Bayes estimatorIn estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is maximum a posteriori estimation. Suppose an unknown parameter is known to have a prior distribution .
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.
Estimation theoryEstimation 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.
Robust statisticsRobust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location, scale, and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivation is to provide methods with good performance when there are small departures from a parametric distribution.
Simple linear regressionIn statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the x and y coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent variable. The adjective simple refers to the fact that the outcome variable is related to a single predictor.
HazardA hazard is a potential source of harm. Substances, events, or circumstances can constitute hazards when their nature would allow them, even just theoretically, to cause damage to health, life, property, or any other interest of value. The probability of that harm being realized in a specific incident, combined with the magnitude of potential harm, make up its risk, a term often used synonymously in colloquial speech.
Hazard analysisA hazard analysis is used as the first step in a process used to assess risk. The result of a hazard analysis is the identification of different types of hazards. A hazard is a potential condition and exists or not (probability is 1 or 0). It may, in single existence or in combination with other hazards (sometimes called events) and conditions, become an actual Functional Failure or Accident (Mishap). The way this exactly happens in one particular sequence is called a scenario.
Prostate cancerProstate cancer is the uncontrolled growth of cells in the prostate, a gland in the male reproductive system just below the bladder. Early prostate cancer usually causes no symptoms. As the tumor grows, it can damage nearby organs causing erectile dysfunction, blood in the urine or semen, and trouble urinating. Some tumors eventually spread to other areas of the body, particularly the bones and lymph nodes. There, tumors cause severe bone pain, leg weakness or paralysis, and eventually death.
Discrete time and continuous timeIn mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time views values of variables as occurring at distinct, separate "points in time", or equivalently as being unchanged throughout each non-zero region of time ("time period")—that is, time is viewed as a discrete variable. Thus a non-time variable jumps from one value to another as time moves from one time period to the next.
Benign prostatic hyperplasiaBenign prostatic hyperplasia (BPH), also called prostate enlargement, is a noncancerous increase in size of the prostate gland. Symptoms may include frequent urination, trouble starting to urinate, weak stream, inability to urinate, or loss of bladder control. Complications can include urinary tract infections, bladder stones, and chronic kidney problems. The cause is unclear. Risk factors include a family history, obesity, type 2 diabetes, not enough exercise, and erectile dysfunction.
