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| Ambos lados da revisão anterior Revisão anterior Próxima revisão | Revisão anterior Próxima revisão Ambos lados da revisão seguinte | ||
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disciplinas:verao2007:exercicios [2007/02/17 20:50] paulojus |
disciplinas:verao2007:exercicios [2007/02/17 22:20] paulojus |
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| * try to estimate the anisotropy parameters \\ Compare the results and repeat the exercise for $\phi_R=4$. | * try to estimate the anisotropy parameters \\ Compare the results and repeat the exercise for $\phi_R=4$. | ||
| - (10) Consider a stationary trans-Gaussian model with known transformation function $h(\cdot)$, let $x$ be an arbitrary | - (10) Consider a stationary trans-Gaussian model with known transformation function $h(\cdot)$, let $x$ be an arbitrary | ||
| - | location within the study region and define $T=h^{- 1}{S(x)}$. Find explicit expressions for ${\rm P}(T>c|Y)$ where | + | location within the study region and define </m>T=h^{-1}{S(x)}</m>. Find explicit expressions for ${\rm P}(T>c|Y)$ where |
| $Y=(Y_1,...,Y_n)$ denotes the observed measurements on the untransformed scale and: | $Y=(Y_1,...,Y_n)$ denotes the observed measurements on the untransformed scale and: | ||
| - | * $h(u)=u$ | + | * <m>h(u)=u</m> |
| - | * $h(u) = \log u$ | + | * <m>h(u) = \log u</m> |
| - | * $h(u) = \sqrt{u}$. | + | * <m>h(u) = sqrt{u}</m>. |
| - (11) Analyse the Paraná data-set or any other data set of your choice assuming priors obtaining: | - (11) Analyse the Paraná data-set or any other data set of your choice assuming priors obtaining: | ||
| * a map of the predicted values over the area | * a map of the predicted values over the area | ||
| Linha 70: | Linha 70: | ||
| - (15) Obtain simulations from the Poison model as shown in Figure 4.1 of the text book for the course. | - (15) Obtain simulations from the Poison model as shown in Figure 4.1 of the text book for the course. | ||
| - (15) Try to reproduce or mimic the results shown in Figure 4.2 of the text book for the course simulating a data set and obtaining a similar data-analysis. **Note:** for the example in the book we have used //set.seed(34)//. | - (15) Try to reproduce or mimic the results shown in Figure 4.2 of the text book for the course simulating a data set and obtaining a similar data-analysis. **Note:** for the example in the book we have used //set.seed(34)//. | ||
| - | - (16) Reproduce the simulated binomial data shown in Figure 4.6. Use the package //geoRglm// in conjunction with priors of your choice to obtain predictive distributions for the signal $S(x)$ at locations $x=(0.6, 0.6)$ and $x=(0.9, 0.5)$. Compare the predictive inferences which you obtained in the previous exercise with those obtained by fitting a linear Gaussian model to the empirical logit transformed data, $\log\{(y+0.5)/(n-y+0.5)\}$. Compare the results of the two previous analysis and comment generally. | + | - (16) Reproduce the simulated binomial data shown in Figure 4.6. Use the package //geoRglm// in conjunction with priors of your choice to obtain predictive distributions for the signal $S(x)$ at locations $x=(0.6, 0.6)$ and $x=(0.9, 0.5)$. Compare the predictive inferences which you obtained in the previous exercise with those obtained by fitting a linear Gaussian model to the empirical logit transformed data, <m>log{(y+0.5)/(n-y+0.5)}</m>. Compare the results of the two previous analysis and comment generally. |
| ==== Semana 5 ==== | ==== Semana 5 ==== | ||
