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 .
Admissible decision ruleIn 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. Define sets , and , where are the states of nature, the possible observations, and the actions that may be taken. An observation of is distributed as and therefore provides evidence about the state of nature .
FractionA fraction (from fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. A common, vulgar, or simple fraction (examples: and ) consists of an integer numerator, displayed above a line (or before a slash like ), and a non-zero integer denominator, displayed below (or after) that line.
Irreducible fractionAn irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). In other words, a fraction a/b is irreducible if and only if a and b are coprime, that is, if a and b have a greatest common divisor of 1. In higher mathematics, "irreducible fraction" may also refer to rational fractions such that the numerator and the denominator are coprime polynomials.
Population growthPopulation growth is the increase in the number of people in a population or dispersed group. Actual global human population growth amounts to around 83 million annually, or 1.1% per year. The global population has grown from 1 billion in 1800 to 7.9 billion in 2020. The UN projected population to keep growing, and estimates have put the total population at 8.6 billion by mid-2030, 9.8 billion by mid-2050 and 11.2 billion by 2100.
Rabies vaccineThe rabies vaccine is a vaccine used to prevent rabies. There are a number of rabies vaccines available that are both safe and effective. They can be used to prevent rabies before, and, for a period of time, after exposure to the rabies virus, which is commonly caused by a dog bite or a bat bite. Doses are usually given by injection into the skin or muscle. After exposure, the vaccination is typically used along with rabies immunoglobulin. It is recommended that those who are at high risk of exposure be vaccinated before potential exposure.
Egyptian fractionAn Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for instance the Egyptian fraction above sums to . Every positive rational number can be represented by an Egyptian fraction.
World populationIn demographics, the world population is the total number of humans currently living. It was estimated by the United Nations to have exceeded eight billion in mid-November 2022. It took over 200,000 years of human prehistory and history for the human population to reach one billion and only 219 years more to reach 8 billion. The human population has experienced continuous growth following the Great Famine of 1315–1317 and the end of the Black Death in 1350, when it was nearly 370,000,000.
Population dynamicsPopulation dynamics is the type of mathematics used to model and study the size and age composition of populations as dynamical systems. Population dynamics has traditionally been the dominant branch of mathematical biology, which has a history of more than 220 years, although over the last century the scope of mathematical biology has greatly expanded. The beginning of population dynamics is widely regarded as the work of Malthus, formulated as the Malthusian growth model.
Yes–no questionIn linguistics, a yes–no question, also known as a binary question, a polar question, or a general question, is a question whose expected answer is one of two choices, one that provides an affirmative answer to the question versus one that provides a negative answer to the question. Typically, in English, the choices are either "yes" or "no". Yes–no questions present an exclusive disjunction, namely a pair of alternatives of which only one is a felicitous answer.
Population declinePopulation decline, also known as depopulation, is a reduction in a human population size. Over the long term, stretching from prehistory to the present, Earth's total human population has continued to grow; however, current projections suggest that this long-term trend of steady population growth may be coming to an end. Until the beginning of the Industrial Revolution, the global population grew very slowly, at about 0.04% per year. After about 1800, the growth rate accelerated to a peak of 2.
