### Table 3: Posterior means, standard deviations, and 95% credible intervals for the third (Delaware) and the fth state (Florida) in Example II. Here, \Standard Wishart quot; is a Wishart distribution with estimated scale matrix and df= 4, and \Wishart HP quot; and \Givens HP quot; are respectively, the Wishart and Givens-angle hierarchical priors.

1999

"... In PAGE 16: ... In tting the Givens-angle HP, the random walk Metropolis algorithm was used to sample from the approximate marginal posterior distribution for D?. The results of tting the models appear in Table3 . The two states that appear in the table were chosen to be representative of a small sample, Delaware (n3 = 7) and a large sample size, Florida (n5 = 249).... ..."

Cited by 17

### TABLE IV SIMULATION OF AN INVERTED WISHART DISTRIBUTION

2006

Cited by 1

### Table 2: Computational comparison of Gibbs sampler with Importance Sampling. The numbers in each column are the ratios of Monte Carlo variances for 2000 iterations. MCMC? denotes posterior simulation without using fact that the full conditional of D?1 is Wishart.

1999

"... In PAGE 15: ... For the MCMC scheme we computed a Normal approximation to the log matrix D for each iteration and sampled from this using a Metropolis step. We ran 2000 iterations of each method and computed the time to run the chain and the Monte Carlo standard errors of the posterior means for each method ( Table2 ). For the MCMC runs, we computed the Monte Carlo standard error using the method of batch means (e.... In PAGE 15: ... We have also computed the ratio of the simulation variances for MCMC to that of importance sampling after 2000 iterations (for MCMC, 2000 iterations following burn-in). These are shown in Table2 , and show that the importance sampling scheme is generally somewhat more e cient in terms of variability per generated value. Taken together, the importance sampling algorithm is at least a reasonable competitor to the MCMC scheme and would appear to be much more e cient than the MCMC scheme when a non-conjugate prior is used for D.... ..."

Cited by 17

### Table 1: Distributions for each parameter of a number of exponential family distributions if the model is to satisfy conjugacy constraints. Conjugacy also holds if the distributions are replaced by their multivariate counterparts e.g. the distribution conjugate to the precision matrix of a multivariate Gaussian is a Wishart distribution. Where None is specified, no standard distribution satisfies conjugacy.

2005

"... In PAGE 15: ... A variable with an Exponential or Poisson distribution can have a gamma prior over its scale or mean respectively, although, as these distributions do not lead to hierarchies, they may be of limited interest. These constraints are listed in Table1 . This table can be encoded in implementations of the variational message passing algorithm and used during initialisation to check the conjugacy of the supplied model.... ..."

Cited by 22

### Table 1: Distributions for each parameter of a number of exponential family distributions if the model is to satisfy conjugacy constraints. Conjugacy also holds if the dis- tributions are replaced by their multivariate counterparts e.g. the distribution conjugate to the precision matrix of a multivariate Gaussian is a Wishart distri- bution. Where None is specified, no standard distribution satisfies conjugacy.

2005

"... In PAGE 16: ... A variable with an Exponential or Poisson distribution can have a Gamma prior over its scale or mean respectively, although, as these distributions do not lead to hierarchies, they may be of limited interest. These constraints are listed in Table1 . This table can be encoded in implementations of the Variational Message Passing algorithm and used during initialisation to check the conjugacy of the supplied model.... ..."

Cited by 22

### TABLE V TRAFFIC MATRIX FOR THE RANDOM TRAFFIC PATTERN

### Table 2: Random Covariance Matrix Results, = 0:005 m

1992

"... In PAGE 6: ... Since accurate values for F were not known, the values used were obtained using the subregion adaptive software with requested absolute accuracy = 0:00025. In Table2 the results for these tests are reported. Table 2: Random Covariance Matrix Results, = 0:005 m... ..."

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### Table 3: Simulation results for the data matrix of random numbers.

"... In PAGE 12: ...Somewhat different results are derived for the random consensus reported in Table3 . Here we observed STATIS to perform better than GPA in most of the simulations.... In PAGE 12: ... It also performed slightly better than STATIS if there are only good assessors and no outliers. ( Table3 about here) 6 Dimensionality We investigate on the surprising result that in Tables 1 and 2 STATIS performed better when we considered only poor assessors, while in Table 3 GPA performed better when we considered no good assessors and almost equal numbers of ordinary and poor assessors. What happens if there are only poor assessors? These have been simulated with random errors that have 25 times the variance of the entries of C.... In PAGE 12: ... It also performed slightly better than STATIS if there are only good assessors and no outliers. (Table 3 about here) 6 Dimensionality We investigate on the surprising result that in Tables 1 and 2 STATIS performed better when we considered only poor assessors, while in Table3 GPA performed better when we considered no good assessors and almost equal numbers of ordinary and poor assessors. What happens if there are only poor assessors? These have been simulated with random errors that have 25 times the variance of the entries of C.... ..."

### Table 1: Exact matrix inversion over pseudorandom and truly random input

"... In PAGE 3: ... Q-pivoting can be applied to build A?1 from scratch, using d rank-1 updates. This process is used in Table1 to evaluate the e ciency of multiple precision integer arithmetic in this context. Note that other exact arithmetic methods for solv- ing linear systems (e.... ..."