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The following outline is provided as an overview of and topical guide to statistics:
A likelihood function measures how well a statistical model explains observed data by calculating the probability of seeing that data under different parameter values of the model. It is constructed from the joint probability distribution of the random variable that (presumably) generated the observations. When evaluated on the actual data points, it becomes a function solely of the model parameters.
In statistics, point estimation involves the use of sample data to calculate a single value which is to serve as a "best guess" or "best estimate" of an unknown population parameter. More formally, it is the application of a point estimator to the data to obtain a point estimate.
In psychometrics, item response theory (IRT) is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables. It is a theory of testing based on the relationship between individuals' performances on a test item and the test takers' levels of performance on an overall measure of the ability that item was designed to measure. Several different statistical models are used to represent both item and test taker characteristics. Unlike simpler alternatives for creating scales and evaluating questionnaire responses, it does not assume that each item is equally difficult. This distinguishes IRT from, for instance, Likert scaling, in which "All items are assumed to be replications of each other or in other words items are considered to be parallel instruments". By contrast, item response theory treats the difficulty of each item as information to be incorporated in scaling items.
In statistics, an expectation–maximization (EM) algorithm is an iterative method to find (local) maximum likelihood or maximum a posteriori (MAP) estimates of parameters in statistical models, where the model depends on unobserved latent variables. The EM iteration alternates between performing an expectation (E) step, which creates a function for the expectation of the log-likelihood evaluated using the current estimate for the parameters, and a maximization (M) step, which computes parameters maximizing the expected log-likelihood found on the E step. These parameter-estimates are then used to determine the distribution of the latent variables in the next E step. It can be used, for example, to estimate a mixture of gaussians, or to solve the multiple linear regression problem.
In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population. However, while problems associated with "mixture distributions" relate to deriving the properties of the overall population from those of the sub-populations, "mixture models" are used to make statistical inferences about the properties of the sub-populations given only observations on the pooled population, without sub-population identity information. Mixture models are used for clustering, under the name model-based clustering, and also for density estimation.
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory.
Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data. An estimator attempts to approximate the unknown parameters using the measurements. In estimation theory, two approaches are generally considered:
Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics that can be used to estimate the posterior distributions of model parameters.
Computational statistics, or statistical computing, is the study which is the intersection of statistics and computer science, and refers to the statistical methods that are enabled by using computational methods. It is the area of computational science specific to the mathematical science of statistics. This area is fast developing. The view that the broader concept of computing must be taught as part of general statistical education is gaining momentum.
Karl Gustav Jöreskog is a Swedish statistician. Jöreskog is a professor emeritus at Uppsala University, and a co-author of the LISREL statistical program. He is also a member of the Royal Swedish Academy of Sciences. Jöreskog received his bachelor's, master's, and doctoral degrees at Uppsala University. He is also a former student of Herman Wold. He was a statistician at Educational Testing Service (ETS) and a visiting professor at Princeton University.
In statistics, maximum spacing estimation (MSE or MSP), or maximum product of spacing estimation (MPS), is a method for estimating the parameters of a univariate statistical model. The method requires maximization of the geometric mean of spacings in the data, which are the differences between the values of the cumulative distribution function at neighbouring data points.
Psychometric software refers to specialized programs used for the psychometric analysis of data obtained from tests, questionnaires, polls or inventories that measure latent psychoeducational variables. Although some psychometric analyses can be performed using general statistical software such as SPSS, most require specialized tools designed specifically for psychometric purposes.
Anton K. Formann was an Austrian research psychologist, statistician, and psychometrician. He is renowned for his contributions to item response theory, latent class analysis, the measurement of change, mixture models, categorical data analysis, and quantitative methods for research synthesis (meta-analysis).
In statistics, a fixed-effect Poisson model is a Poisson regression model used for static panel data when the outcome variable is count data. Hausman, Hall, and Griliches pioneered the method in the mid 1980s. Their outcome of interest was the number of patents filed by firms, where they wanted to develop methods to control for the firm fixed effects. Linear panel data models use the linear additivity of the fixed effects to difference them out and circumvent the incidental parameter problem. Even though Poisson models are inherently nonlinear, the use of the linear index and the exponential link function lead to multiplicative separability, more specifically
Constance van Eeden was a Dutch mathematical statistician who made "exceptional contributions to the development of statistical sciences in Canada". She was interested in nonparametric statistics including maximum likelihood estimation and robust statistics, and did foundational work on parameter spaces.
Friedrich Maria Urban was a psychologist from the Austro-Hungarian Empire, known for the introduction of probability weightings used in experimental psychology.
Siddhartha Chib is an econometrician and statistician, the Harry C. Hartkopf Professor of Econometrics and Statistics at Washington University in St. Louis. His work is primarily in Bayesian statistics, econometrics, and Markov chain Monte Carlo methods.
In statistics, cluster analysis is the algorithmic grouping of objects into homogeneous groups based on numerical measurements. Model-based clustering bases this on a statistical model for the data, usually a mixture model. This has several advantages, including a principled statistical basis for clustering, and ways to choose the number of clusters, to choose the best clustering model, to assess the uncertainty of the clustering, and to identify outliers that do not belong to any group.
References
- 1 2 3 4 Aitkin, Murray (23 May 2015). "Curriculum Vitae" (PDF). Retrieved 19 July 2021.
- 1 2 Agresti, Alan; Bartolucci, Francesco; Mira, Antonietta (8 February 2021). "Reflections on Murray Aitkin's contributions to nonparametric mixture models and Bayes factors". Statistical Modelling. 22 (1–2): 33–45. doi: 10.1177/1471082X20981312 . ISSN 1471-082X.
- ↑ Bock, R. Darrell; Aitkin, Murray (1 December 1981). "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm". Psychometrika. 46 (4): 443–459. doi:10.1007/BF02293801. ISSN 1860-0980. S2CID 122123206.
- ↑ "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm". scholar.google.co.uk. Retrieved 19 July 2021.
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