In Example 4.7 (motorcycle data) use a one-dimensional thin plate spline function with random coefficients to model

Question:

In Example 4.7 (motorcycle data) use a one-dimensional thin plate spline function with random coefficients to model the non-linear effect. Use the mixed replicate predictive scheme to assess the proportion of poorly fitted cases (e.g. posterior predictive probabilities that \(y_{i}\) exceeds \(y_{\text {rep }, i}\) that are under 0.05 or over 0.95 ). Assess improvements to predictive fit through

(a) replacing the constant varance assumption for \(\varepsilon_{t}\) by a scale mixture of normals (equivalent to Student \(t\) ) with unknown degrees of freedom, and

(b) modelling the error variances \(h_{t}=\log \left(\sigma_{t}^{2}\right)\) in relation to \(x_{t}\), also using a thin plate spline.

Data from Example 4.7
image text in transcribed

image text in transcribed

image text in transcribed

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question
Question Posted: