paul-buerkner/brms

Add support for a continuous time AR(1) analogue to cor_ar()

Open

#741 建立於 2019年8月29日

在 GitHub 查看
 (8 留言) (5 反應) (0 負責人)R (1,402 star) (220 fork)batch import
autocorrelationfeaturegood first issue

描述

The discrete time AR(1) correlation structure can be generalised to the continuous time setting.

A continuous time AR(1) or CAR(1) correlation structure can be defined as

h(s, ϕ) = ϕs, s ≥ 0, ϕ ≥ 0

where s is a non-negative real. In contrast to the AR(1), the correlation parameter ϕ is constrained to be non-negative. The CAR(1) correlation function is a univariate special case of the exponential spatial correlation function.

The nlme package has an implementation of this correlation function in its nlme::corCAR1().

A cor_car1() function in brms mirroring cor_ar() but for the CAR(1) correlation would be very useful for modelling longitudinal data for example in settings where the observations are not regularly spaced in time.

There is a small amount of discussion of this on the Stan Discourse site.

貢獻者指南

技術棧
r
領域
data
議題類型
feature
難度面向新貢獻者的預計實作難度，1 表示很小改動，5 表示專家級工作。
4
預計時間有經驗貢獻者完成調查、實作、測試並準備 pull request 的粗略時間範圍。
over 1 week
活動狀態議題目前的可參與程度：新鮮、活躍、陳舊、阻塞或等待維護者輸入。
stale
清晰度議題是否清楚說明預期改動、驗收標準和下一步。
clear
前置要求
R programmingStan modeling languageBayesian statisticsbrms package structure
新手友善度1-100 的估計分數，表示該議題對首次貢獻者的友善程度。
15
研究方向
Study the implementation of corCAR1 in nlme and the existing cor ar() in brms. Adapt the continuous time AR(1) correlation structure to brms' framework, ensuring the parameter phi is constrained to be non negative. Refer to the Stan Discourse discussion for guidance on implementing the covariance function. Modify relevant Stan files (e.g., 'stan/.../cor ar.stan') and R functions.