Concept
Bayes estimator
Related concepts (16)
Minimum mean square error
In statistics and signal processing, a minimum mean square error (MMSE) estimator is an estimation method which minimizes the mean square error (MSE), which is a common measure of estimator quality, of the fitted values of a dependent variable. In the Bayesian setting, the term MMSE more specifically refers to estimation with quadratic loss function. In such case, the MMSE estimator is given by the posterior mean of the parameter to be estimated.
Maximum a posteriori estimation
In Bayesian statistics, a maximum a posteriori probability (MAP) estimate is an estimate of an unknown quantity, that equals the mode of the posterior distribution. The MAP can be used to obtain a point estimate of an unobserved quantity on the basis of empirical data. It is closely related to the method of maximum likelihood (ML) estimation, but employs an augmented optimization objective which incorporates a prior distribution (that quantifies the additional information available through prior knowledge of a related event) over the quantity one wants to estimate.
Poisson distribution
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson ('pwɑːsɒn; pwasɔ̃). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume.
Efficiency (statistics)
In statistics, efficiency is a measure of quality of an estimator, of an experimental design, or of a hypothesis testing procedure. Essentially, a more efficient estimator needs fewer input data or observations than a less efficient one to achieve the Cramér–Rao bound. An efficient estimator is characterized by having the smallest possible variance, indicating that there is a small deviance between the estimated value and the "true" value in the L2 norm sense.
Bootstrapping (statistics)
Bootstrapping is any test or metric that uses random sampling with replacement (e.g. mimicking the sampling process), and falls under the broader class of resampling methods. Bootstrapping assigns measures of accuracy (bias, variance, confidence intervals, prediction error, etc.) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Bootstrapping estimates the properties of an estimand (such as its variance) by measuring those properties when sampling from an approximating distribution.
Estimation 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.
Maximum likelihood estimation
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference.
Point estimation
In statistics, point estimation involves the use of sample data to calculate a single value (known as a point estimate since it identifies a point in some parameter space) which is to serve as a "best guess" or "best estimate" of an unknown population parameter (for example, the population mean). More formally, it is the application of a point estimator to the data to obtain a point estimate. Point estimation can be contrasted with interval estimation: such interval estimates are typically either confidence intervals, in the case of frequentist inference, or credible intervals, in the case of Bayesian inference.
Loss function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains, variously called a reward function, a profit function, a utility function, a fitness function, etc.
Decision theory
Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory and analytic philosophy concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome. There are three branches of decision theory: Normative decision theory: Concerned with the identification of optimal decisions, where optimality is often determined by considering an ideal decision-maker who is able to calculate with perfect accuracy and is in some sense fully rational.