### Table 2. Number of unobserved heroin users with 95% CI estimated using the poisson mixture model

"... In PAGE 11: ...which is known to penalize complex models more strongly than the Akaike-type criteria. For the heroin data, Table2 provides clear and consistent evidence that four components are required. No further components are possible since the four- component estimate is already the nonparametric maximum likelihood estimate, so that no further increase in the likelihood is possible.... ..."

### Table 2: In uence of prior distribution N( , ?1) for on the posterior distribution of k. Acidity data: mixture model with Poisson (prior P(10) for k), random and default parameter values.

1994

"... In PAGE 16: ... Table 1), a posterior distribution mostly concentrated on k = 2 or 3, with moderate variation between the 3 cases, p(k = 2jy) being equal to 0:42; 0; 65 and 0:43 respectively. However, the Laplace approximation estimates for p(k = 2jy) given in Crawford apos;s Table2 vary over many orders of magnitude.... ..."

Cited by 2

### Table 2: In uence of prior distribution N( , ?1) for on the posterior distribution of k. Acidity data: mixture model with Poisson (prior P(10) for k), random and default parameter values.

1994

"... In PAGE 16: ... Table 1), a posterior distribution mostly concentrated on k = 2 or 3, with moderate variation between the 3 cases, p(k = 2jy) being equal to 0:42; 0; 65 and 0:43 respectively. However, the Laplace approximation estimates for p(k = 2jy) given in Crawford apos;s Table2 vary over many orders of magnitude.... ..."

Cited by 2

### Table 2: In uence of prior distribution N( , ?1) for on the posterior distribution of k. Acidity data: mixture model with Poisson (prior P(10) for k), random and default parameter values.

1994

"... In PAGE 16: ... Table 1), a posterior distribution mostly concentrated on k = 2 or 3, with moderate variation between the 3 cases, p(k = 2jy) being equal to 0:42; 0; 65 and 0:43 respectively. However, the Laplace approximation estimates for p(k = 2jy) given in Crawford apos;s Table2 vary over many orders of magnitude. 5.... ..."

Cited by 2

1994

"... In PAGE 16: ... Table 1), a posterior distribution mostly concentrated on k = 2 or 3, with moderate variation between the 3 cases, p(k = 2jy) being equal to 0:42; 0; 65 and 0:43 respectively. However, the Laplace approximation estimates for p(k = 2jy) given in Crawford apos;s Table2 vary over many orders of magnitude.... ..."

Cited by 2

### Table 1: Observed two-week home run counts, expected counts under a Poisson model, and Pearson residuals for Schmidt data. A popular method of modeling the overdispersion that we observe in Table 1 is based on the use of mixtures. Suppose that the counts yi are independently distributed from Poisson distributions with di erent means i. We suppose that 1; :::; 178 are a random sample from a Gamma distribution with mean and scale parameter b g( i) = b?1 i

"... In PAGE 5: ... The maximum likelihood estimate for this data is ^ = yobs = 2:82. To see how well this model ts the data, Table1 displays a frequency table of the observed counts and the tted counts based on the Poisson model. The third row of the table gives the Pearson residuals f(observed - expected)/pexpectedg.... ..."

### Table 1: Simulation results comparing spatial mixture and BYM models.

2000

"... In PAGE 19: ...1.45+ thru 2.54 CAR, SMR Figure 14: True risks and observed SMRs for the \CAR quot; data set The spatial mixture and the BYM are compared on the basis of ramse, DIC, E(D), pD and E(L). Each line of Table1 corresponds to the criterion averaged over 6 independent Poisson replications of the data pattern (the rst replication having been displayed previously for the rst ve cases). From the table, one can see that the spatial mixture model gives more faithful estimation of the underlying risks, with smaller ramse in most cases.... In PAGE 20: ... In the balance between recovering the true underlying scene and tting the data, the mixture model is clearly less in uenced by the data than the BYM model and able to e ect some spatially adaptive smoothing in a variety of situations. Complementing the results of Table1 , we display the map of posterior means of f ig estimated by the BYM model for two data sets in Figures 15 and 16 (left panels). Comparing these with those corresponding to our mixture model (Figures 7 and 8), against the maps of the simulated risks (Figures 2 and 3) there is evidence of remaining noise, unsmoothed by the analysis.... In PAGE 20: ... Also, these maps stay closer to the data than the corresponding ones for the mixture model. This illustrates what was quanti ed by the ramse in Table1 , that recovery of the unblurred picture is less e ective for the BYM model. It is also interesting to see that the map of posterior variability of the risks for these 2 data sets (right panel) is quite di erent to that of the mixture model (the standard deviations are plotted on the same scale).... ..."

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### Table 2. Modeling calculations for the temperature dependence of fracture toughness in the TiNb/TiAl composite Temperature (8C) 25 650 800

1998