Parsimonious Parameterization of Age-Period-Cohort Models by Bayesian Shrinkage

2018

AEF

Self Cite

Opioid mortality rates have been increasing sharply, but not uniformly by age. Peak ages have recently dropped from the mid-40s to the mid-30s. There are two age peaks that have been moving up diagonally, with years of birth around 1960 and 1980 staying near the tops, and those around 1970 generally lower. We model this history with the Lee-Carter plus cohorts mortality model, which includes variable trends by age, and a generalization of it. This can be fit by maximum likelihood estimation (MLE) but statistical methods that shrink parameters towards zero (regularization) give lower predictive variances than MLE does. We address how to apply regularization to age-period-cohort models. Frequentist and Bayesian regularization are explored. The latter has some practical advantages.

Section: Methodology For Opioid Applicationmentioning

confidence: 99%

“…The dummies specify how many times a given slope change is summed in the calculation of the level parameter for a data point. Venter and Şahin (2017) use a similar approach. A related paper is Gao and Meng (2017), who use Bayesian regularization for cubic spline fitting of an age-cohort model.…”

Section: Introductionmentioning

confidence: 99%

Regularized Age-Period-Cohort Modeling of Opioid Mortality Rates

2018

AEF

Self Cite

“…Actually Hunt and Blake (2014) allow the possibility of different trends with different age weights either simultaneously or in succession. Venter and Şahin (2018) suggest an informal test for the need for multiple trends, and find that they indeed help in modeling the US male population for ages 30-89. In the example here we fit the model to ages 50 and up, and did this test, which suggested that one trend is sufficient, so the model is presented in that form.…”

Section: Joint Mortality Modeling By Shrinkagementioning

confidence: 99%

Semiparametric Regression for Dual Population Mortality

Şahın

2019

SSRN Journal

Self Cite

Parameter shrinkage applied optimally can always reduce error and projection variances from those of maximum likelihood estimation. Many variables that actuaries use are on numerical scales, like age or year, which require parameters at each point. Rather than shrinking these towards zero, nearby parameters are better shrunk towards each other. Semiparametric regression is a statistical discipline for building curves across parameter classes using shrinkage methodology. It is similar to but more parsimonious than cubic splines. We introduce it in the context of Bayesian shrinkage and apply it to joint mortality modeling for related populations, with Swedish and Danish mortality as an illustration. Bayesian shrinkage of slope changes of linear splines is an approach to semiparametric modeling that evolved in the actuarial literature. It has some theoretical and practical advantages, like closed-form curves, direct and transparent determination of degree of shrinkage and of placing knots for the splines, and quantifying goodness of fit. It is also relatively easy to apply to the many nonlinear models that arise in actuarial work.

“…Selecting the scale parameter of the Laplace or Cauchy prior for MCMC, or the λ shrinkage parameter for lasso or ridge regression, requires a balancing of parsimony and goodness of fit. Taking the parameter that optimizes elpd loo is one way to proceed, and that was the approach taken in G. Venter and Şahin (2017). However this is not totally compatible with the posterior mean philosophy, as it is a combination of Bayesian and predictive optimization.…”

Section: C Selecting the Degree Of Shrinkagementioning

confidence: 99%

“…G. G. Venter, Gutkovich, and Gao (2017) model loss triangles with row, column, and diagonal parameters in slope change form fit by random effects and lasso. G. Venter and Şahin (2017) use Bayesian shrinkage priors for the same purpose in a mortality model that is similar to reserve models. G. Gao and Meng (2017) use shrinkage priors on cubic spline models of loss development.…”

Section: Introductionmentioning

confidence: 99%

Loss Reserving Using Estimation Methods Designed for Error Reduction

2018

SSRN Journal

Self Cite

Maximum likelihood estimation has been the workhorse of statistics for decades, but alternative methods are proving to give more accurate predictions. The rather vaguesounding term "regularization" is used for these. Their basic feature is shrinking fitted values towards the overall mean, much like in credibility. These methods are introduced and applied to loss reserving.Improved estimation of ranges is also addressed, in part by a focus on the variance and skewness of residual distributions. For variance, if large losses pay later, as is typical, the variance in the later columns does not reduce as fast as the mean does. This can be modeled by making the variance proportional to a power of the mean less than 1.Skewness can be modeled using the three-parameter Tweedie distribution, which for a variable Z has variance = φµ p , p ≥ 1. It is reparameterized here in a, b, p to have mean = ab, variance = ab 2 , and skewness = pa −1/2 . Then the distribution of the sum of N individual claims has parameters aN, b, p, and cZ has parameters a, bc, p. These properties are both useful in actuarial applications.