|Term, with Synonyms and Cross-References||Definition||Notes and Comments|
|algorithm||A finite list of well-defined instructions that, when executed, proceed through a finite number of well-defined successive states, eventually terminating and producing an output.||The instructions and executions are not necessarily deterministic; some algorithms incorporate random input (see Monte Carlo simulation).|
See also estimation (of parameters in probability models).
|The result of a computation or assessment that may not be exactly correct but that is adequate for a particular purpose.c|
Synonyms: arithmetic mean, sample mean See also mean.
|The sum of n numbers divided by n.d,e,f||The average is a simple arithmetic operation requiring a set of n numbers. It is often confused with the mean (or expected value), which is a property of a probability distribution. One reason for this confusion is that the average of a set of realizations of a random variable is often a good estimator of the mean of the random variable’s distribution.|
See also prior probability.
|An approach that uses observations (data) to constrain uncertain parameters in a probabilistic model. The constrained uncertainty is described by a posterior probability distribution, produced using Bayes’s theorem to combine the prior probability distribution with the probabilistic model of the observations.||In most problems the Bayesian approach produces a high-dimensional probability distribution describing the joint uncertainty in all of the model parameters. Functionals or integrals of this posterior distribution are typically used to summarize the posterior uncertainty. These summaries are typically produced by means of numerical approximation or sampling methods such as Markov chain Monte Carlo.|
See also verification, solution verification.
|The process of determining and documenting the extent to which a computer program (“code”) correctly solves the equations of the mathematical model.|
Synonym: computer model See also model (simulation).
|Computer code that (approximately) solves the equations of the mathematical model.||In physically based applications the computational model might encode physical rules such as conservation of mass or momentum. In other applications the computational model might also produce a Monte Carlo or a discrete-event realization.|
|conditional probability See also probability.||The probability of an event supposing (i.e., “conditioned on”) the occurrence of other specified events.||In the Bayesian approach the posterior distribution is a conditional probability distribution, conditioned on the physical observations. It is important to note that subjectively assessed probabilities are based on the state of knowledge that holds at the time of the probability assessment.|