paul-buerkner/brms

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

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#741 opened on Aug 29, 2019

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Description

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.

Contributor guide

Tech stack
r
Domain
data
Issue type
feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
4
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
over 1 week
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
stale
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
clear
Prerequisites
R programmingStan modeling languageBayesian statisticsbrms package structure
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
15
Research direction
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.