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Binomial distribution conjugate prior

A lrLL[uently encountered problem requires estimating a failure probability based on the number of failures, M, in N tests. These updates are assumed to be binomially distributed (equation 2.4-10) as p r N). Conjugate to the binomial distribution is the beta prior (equation 2.6-20), where / IS the probability of failure. [Pg.54]

A number of issues arise in using the available data to estimate (he rates of location-dependent fire occurrence. These include the possible reduction in the frequency of fires due to increased awareness. Apostolakis and Kazarians (1980) use the data of Table 5.2-1 and Bayesian analysis to obtain the results in Table 5.2-2 using conjugate priors (Section 2.6.2), Since the data of Table 5.2-1 are binomially distributed, a gamma prior is used, with a and P being the parameters of the gamma prior as presented inspection 2.6.3.2. For example, in the cable- spreading room fromTable 5.2-2, the values of a and p (0.182 and 0.96) yield a mean frequency of 0.21, while the posterior distribution a and p (2.182 and 302,26) yields a mean frequency of 0.0072. [Pg.198]

Conjugate prior for binomial(n, tt) distribution is the befa(a, b) distribution. The conjugate prior will have the form... [Pg.64]

When the observation comes from the binomial n, tt) distribution, the conjugate prior distribution for tt is beta a, b). The posterior is beta a, b ) where the constants are found by... [Pg.89]


See other pages where Binomial distribution conjugate prior is mentioned: [Pg.39]    [Pg.137]    [Pg.405]   
See also in sourсe #XX -- [ Pg.64 ]




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