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  2. Statistical assumption - Wikipedia

    en.wikipedia.org/wiki/Statistical_assumption

    Model-based assumptions. These include the following three types: Distributional assumptions. Where a statistical model involves terms relating to random errors, assumptions may be made about the probability distribution of these errors. [5] In some cases, the distributional assumption relates to the observations themselves. Structural assumptions.

  3. Mathematical proof - Wikipedia

    en.wikipedia.org/wiki/Mathematical_proof

    Modern proof theory treats proofs as inductively defined data structures, not requiring an assumption that axioms are "true" in any sense. This allows parallel mathematical theories as formal models of a given intuitive concept, based on alternate sets of axioms, for example axiomatic set theory and non-Euclidean geometry.

  4. Likelihood principle - Wikipedia

    en.wikipedia.org/wiki/Likelihood_principle

    Unrealized events play a role in some common statistical methods. For example, the result of a significance test depends on the p-value, the probability of a result as extreme or more extreme than the observation, and that probability may depend on the design of the experiment. To the extent that the likelihood principle is accepted, such ...

  5. Statistical model - Wikipedia

    en.wikipedia.org/wiki/Statistical_model

    Informally, a statistical model can be thought of as a statistical assumption (or set of statistical assumptions) with a certain property: that the assumption allows us to calculate the probability of any event. As an example, consider a pair of ordinary six-sided dice. We will study two different statistical assumptions about the dice.

  6. Likelihood function - Wikipedia

    en.wikipedia.org/wiki/Likelihood_function

    For an observation from the discrete component, the likelihood function for an observation from the discrete component is simply = (), where is the index of the discrete probability mass corresponding to observation , because maximizing the probability mass (or probability) at amounts to maximizing the likelihood of the specific observation.

  7. Prior probability - Wikipedia

    en.wikipedia.org/wiki/Prior_probability

    An informative prior expresses specific, definite information about a variable. An example is a prior distribution for the temperature at noon tomorrow. A reasonable approach is to make the prior a normal distribution with expected value equal to today's noontime temperature, with variance equal to the day-to-day variance of atmospheric temperature, or a distribution of the temperature for ...

  8. Foundations of statistics - Wikipedia

    en.wikipedia.org/wiki/Foundations_of_statistics

    Classical hypothesis testing, for instance, has often relied on the assumption of data normality. To reduce reliance on this assumption, robust and nonparametric statistics have been developed. Bayesian statistics, on the other hand, interpret new observations based on prior knowledge, assuming continuity between the past and present.

  9. Data assimilation - Wikipedia

    en.wikipedia.org/wiki/Data_assimilation

    Data assimilation is a mathematical discipline that seeks to optimally combine theory (usually in the form of a numerical model) with observations. There may be a number of different goals sought – for example, to determine the optimal state estimate of a system, to determine initial conditions for a numerical forecast model, to interpolate sparse observation data using (e.g. physical ...