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In probability theory and statistics, the empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, [1] i.e. by means not of a theoretical sample space but of an actual experiment.
In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. [1] An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one.
In practice, a statistic is computed based on the experimental data and the probability of obtaining a value greater than that statistic under a default or "null" model is compared to a predetermined threshold. This threshold represents the level of discord required (typically established by convention).
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations , probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms .
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.
Bayesian experimental design provides a general probability-theoretical framework from which other theories on experimental design can be derived. It is based on Bayesian inference to interpret the observations/data acquired during the experiment. This allows accounting for both any prior knowledge on the parameters to be determined as well as ...
In probability theory, an event is a set of outcomes of an experiment (a subset of the sample space) to which a probability is assigned. [1] A single outcome may be an element of many different events, [2] and different events in an experiment are usually not equally likely, since they may include very different groups of outcomes. [3]
The application of theoretical sampling provides a structure to data collection as well as data analysis. It is based on the need to collect more data to examine categories and their relationships and assures that representativeness exists in the category. [5] Theoretical sampling has inductive as well as deductive characteristics. [6]