Appendix C

ANSWERS TO COMMON QUESTIONS

In 1994-95 Bayesian modelling projects were performed by 8 of the 10 provincial transportation agencies with technical support provided by C-SHRP. A workshop was held at the mid-point of the projects to review each application and provide technical guidance. The following questions and answers are derived from this workshop.

1 - What's the difference between Bayesian Statistics and Bayesian regression?

Bayesian Statistics is any statistical method tracing its roots to Bayes Theorem. Bayesian regression is one of these methods.

2 - How is Bayesian regression useful in experiment design?

Basically, one can develop a prior based on expert judgment and complete an analysis before collecting any (expensive) data. Problems with the model form, inference space, certain variables, etc. can be identified and corrected before data collection begins.

3 - Why would I want to create separate regression models which apply to different types of roads?

Segmentation of the problem into separate models can result in a model with improved predictive capability and statistics. For example, it may be useful to develop separate models for different environmental regions or design classes. It is often much more practical to create a separate model for an environmental region rather than to try to identify and incorporate a number of environmental contributory variables.

4 - What is the importance of explicitly defining variables?

It is critical that all experts understand and interpret each variable consistently. If they do not, the judgment that is elicited will obviously be unclear and flawed. To be certain there are no misunderstandings, a formal encoding package containing the definitions should be developed.

5 - What if I have no distresses to measure in the early life of a pavement, how can I develop a model?

One option is to develop two models. The first model, known as the initiation model, forecasts the time until any significant distress occurs. The second model, known as the propagation model, predicts the amount of distress as a function of time and other variables.

6 - What is the difference between a Linear Model and a Non-Linear model?

Linear models are the only type of models which can be solved deterministically using linear regression. In a linear model, the partial derivative of each independent variable (or cluster term) does not contain any other independent variable. Non-linear models do not have a direct solution and must be solved with an iteration procedure.

Within the general class of linear models, we also characterize the models as simple additive or curvi-linear. Curvi-linear models contain at least one transform and result in the dependent variable not having a straight line relation with every independent variable Xi.

7 - When should I use a transform?

Transforms should be used to reflect structural relationships in your model. In general, a transform will be useful if it results in a variable that is more closely correlated with the dependent variable. Finding appropriate transforms for a regression model is typically a trial and error process, with model performance evaluated in successive trials. Investigating the residual error for correlation with contributory variables, using scatter plots for example, can also be a useful technique.

8 - What is the purpose of the G-prior?

The G-prior is a prior technique used to overcome the difficulty of determining a variance/covariance matrix through direct elicitation. While coefficient means can often be directly assessed, it is impractical to try to directly assess variance and covariance terms.

9 - How can I weight a prior?

The 'weight' of the prior can be adjusted by changing the value of 'G' in a G-prior or by direct manipulation of the variance covariance matrix in an N-prior. Decreasing the variance of the prior will tend to draw the posterior means closer to the prior. No formal method for weighting has been used in the C-SHRP Bayesian project.

10 - Should I combine the views of several experts into one prior?

Combination of the views of several experts should be avoided, particularly where it results in an unnatural, forced consensus of views. For example, where two experts disagree about the sign of a coefficient there is likely no point in combining their views. An argument can be made for combining compatible viewpoints however. The 10-step template advocates comparison of the views of experts in an attempt to identify a reasonable consensus to use as a prior.

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