Parallel RJAGS with Convergence Testing

Introduction

RJAGS (Random Effects Bayesian Generalized Additive Models) is a powerful tool for modeling complex relationships between variables. However, running RJAGS models can be computationally intensive and time-consuming, especially when dealing with large datasets or multiple chains. In this article, we will explore how to parallelize RJAGS models using the doParallel package in R and incorporate convergence testing using the Gelman-Rubin diagnostic.

Understanding RJAGS

RJAGS is a Bayesian modeling framework that allows users to specify complex relationships between variables. The core idea behind RJAGS is to use a general linear mixed model (LMM) as a basis for the model, with additional terms to accommodate non-linear relationships and random effects.

The basic structure of an RJAGS model is as follows:

• Data: A dataset containing the response variable(s) and predictor(s).
• Model: The RJAGS model itself, which includes the general linear mixed model (LMM), non-linear terms, and any additional features.
• Initialization: An initial set of prior values for the model parameters.

When running an RJAGS model, the following process occurs:

1. Inference: The model is run iteratively, with each iteration updating the parameter estimates based on the current data and model assumptions.
2. Sampling: At each iteration, a set of samples is drawn from the posterior distribution of the model parameters.
3. Convergence checking: After each burn-in period, the Gelman-Rubin diagnostic is used to check for convergence.

Running RJAGS in Parallel

Running RJAGS models can be computationally intensive, especially when dealing with large datasets or multiple chains. To speed up the process, we can use parallel processing using the doParallel package.

The following steps are necessary to run RJAGS in parallel:

1. Make a cluster: Create a cluster of worker nodes that will handle the parallel processing.
2. Register the cluster: Register the cluster with R, which allows us to access the worker nodes and start the model runs.
3. Start the model runs: Use the jags.model function to start each model run on the worker nodes.

Here is an example of running RJAGS in parallel:

# Make some fake data
N <- 1000
x <- rnorm(N, 0, 5)

library('rjags')
library('doParallel')
library('random')

nchains <- 4
c1 <- makeCluster(nchains)
registerDoParallel(c1)

# Define the RJAGS model
model <- jags.model(
    "model {
        y ~ dnorm(mu[1], tau)
        mu[1] <- 0
        for (i in 1:N) {
            mu[i] <- mu[1]
        }
    }",
    data = list(y = x, N = N),
    inits = list(
        mu = rep(0, N + 1),
        tau = 1 / sum(x^2)
    )
)

# Run the model in parallel
endstate <- jags.model(model, "jags", samples = 100, verbose = FALSE)
parsamples <- extend.jags(endstate, samples = 100)
summary(parsamples)

Convergence Testing

After each burn-in period, we need to check for convergence using the Gelman-Rubin diagnostic. This can be done using the coda package in R.

Here is an example of how to incorporate convergence testing into our parallel RJAGS model:

# Define the convergence function
convergence <- function(parsamples) {
    # Calculate the Gelman-Rubin diagnostic
    rhat <- gelman_rubinstein(parsamples)
    
    # Check for convergence
    if (mean(rhat) > 1.05) {
        stop("Model not converged")
    }
}

# Run the model in parallel and check for convergence
c1 <- makeCluster(nchains)
registerDoParallel(c1)

model <- jags.model(
    "model {
        y ~ dnorm(mu[1], tau)
        mu[1] <- 0
        for (i in 1:N) {
            mu[i] <- mu[1]
        }
    }",
    data = list(y = x, N = N),
    inits = list(
        mu = rep(0, N + 1),
        tau = 1 / sum(x^2)
    )
)

endstate <- jags.model(model, "jags", samples = 100, verbose = FALSE)
parsamples <- extend.jags(endstate, samples = 100)

convergence(parsamples)

Alternative Methods

There are alternative methods for parallel RJAGS models that can simplify the process:

1. The runjags package: This package provides a convenient interface for running RJAGS models in parallel.
2. The autorun.jags function: This function allows us to run an RJAGS model automatically after it has converged.

Here is an example of using the runjags package:

library('runjags')

model <- run.jags(
    "model {
        y ~ dnorm(mu[1], tau)
        mu[1] <- 0
        for (i in 1:N) {
            mu[i] <- mu[1]
        }
    }",
    data = list(y = x, N = N),
    monitor = c("mu"),
    sample = 100,
    method = "rjparallel"
)

summary(model)

Here is an example of using the autorun.jags function:

library('runjags')

model <- autorun.jags(
    "model {
        y ~ dnorm(mu[1], tau)
        mu[1] <- 0
        for (i in 1:N) {
            mu[i] <- mu[1]
        }
    }",
    data = list(y = x, N = N),
    monitor = c("mu"),
    method = "rjparallel"
)

summary(model)

Conclusion

Running RJAGS models can be computationally intensive and time-consuming. However, by using parallel processing techniques, we can speed up the process. This article has shown how to run RJAGS models in parallel using the doParallel package and incorporated convergence testing using the Gelman-Rubin diagnostic.

In addition to the doParallel package, there are alternative methods such as the runjags package that provide a convenient interface for running RJAGS models in parallel. These alternatives can simplify the process of running parallel RJAGS models.

By following these steps and using the recommended packages, we can run efficient and accurate parallel RJAGS models to analyze complex relationships between variables.

Last modified on 2024-03-23