics, identifiability is a property which a model must satisfy for precise inference to be possible. A model is identifiable if it is theoretically possible to learn the true values of this model's underlying parameters after obtaining an infinite number of observations from it. Mathematically, this is equivalent to saying that different values of the parameters must generate different probability distributions of the observable variables. Usually the model is identifiable only under certain technical restrictions, in which case the set of these requirements is called the identification conditions. A model that fails to be identifiable is said to be non-identifiable or unidentifiable: two or more parametrizations are observationally equivalent. In some cases, even though a model is non-identifiable, it is still possible to learn the true values of a certain subset of the model parameters. In this case we say that the model is partially identifiable. In other cases it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internal Validity
Internal validity is the extent to which a piece of evidence supports a claim about cause and effect, within the context of a particular study. It is one of the most important properties of scientific studies and is an important concept in reasoning about evidence more generally. Internal validity is determined by how well a study can rule out alternative explanations for its findings (usually, sources of systematic error or 'bias'). It contrasts with external validity, the extent to which results can justify conclusions about other contexts (that is, the extent to which results can be generalized). Details Inferences are said to possess internal validity if a causal relationship between two variables is properly demonstrated.Shadish, W., Cook, T., and Campbell, D. (2002). Experimental and Quasi-Experimental Designs for Generilized Causal Inference Boston:Houghton Mifflin. A valid causal inference may be made when three criteria are satisfied: # the "cause" precedes the " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Identifiability Analysis
Identifiability analysis is a group of methods found in mathematical statistics that are used to determine how well the parameters of a model are estimated by the quantity and quality of experimental data.Cobelli & DiStefano (1980) Therefore, these methods explore not only identifiability of a model, but also the relation of the model to particular experimental data or, more generally, the data collection process. Introduction Assuming a model is fit to experimental data, the goodness of fit does not reveal how reliable the parameter estimates are. The goodness of fit is also not sufficient to prove the model was chosen correctly. For example, if the experimental data is noisy or if there is an insufficient number of data points, it could be that the estimated parameter values could vary drastically without significantly influencing the goodness of fit. To address these issues the identifiability analysis could be applied as an important step to ensure correct choice of model, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
All Models Are Wrong
All or ALL may refer to: Language * All, an indefinite pronoun in English * All, one of the English determiners * Allar language (ISO 639-3 code) * Allative case (abbreviated ALL) Music * All (band), an American punk rock band * ''All'' (All album), 1999 * ''All'' (Descendents album) or the title song, 1987 * ''All'' (Horace Silver album) or the title song, 1972 * ''All'' (Yann Tiersen album), 2019 * "All" (song), by Patricia Bredin, representing the UK at Eurovision 1957 * " All (I Ever Want)", a song by Alexander Klaws, 2005 * "All", a song by Collective Soul from '' Hints Allegations and Things Left Unsaid'', 1994 Science and mathematics * ALL (complexity), the class of all decision problems in computability and complexity theory * Acute lymphoblastic leukemia * Anterolateral ligament Sports * American Lacrosse League * Arena Lacrosse League, Canada * Australian Lacrosse League Other uses * All, Missouri, a community in the United States * All, a brand of Sun P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Regression Validation
In statistics, regression validation is the process of deciding whether the numerical results quantifying hypothesized relationships between variables, obtained from regression analysis, are acceptable as descriptions of the data. The validation process can involve analyzing the goodness of fit of the regression, analyzing whether the regression residuals are random, and checking whether the model's predictive performance deteriorates substantially when applied to data that were not used in model estimation. Goodness of fit One measure of goodness of fit is the ''R''2 ( coefficient of determination), which in ordinary least squares with an intercept ranges between 0 and 1. However, an ''R''2 close to 1 does not guarantee that the model fits the data well: as Anscombe's quartet shows, a high ''R''2 can occur in the presence of misspecification of the functional form of a relationship or in the presence of outliers that distort the true relationship. One problem with the ''R' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorandom Number Generator
A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's ''seed'' (which may include truly random values). Although sequences that are closer to truly random can be generated using hardware random number generators, ''pseudorandom number generators'' are important in practice for their speed in number generation and their reproducibility. PRNGs are central in applications such as simulations (e.g. for the Monte Carlo method), electronic games (e.g. for procedural generation), and cryptography. Cryptographic applications require the output not to be predictable from earlier outputs, and more elaborate algorithms, which do not inherit the linearity of simpler PRNGs, are needed. Good statis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
