named_after markov chain monte carlo
Probability is the measure of the likelihood that an event will occur . Probability is quantified as a number between 0 and ___MASK84___ ( where 0 indicates impossibility and ___MASK84___ indicates certainty ). The higher the probability of an event , the more certain that the event will occur . A simple example is the tossing of a fair ( unbiased ) coin . Since the coin is unbiased , the two outcomes (" head " and " tail ") are both equally probable ; the probability of " head " equals the probability of " tail ". Since no other outcomes are possible , the probability is ___MASK84___ / 2 ( or 50 %), of either " head " or " tail ". In other words , the probability of " head " is ___MASK84___ out of 2 outcomes and the probability of " tail " is also ___MASK84___ out of 2 outcomes , expressed as 0 . ___MASK72___ when converted to decimal , with the above - mentioned quantification system . This type of probability is also called a priori probability . A molecule is an electrically neutral group of two or more atoms held together by chemical bonds . Molecules are distinguished from ions by their lack of electrical ___MASK27___ . However , in quantum physics , organic chemistry , and biochemistry , the term " molecule " is often used less strictly , also being applied to polyatomic ions . In probability theory and related fields , a Markov process is a specific type of a mathematical object known as a stochastic or random process , which is usually defined as a collection of random variables . Historically , the random variables were associated with or indexed by some set of numbers , usually viewed as ___MASK3___ , giving the interpretation of a stochastic process representing numerical values of some random system evolving over ___MASK3___ , such as an electrical current fluctuating due to thermal noise or the movement of a gas molecule . Markov processes are stochastic processes that have the property that the next value of the process depends on the current value , but it is conditionally independent of the previous values of the stochastic process  in other words , the behavior of the process in the future is stochastically independent of its behavior in the past , given the current state of the process . For a stochastic process to be a Markov process , it must have this property , which is referred to as the Markov property The adjective Markovian is used to describe something that is related to a Markov process . In probability theory and statistics , the term Markov property refers to the memoryless property of a stochastic process . It is named after the ___MASK30___ mathematician ___MASK57___ . Gas is one of the four fundamental states of matter ( the others being solid , liquid , and plasma ). A pure gas may be made ___MASK62___ of individual atoms ( e . g . a noble gas like neon ), elemental molecules made from one type of atom ( e . g . oxygen ), or compound molecules made from a variety of atoms ( e . g . carbon dioxide ). A gas mixture would contain a variety of pure gases much like the air . What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles . This separation usually makes a colorless gas invisible to the human observer . The interaction of gas particles in the presence of electric and gravitational fields are considered negligible as indicated by the constant velocity vectors in the image . One type of commonly known gas is steam . In probability theory and related fields , a stochastic or random process is a mathematical object usually defined as a collection of random variables . Historically , the random variables were associated with or indexed by a set of numbers , usually viewed as points in ___MASK3___ , giving the interpretation of a stochastic process representing numerical values of some system randomly changing over ___MASK3___ , such as the growth of a bacterial population , an electrical current fluctuating due to thermal noise , or the movement of a gas molecule . Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner . They have applications in many disciplines including sciences such as biology , chemistry , ecology , neuroscience , and physics as well as technology and engineering fields such as image processing , signal processing , information theory , computer science , cryptography and telecommunications . Furthermore , seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance . Statistics is the study of the collection , analysis , interpretation , presentation , and organization of data . In applying statistics to , e . g ., a scientific , industrial , or social problem , it is conventional to begin with a statistical population or a statistical model process to be studied . Populations can be diverse topics such as " all people living in a country " or " every atom composing a crystal ". Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments . In statistics , Markov chain Monte Carlo ( MCMC ) methods are a class of algorithms for sampling from a probability distribution based on constructing a Markov chain that has the desired distribution as its equilibrium distribution . The state of the chain after a number of steps is then used as a sample of the desired distribution . The quality of the sample improves as a function of the number of steps . Random walk Monte Carlo methods make ___MASK62___ a large subclass of MCMC methods . Probability theory is the branch of ___MASK70___ concerned with probability , the analysis of random phenomena . The ___MASK73___ objects of probability theory are random variables , stochastic processes , and events : mathematical abstractions of non - deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion . In probability theory and statistics , a probability distribution is a mathematical function that , stated in simple terms , can be thought of as providing the probability of occurrence of different possible outcomes in an experiment . For instance , if the random variable X is used to denote the outcome of a coin toss (' the experiment '), then the probability distribution of X would take the value 0 . ___MASK72___ for formula_1 , and 0 . ___MASK72___ for formula_2 . Debt , AIDS , Trade , ___MASK12___ ( DATA ) was a multinational non - government organization founded in January 2002 in ___MASK21___ by ___MASK79___ ' s Bono along with Bobby Shriver and activists from the Jubilee 2000 Drop the Debt campaign . ___MASK3___ is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future . ___MASK3___ is a component quantity of various measurements used to sequence events , to compare the duration of events or the intervals between them , and to quantify rates of change of quantities in material reality or in the conscious experience . ___MASK3___ is often referred to as the fourth dimension , along with the three spatial dimensions . A mathematical object is an abstract object arising in ___MASK70___ . The concept is studied in philosophy of ___MASK70___ . Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it . The ___MASK42___ has been applied in the study of mathematics and logic since before Aristotle ( 384  322 B . ___MASK32___ .), though " analysis " as a formal concept is a relatively recent development .