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calculate dXt · dXt by the box calculus and verify that your expression for dYt shows that the box calculus formula (8.28) is valid for Yt.

(A Box Calculus Verification). The purpose of this exercise is to generalize and unify the calculations we made for functions of Brownian motion with drift and geometric Brownian motion. It provides a proof of the validity of the box calculus for processes that are functions of Brownian motion and time. A)     Let Xt = f(t, Bt), … Read more

apply an ordered logistic model by data augmentation by direct sampling from a logistic and by sampling from a normal using scale mixing with an appropriate degrees of freedom.

In Example 7.5 (attitudes to working mothers) compare inferences from the residuals Wi − Xiβ with those based on Monte Carlo estimates of the conditional predictive ordinates (harmonic means of the sampled normal likelihoods for each subject). In Example 7.5 apply an ordered logistic model by data augmentation by direct sampling from a logistic and by … Read more

illustrate a multiple comparison model where both fixed and random effects approaches to the permanent subject effect may be relevant, consider data from Horrace and Schmidt (2000) applied to loglinear production functions.

In Example 11.6 (Indonesian rice farm data) assess gain from introducing AR1 errors (in addition to unstructured errors) in both random and fixed effects bi models. Also find the posterior probabilities that farms 1 to 171 are the best – in terms of having highest bi after allowing for inputs. Which farm has the highest probability of … Read more

compare a 5-point discrete mixture on the log-logistic shape parameter with the variable scale model to downweight aberrant cases, namely ui ∼ L(ηi, 1/(κθi)) where θi are gamma with mean 1, and ui = log(ti).

In Example 13.2 compare a 5-point discrete mixture on the log-logistic shape parameter with the variable scale model to downweight aberrant cases, namely ui ∼ L(ηi, 1/(κθi)) where θi are gamma with mean 1, and ui = log(ti). Commuter delay in work-to-home trips Washington et al. (2003) consider the durations of delay in work-to-home trips for 96 Seattle … Read more

Select biologically relevant information to use as vertex labels. What labels did you choose and why?

Project: Section 1.3 focuses on using unlabeled, unrooted trees to model RNA secondary structure. However, rooted and/or labeled trees can also be used to model important aspects of RNA secondary structure. Explore this idea and how it affects the estimates of the number of possible RNA secondary structure techniques. As part of this exploration, consider … Read more

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