|
List Of Statistical Topics
0–9 * 1.96 *2SLS (two-stage least squares) redirects to instrumental variable *3SLS – see three-stage least squares *68–95–99.7 rule *100-year flood A *A priori probability *Abductive reasoning *Absolute deviation *Absolute risk reduction *Absorbing Markov chain *ABX test * Accelerated failure time model *Acceptable quality limit *Acceptance sampling *Accidental sampling *Accuracy and precision * Accuracy paradox * Acquiescence bias * Actuarial science *Adapted process * Adaptive estimator * Additive Markov chain *Additive model *Additive smoothing *Additive white Gaussian noise *Adjusted Rand index – see Rand index (subsection) * ADMB software *Admissible decision rule *Age adjustment * Age-standardized mortality rate *Age stratification *Aggregate data * Aggregate pattern *Akaike information criterion *Algebra of random variables *Algebraic statistics *Algorithmic inference *Algorithms for calculating variance *All models are wrong *All-pairs testing * Allan varia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), 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 statistical survey, surveys and experimental design, 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 sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Accuracy Paradox
The accuracy paradox is the paradoxical finding that accuracy is not a good metric for predictive models when classifying in predictive analytics. This is because a simple model may have a high level of accuracy but be too crude to be useful. For example, if the incidence of category A is dominant, being found in 99% of cases, then predicting that case is category A will have an accuracy of 99%. Precision and recall are better measures in such cases. The underlying issue is that there is a class imbalance between the positive class and the negative class. Prior probabilities for these classes need to be accounted for in error analysis. Precision and recall help, but precision too can be biased by very unbalanced class priors in the test sets. Example For example, a city of 1 million people has ten terrorists. A profiling system results in the following confusion matrix: Even though the accuracy is ≈ 99.9%, 990 out of the 1000 positive predictions are incorrect. The prec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Age-standardized Mortality Rate
In epidemiology and demography, age adjustment, also called age standardization, is a technique used to allow statistical populations to be compared when the age profiles of the populations are quite different. Example For example, in 2004/5, two Australian health surveys investigated rates of long-term circulatory system health problems (e.g. heart disease) in the general Australian population, and specifically in the Indigenous Australian population. In each age category over age 24, Indigenous Australians had markedly higher rates of circulatory disease than the general population: 5% vs 2% in age group 25–34, 12% vs 4% in age group 35–44, 22% vs 14% in age group 45–54, and 42% vs 33% in age group 55+. However, overall, these surveys estimated that 12% of all Indigenous Australians had long-term circulatory problems compared to 18% of the overall Australian population. To understand this "apparent contradiction", we note that this only includes age groups over 24 and igno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Age Adjustment
In epidemiology and demography, age adjustment, also called age standardization, is a technique used to allow statistical populations to be compared when the age profiles of the populations are quite different. Example For example, in 2004/5, two Australian health surveys investigated rates of long-term circulatory system health problems (e.g. heart disease) in the general Australian population, and specifically in the Indigenous Australian population. In each age category over age 24, Indigenous Australians had markedly higher rates of circulatory disease than the general population: 5% vs 2% in age group 25–34, 12% vs 4% in age group 35–44, 22% vs 14% in age group 45–54, and 42% vs 33% in age group 55+. However, overall, these surveys estimated that 12% of all Indigenous Australians had long-term circulatory problems compared to 18% of the overall Australian population. To understand this "apparent contradiction", we note that this only includes age groups over 24 and igno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Admissible Decision Rule
In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always "better" than it (or at least sometimes better and never worse), in the precise sense of "better" defined below. This concept is analogous to Pareto efficiency. Definition Define sets \Theta\,, \mathcal and \mathcal, where \Theta\, are the states of nature, \mathcal the possible observations, and \mathcal the actions that may be taken. An observation x \in \mathcal\,\! is distributed as F(x\mid\theta)\,\! and therefore provides evidence about the state of nature \theta\in\Theta\,\!. A decision rule is a function \delta:\rightarrow , where upon observing x\in \mathcal, we choose to take action \delta(x)\in \mathcal\,\!. Also define a loss function L: \Theta \times \mathcal \rightarrow \mathbb, which specifies the loss we would incur by taking action a \in \mathcal when the true state of nature is \theta \in \Theta. Usually we will take thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ADMB
ADMB or AD Model Builder is a free and open source software suite for non-linear statistical modeling. It was created by David Fournier and now being developed by the ADMB Project, a creation of the non-profit ADMB Foundation. The "AD" in AD Model Builder refers to the automatic differentiation capabilities that come from the AUTODIF Library, a C++ language extension also created by David Fournier, which implements reverse mode automatic differentiation. A related software package, ADMB-RE, provides additional support for modeling random effects. Features and use Markov chain Monte Carlo methods are integrated into the ADMB software, making it useful for Bayesian modeling. In addition to Bayesian hierarchical models, ADMB provides support for modeling random effects in a frequentist framework using Laplace approximation and importance sampling. ADMB is widely used by scientists in academic institutions, government agencies, and international commissions, most commonly for ecologic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rand Index
The RAND Corporation (from the phrase "research and development") is an American nonprofit global policy think tank created in 1948 by Douglas Aircraft Company to offer research and analysis to the United States Armed Forces. It is financed by the U.S. government and private endowment, corporations, universities and private individuals. The company assists other governments, international organizations, private companies and foundations with a host of defense and non-defense issues, including healthcare. RAND aims for interdisciplinary and quantitative problem solving by translating theoretical concepts from formal economics and the physical sciences into novel applications in other areas, using applied science and operations research. Overview RAND has approximately 1,850 employees. Its American locations include: Santa Monica, California (headquarters); Arlington, Virginia; Pittsburgh, Pennsylvania; and Boston, Massachusetts. The RAND Gulf States Policy Institute has an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Additive White Gaussian Noise
Additive white Gaussian noise (AWGN) is a basic noise model used in information theory to mimic the effect of many random processes that occur in nature. The modifiers denote specific characteristics: * ''Additive'' because it is added to any noise that might be intrinsic to the information system. * ''White'' refers to the idea that it has uniform power across the frequency band for the information system. It is an analogy to the color white which has uniform emissions at all frequencies in the visible spectrum. * ''Gaussian'' because it has a normal distribution in the time domain with an average time domain value of zero. Wideband noise comes from many natural noise sources, such as the thermal vibrations of atoms in conductors (referred to as thermal noise or Johnson–Nyquist noise), shot noise, black-body radiation from the earth and other warm objects, and from celestial sources such as the Sun. The central limit theorem of probability theory indicates that the summation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Additive Smoothing
In statistics, additive smoothing, also called Laplace smoothing or Lidstone smoothing, is a technique used to smooth categorical data. Given a set of observation counts \textstyle from a \textstyle -dimensional multinomial distribution with \textstyle trials, a "smoothed" version of the counts gives the estimator: :\hat\theta_i= \frac \qquad (i=1,\ldots,d), where the smoothed count \textstyle and the "pseudocount" ''α'' > 0 is a smoothing parameter. ''α'' = 0 corresponds to no smoothing. (This parameter is explained in below.) Additive smoothing is a type of shrinkage estimator, as the resulting estimate will be between the empirical probability ( relative frequency) \textstyle , and the uniform probability \textstyle . Invoking Laplace's rule of succession, some authors have argued that ''α'' should be 1 (in which case the term add-one smoothing is also used), though in practice a smaller value is typically chosen. From a Bayesian point of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Additive Model
In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an essential part of the ACE algorithm. The ''AM'' uses a one-dimensional smoother to build a restricted class of nonparametric regression models. Because of this, it is less affected by the curse of dimensionality than e.g. a ''p''-dimensional smoother. Furthermore, the ''AM'' is more flexible than a standard linear model, while being more interpretable than a general regression surface at the cost of approximation errors. Problems with ''AM'', like many other machine learning methods, include model selection, overfitting, and multicollinearity. Description Given a data set \_^n of ''n'' statistical units, where \_^n represent predictors and y_i is the outcome, the ''additive model'' takes the form : \mathrm x_, \ldots, x_= \beta_0+\sum_^p f_j(x_) or : Y= \beta_0+\sum_^p f_j(X_)+\varepsilon Where \mathrm \epsilon = 0, \mathrm(\eps ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Additive Markov Chain
In probability theory, an additive Markov chain is a Markov chain with an additive conditional probability function. Here the process is a discrete-time Markov chain of order ''m'' and the transition probability to a state at the next time is a sum of functions, each depending on the next state and one of the ''m'' previous states. Definition An additive Markov chain of order ''m'' is a sequence of random variables ''X''1, ''X''2, ''X''3, ..., possessing the following property: the probability that a random variable ''X''''n'' has a certain value ''x''''n'' under the condition that the values of all previous variables are fixed depends on the values of ''m'' previous variables only (Markov chain of order ''m''), and the influence of previous variables on a generated one is additive, :\Pr(X_n=x_n\mid X_=x_, X_=x_, \dots, X_=x_) = \sum_^ f(x_n,x_,r). Binary case A binary additive Markov chain is where the state space of the chain consists on two values only, ''X''n&n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adaptive Estimator
In statistics, an adaptive estimator is an estimator in a parametric or semiparametric model with nuisance parameters such that the presence of these nuisance parameters does not affect efficiency of estimation. Definition Formally, let parameter ''θ'' in a parametric model consists of two parts: the parameter of interest , and the nuisance parameter . Thus . Then we will say that \scriptstyle\hat\nu_n is an adaptive estimator of ''ν'' in the presence of ''η'' if this estimator is regular, and efficient for each of the submodels : \mathcal_\nu(\eta_0) = \big\. Adaptive estimator estimates the parameter of interest equally well regardless whether the value of the nuisance parameter is known or not. The necessary condition for a regular parametric model to have an adaptive estimator is that : I_(\theta) = \operatorname , z_\nu z_\eta' \,= 0 \quad \text\theta, where ''z''''ν'' and ''z''''η'' are components of the score function corresponding to parameters ''ν ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
