Sentence examples for multivariate prior distributions from inspiring English sources

Parameter covariance can be modeled by multivariate prior distributions (Burmaster and Murray 1998) or joint posterior distributions obtained by Bayesian multilevel modeling (Bois et al. 1990; Wakefield 1996).

The non-informative prior distributions as used for the parameters of the random effects second-order fractional polynomial model with heterogeneity corresponding to d 0, d 1 and d2 are presented (according to equation 6): (9) For a first order fractional polynomial model these 3-dimensional multivariate prior distributions are reduced to bivariate normal distributions.

Due to a lack of prior knowledge of the dependency structure between the parameters, the multivariate prior distribution p(x k | k) of model k was taken to be the product of the univariate prior distributions p (x r k | k ) for each parameter x r k, i.e. p (x k | k ) = ∏ r p (x r k | k ).

The closed-form solutions with a multivariate normal prior distribution are derived in the Supporting Information.

In Appendix B, we describe the multivariate normal prior distribution used to optimize the design of the DCE.

For structural coefficients, a multivariate normal prior distribution was assumed as N(1λ0, Iτ), where hyperparameters were λ0 = 0 and τ = 10 000.

Based on expert interviews and literature review, we ranked the eleven performance domains in order of importance and specified mean parameter values and variances for the multivariate normal prior distribution.

We also ranked the performance domains in order of expected importance and expressed our uncertainty regarding the a priori orderings of the performance domains and the performance outcomes in a multivariate normal prior distribution.

Assume therein a multivariate normal process (11) Then, the prior distributions for vectors b,, X = { A, B, S}, and e p are specified.

αs are specified flat prior distributions, β1sx and β2si are assigned multivariate conditional autoregressive priors and β3sx are given γ (1,1) priors.

As prior distributions for the Bayesian model fitting we used a multivariate normal distribution with zero mean and a diagonal covariance matrix with large variances (σ = 1010) for fixed effects and an inverse Wishart distribution with degrees of freedom equal to one and the inverse scale equal to the unconditional variance of the response variable.