credible interval

(noun)

An interval in the domain of a posterior probability distribution used for interval estimation.

Related Terms

Examples of credible interval in the following topics:

  • Variation and Prediction Intervals

    • A prediction interval bears the same relationship to a future observation that a frequentist confidence interval or Bayesian credible interval bears to an unobservable population parameter.
    • Prediction intervals predict the distribution of individual future points, whereas confidence intervals and credible intervals of parameters predict the distribution of estimates of the true population mean or other quantity of interest that cannot be observed.
    • Then, confidence intervals and credible intervals may be used to estimate the population mean $\mu$ and population standard deviation $\sigma$ of the underlying population, while prediction intervals may be used to estimate the value of the next sample variable, $X_{n+1}$.
    • Alternatively, in Bayesian terms, a prediction interval can be described as a credible interval for the variable itself, rather than for a parameter of the distribution thereof.
    • Formulate a prediction interval and compare it to other types of statistical intervals.

  • Estimating the Target Parameter: Interval Estimation

    • Interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter.
    • Interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter.
    • The most prevalent forms of interval estimation are:
    • How can we construct a confidence interval for an unknown population mean $\mu$ when we don't know the population standard deviation $\sigma$?
    • The method for calculating a confidence interval assumes that individual observations are independent.

  • What Is a Confidence Interval?

    • A confidence interval is a type of interval estimate of a population parameter and is used to indicate the reliability of an estimate.
    • A confidence interval can be used to describe how reliable survey results are.
    • A confidence interval is a type of estimate (like a sample average or sample standard deviation), in the form of an interval of numbers, rather than only one number.
    • Bayesian inference provides further answers in the form of credible intervals.
    • The confidence interval approach does not allow this, as in this formulation (and at this same stage) both the bounds of the interval and the true values are fixed values; no randomness is involved.

  • Descriptive or Inferential Statistics?

    • a confidence interval (or set estimate); i.e., an interval constructed using a data set drawn from a population so that, under repeated sampling of such data sets, such intervals would contain the true parameter value with the probability at the stated confidence level
    • a credible interval; i.e., a set of values containing, for example, 95% of posterior belief

  • Defining Credibility

    • What is credibility?
    • Here are some tips for earning credibility on a subjective level:
    • Here are three ways to establish objective credibility:
    • What is credibility?
    • Credibility is personal.

  • Types and Elements of Credibility

    • Experience, training, and associations and connections are all important factors that can boost credibility.
    • What would be the best source of credibility in that situation?
    • If so, mention it during your speech to build your credibility.
    • If you want to be seen as a credible person, align yourself with other credible people.
    • These mountaineers are scaling a sheer cliff in the Rhone-Alps of France, giving them credibility from experience.

  • Interval Notation

    • The two numbers are called the endpoints of the interval.
    • Bounded intervals are also commonly known as finite intervals.
    • For example, the interval $(1,10)$ is considered bounded; the interval $(- \infty, + \infty)$ is considered unbounded.
    • Representations of open and closed intervals on the real number line.
    • Use interval notation to show how a set of numbers is bounded

  • Interpreting confidence intervals

    • A careful eye might have observed the somewhat awkward language used to describe confidence intervals.
    • Incorrect language might try to describe the confidence interval as capturing the population parameter with a certain probability.
    • Another especially important consideration of confidence intervals is that they only try to capture the population parameter.
    • Our intervals say nothing about the confidence of capturing individual observations, a proportion of the observations, or about capturing point estimates.
    • Confidence intervals only attempt to capture population parameters.

  • Inverting Intervals

    • To invert any interval, simply imagine that one of the notes has moved one octave, so that the higher note has become the lower and vice-versa.
    • Because inverting an interval only involves moving one note by an octave (it is still essentially the "same" note in the tonal system), intervals that are inversions of each other have a very close relationship in the tonal system.
    • To name the new interval, subtract the name of the old interval from 9.
    • The inversion of a major interval is minor, and of a minor interval is major.
    • The inversion of an augmented interval is diminished and of a diminished interval is augmented.

  • Summary of the Types of Intervals

    • An augmented interval is one half step larger than the perfect or major interval.
    • A diminished interval is one half step smaller than the perfect or minor interval.
    • To find the inversion's number name, subtract the interval number name from 9.
    • Inversions of major intervals are minor, and inversions of minor intervals are major.
    • Inversions of augmented intervals are diminished, and inversions of diminished intervals are augmented.