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Smoothing over Age and Time

Hat.sigma

This can be set in one of three ways: (1) a scalar which sets $\sigma_{at}$, the prior standard deviation of $E(Y)$, indicating how much to smooth the time trend in $E(Y)$ over age groups. A larger standard deviation represents more prior uncertainty, which allows the data to play a greater role. (2) NA to not smooth in this way. (3) To have YourCast search for a good value based on a target value of the derivative of $E(Y)$ with respect to age and time, set to a vector of elements containing the start and end of a range in sigma in which to look (such as 0.05 and 1.5), the number of values to look at within this range (such as 5), and the target value of the derivative of $E(Y)$ with respect to age and time (such as 0.05). The vector may also include a fifth element, which is the target value of the total standard deviation of $E(Y)$ over all dimensions of the prior (such as 0.1). (You may choose to run YourCast with model=EBAYES on a related data set to find an approximate target value of the derivative and standard deviation automatically.) Default: 0.2.

Hat.sigma.sd

A scalar; the standard deviation of parameter Hat.sigma (for Gibbs sampling only). Default: 0.1.

Hat.a.deriv

A numeric vector, each element of which is $\mathbbm{n}$, the degree of a (discrete) derivative of the smoothness functional of time trends with respect to age groups. Element $k$ of this vector refers to the $(k-1)$th derivative of the time trend v with respect to age, where 0 excludes the derviative, 1 includes it, and values in between include the derivative but weight it down proportionally. The first element of the vector corresponds to the weight on the derivative of the time trend with respect to age of order 0 (the identity operator), the second to the weight on the derivative of order 1 (the 1st derivative), etc. For example, c(0, 1, 1) corresponds to a mixed functional that penalizes the first and second derivatives equally. The higher the order of derivative, the more local smoothness over time; and lowest specified derivative controls the form of prior indifference. Default: c(0, 0, 1), which usually works well.

Hat.t.deriv

A numeric vector, each element of which is $\mathbbm{n}$, the degree of a (discrete) derivative of the smoothness functional of age derivative with respect to time. Element $k$ of this vector refers to the $(k-1)$th derivative of the age derivative with respect to time, where 0 excludes the derviative, 1 includes it, and values in between include the derivative but weight it down proportionally. The first element of the vector corresponds to the weight on the age derivative with respect to time of order 0 (the identity operator), the second to the weight on the derivative of order 1 (the 1st derivative), etc. For example, c(0, 1, 1) corresponds to a mixed functional that penalizes the first and second derivatives equally. The higher the order of derivative, the more local smoothness over time; and lowest specified derivative controls the form of prior indifference. Default: c(0, 0, 1), which usually works well.

Hat.age.weight

A scalar or a numeric vector with weights that determines how much smoothing occurs for different age groups when smoothing over age and time. If set to 0 or NA, age groups are weighted equally in smoothing over time; if set to a nonzero scalar, the weight for age group $a$ is set proportional to $a^$Ht.age.weight; if a vector of length A, the $a$th element is the weight of age group $a$. Default: 0.

Hat.time.weight

A scalar or a numeric vector with weights that determine how much smoothing occurs for different time periods when smoothing over age and time. If 0 or NA, time periods are weighted equally; if set to a nonzero scalar value, the weight for time period $t$ in smoothing time periods is proportional to $t^$Ht.time.weight; if the argument is a vector of length T, the $t$th element is the weight of time period $t$. Default: 0.