We have an opening for a post-doctoral scholar to work on methods for and applications of hierarchical statistical models using the NIMBLE software (https://r-nimble.org) at the University of California, Berkeley. NIMBLE is an R package that combines a new implementation of a model language similar to BUGS/JAGS, a system for writing new algorithms and MCMC samplers, and a compiler that generates C++ for each model and set of algorithms. The successful candidate will work with Chris Paciorek, Perry de Valpine, and potentially other NIMBLE collaborators to pursue a research program with a combination of building and applying methods in NIMBLE. Specific methods and application areas will be determined based on interests of the successful candidate. Applicants should have a Ph.D. in Statistics or a related discipline. We are open to non-Ph.D. candidates who can make a compelling case that they have relevant experience. The position is funded for two years, with an expected start date between October 2018 and June 2019. Applicants should send a cover letter, including a statement of how their interests relate to NIMBLE, the names of three references, and a CV to nimble.stats@gmail.com, with “NIMBLE post-doc application” in the subject. Applications will be considered on a rolling basis starting 15 October, 2018.

# Author Archives: nimble-admin

# Quick guide for converting from JAGS or BUGS to NIMBLE

# Converting to NIMBLE from JAGS, OpenBUGS or WinBUGS

NIMBLE is a hierarchical modeling package that uses nearly the same modeling language as the popular MCMC packages WinBUGS, OpenBUGS and JAGS. NIMBLE makes the modeling language extensible — you can add distributions and functions — and also allows customization of MCMC or other algorithms that use models. Here is a quick summary of steps to convert existing code from WinBUGS, OpenBUGS or JAGS to NIMBLE. For more information, see examples on r-nimble.org or the NIMBLE User Manual.

## Main steps for converting existing code

These steps assume you are familiar with running WinBUGS, OpenBUGS or JAGS through an R package such as R2WinBUGS, R2jags, rjags, or jagsUI.

- Wrap your model code in
`nimbleCode({})`, directly in R. - This replaces the step of writing or generating a separate file containing the model code.
- Alternatively, you can read standard JAGS- and BUGS-formatted code and data files using

`readBUGSmodel`. - Provide information about missing or empty indices
- Example: If
`x`is a matrix, you must write at least`x[,]`to show it has two dimensions. - If other declarations make the size of
`x`clear,`x[,]`will work in some circumstances. - If not, either provide index ranges (e.g.
`x[1:n, 1:m]`) or use the`dimensions`argument to`nimbleModel`to provide the sizes in each dimension. - Choose how you want to run MCMC.
- Use
`nimbleMCMC()`as the just-do-it way to run an MCMC. This will take all steps to

set up and run an MCMC using NIMBLE’s default configuration. - To use NIMBLE’s full flexibility: build the model, configure and build the MCMC, and compile both the model and MCMC. Then run the MCMC via
`runMCMC`or by calling the`run`function of the compiled MCMC. See the NIMBLE User Manual to learn more about what you can do.

See below for a list of some more nitty-gritty additional steps you may need to consider for some models.

## Example: An animal abundance model

This example is adapted from Chapter 6, Section 6.4 of Applied Hierarchical Modeling in Ecology: Analysis of distribution, abundance and species richness in R and BUGS. Volume I: Prelude and Static Models by Marc Kéry and J. Andrew Royle (2015, Academic Press). The book’s web site provides code for its examples.

### Original code

The original model code looks like this:

cat(file = "model2.txt"," model { # Priors for(k in 1:3){ # Loop over 3 levels of hab or time factors alpha0[k] ~ dunif(-10, 10) # Detection intercepts alpha1[k] ~ dunif(-10, 10) # Detection slopes beta0[k] ~ dunif(-10, 10) # Abundance intercepts beta1[k] ~ dunif(-10, 10) # Abundance slopes } # Likelihood # Ecological model for true abundance for (i in 1:M){ N[i] ~ dpois(lambda[i]) log(lambda[i]) <- beta0[hab[i]] + beta1[hab[i]] * vegHt[i] # Some intermediate derived quantities critical[i] <- step(2-N[i])# yields 1 whenever N is 2 or less z[i] <- step(N[i]-0.5) # Indicator for occupied site # Observation model for replicated counts for (j in 1:J){ C[i,j] ~ dbin(p[i,j], N[i]) logit(p[i,j]) <- alpha0[j] + alpha1[j] * wind[i,j] } } # Derived quantities Nocc <- sum(z[]) # Number of occupied sites among sample of M Ntotal <- sum(N[]) # Total population size at M sites combined Nhab[1] <- sum(N[1:33]) # Total abundance for sites in hab A Nhab[2] <- sum(N[34:66]) # Total abundance for sites in hab B Nhab[3] <- sum(N[67:100])# Total abundance for sites in hab C for(k in 1:100){ # Predictions of lambda and p ... for(level in 1:3){ # ... for each level of hab and time factors lam.pred[k, level] <- exp(beta0[level] + beta1[level] * XvegHt[k]) logit(p.pred[k, level]) <- alpha0[level] + alpha1[level] * Xwind[k] } } N.critical <- sum(critical[]) # Number of populations with critical size }")

### Brief summary of the model

This is known as an "N-mixture" model in ecology. The details aren't really important for illustrating the mechanics of converting this model to NIMBLE, but here is a brief summary anyway. The latent abundances `N[i]` at sites `i = 1...M` are assumed to follow a Poisson. The j-th count at the i-th site, `C[i, j]`, is assumed to follow a binomial with detection probability `p[i, j]`. The abundance at each site depends on a habitat-specific intercept and coefficient for vegetation height, with a log link. The detection probability for each sampling occasion depends on a date-specific intercept and coefficient for wind speed. Kéry and Royle concocted this as a simulated example to illustrate the hierarchical modeling approaches for estimating abundance from count data on repeated visits to multiple sites.

## NIMBLE version of the model code

Here is the model converted for use in NIMBLE. In this case, the only changes to the code are to insert some missing index ranges (see comments).

library(nimble) Section6p4_code <- nimbleCode( { # Priors for(k in 1:3) { # Loop over 3 levels of hab or time factors alpha0[k] ~ dunif(-10, 10) # Detection intercepts alpha1[k] ~ dunif(-10, 10) # Detection slopes beta0[k] ~ dunif(-10, 10) # Abundance intercepts beta1[k] ~ dunif(-10, 10) # Abundance slopes } # Likelihood # Ecological model for true abundance for (i in 1:M){ N[i] ~ dpois(lambda[i]) log(lambda[i]) <- beta0[hab[i]] + beta1[hab[i]] * vegHt[i] # Some intermediate derived quantities critical[i] <- step(2-N[i])# yields 1 whenever N is 2 or less z[i] <- step(N[i]-0.5) # Indicator for occupied site # Observation model for replicated counts for (j in 1:J){ C[i,j] ~ dbin(p[i,j], N[i]) logit(p[i,j]) <- alpha0[j] + alpha1[j] * wind[i,j] } } # Derived quantities; unnececssary when running for inference purpose # NIMBLE: We have filled in indices in the next two lines. Nocc <- sum(z[1:100]) # Number of occupied sites among sample of M Ntotal <- sum(N[1:100]) # Total population size at M sites combined Nhab[1] <- sum(N[1:33]) # Total abundance for sites in hab A Nhab[2] <- sum(N[34:66]) # Total abundance for sites in hab B Nhab[3] <- sum(N[67:100])# Total abundance for sites in hab C for(k in 1:100){ # Predictions of lambda and p ... for(level in 1:3){ # ... for each level of hab and time factors lam.pred[k, level] <- exp(beta0[level] + beta1[level] * XvegHt[k]) logit(p.pred[k, level]) <- alpha0[level] + alpha1[level] * Xwind[k] } } # NIMBLE: We have filled in indices in the next line. N.critical <- sum(critical[1:100]) # Number of populations with critical size })

## Simulated data

To carry this example further, we need some simulated data. Kéry and Royle provide separate code to do this. With NIMBLE we could use the model itself to simulate data rather than writing separate simulation code. But for our goals here, we simply copy Kéry and Royle's simulation code, and we compact it somewhat:

# Code from Kery and Royle (2015) # Choose sample sizes and prepare obs. data array y set.seed(1) # So we all get same data set M <- 100 # Number of sites J <- 3 # Number of repeated abundance measurements C <- matrix(NA, nrow = M, ncol = J) # to contain the observed data # Create a covariate called vegHt vegHt <- sort(runif(M, -1, 1)) # sort for graphical convenience # Choose parameter values for abundance model and compute lambda beta0 <- 0 # Log-scale intercept beta1 <- 2 # Log-scale slope for vegHt lambda <- exp(beta0 + beta1 * vegHt) # Expected abundance # Draw local abundance N <- rpois(M, lambda) # Create a covariate called wind wind <- array(runif(M * J, -1, 1), dim = c(M, J)) # Choose parameter values for measurement error model and compute detectability alpha0 <- -2 # Logit-scale intercept alpha1 <- -3 # Logit-scale slope for wind p <- plogis(alpha0 + alpha1 * wind) # Detection probability # Take J = 3 abundance measurements at each site for(j in 1:J) { C[,j] <- rbinom(M, N, p[,j]) } # Create factors time <- matrix(rep(as.character(1:J), M), ncol = J, byrow = TRUE) hab <- c(rep("A", 33), rep("B", 33), rep("C", 34)) # assumes M = 100 # Bundle data # NIMBLE: For full flexibility, we could separate this list # into constants and data lists. For simplicity we will keep # it as one list to be provided as the "constants" argument. # See comments about how we would split it if desired. win.data <- list( ## NIMBLE: C is the actual data C = C, ## NIMBLE: Covariates can be data or constants ## If they are data, you could modify them after the model is built wind = wind, vegHt = vegHt, XvegHt = seq(-1, 1,, 100), # Used only for derived quantities Xwind = seq(-1, 1,,100), # Used only for derived quantities ## NIMBLE: The rest of these are constants, needed for model definition ## We can provide them in the same list and NIMBLE will figure it out. M = nrow(C), J = ncol(C), hab = as.numeric(factor(hab)) )

## Initial values

Next we need to set up initial values and choose parameters to monitor in the MCMC output. To do so we will again directly use Kéry and Royle's code.

Nst <- apply(C, 1, max)+1 # Important to give good inits for latent N inits <- function() list(N = Nst, alpha0 = rnorm(3), alpha1 = rnorm(3), beta0 = rnorm(3), beta1 = rnorm(3)) # Parameters monitored # could also estimate N, bayesian counterpart to BUPs before: simply add "N" to the list params <- c("alpha0", "alpha1", "beta0", "beta1", "Nocc", "Ntotal", "Nhab", "N.critical", "lam.pred", "p.pred")

## Run MCMC with `nimbleMCMC`

Now we are ready to run an MCMC in nimble. We will run only one chain, using the same settings as Kéry and Royle.

samples <- nimbleMCMC( code = Section6p4_code, constants = win.data, ## provide the combined data & constants as constants inits = inits, monitors = params, niter = 22000, nburnin = 2000, thin = 10)

## Detected C as data within 'constants'.

## |-------------|-------------|-------------|-------------| ## |-------------------------------------------------------|

## Work with the samples

Finally we want to look at our samples. NIMBLE returns samples as a simple matrix with named columns. There are numerous packages for processing MCMC output. If you want to use the `coda` package, you can convert a matrix to a coda mcmc object like this:

library(coda) coda.samples <- as.mcmc(samples)

Alternatively, if you call `nimbleMCMC` with the argument `samplesAsCodaMCMC = TRUE`, the samples will be returned as a coda object.

To show that MCMC really happened, here is a plot of `N.critical`:

plot(jitter(samples[, "N.critical"]), xlab = "iteration", ylab = "N.critical", main = "Number of populations with critical size", type = "l")

# Next steps

NIMBLE allows users to customize MCMC and other algorithms in many ways. See the NIMBLE User Manual and web site for more ideas.

## Smaller steps you may need for converting existing code

If the main steps above aren't sufficient, consider these additional steps when converting from JAGS, WinBUGS or OpenBUGS to NIMBLE.

- Convert any use of truncation syntax
- e.g.
`x ~ dnorm(0, tau) T(a, b)`should be re-written as`x ~ T(dnorm(0, tau), a, b)`. - If reading model code from a file using
`readBUGSmodel`, the`x ~ dnorm(0, tau) T(a, b)`syntax will work.

- e.g.
- Possibly split the
`data`into`data`and`constants`for NIMBLE.- NIMBLE has a more general concept of data, so NIMBLE makes a distinction between data and constants.
- Constants are necessary to define the model, such as
`nsite`in`for(i in 1:nsite) {...}`and constant vectors of factor indices (e.g.`block`in`mu[block[i]]`). - Data are observed values of some variables.
- Alternatively, one can provide a list of both constants and data for the
`constants`argument to`nimbleModel`, and NIMBLE will try to determine which is which. Usually this will work, but when in doubt, try separating them.

- Possibly update initial values (
`inits`).- In some cases, NIMBLE likes to have more complete
`inits`than the other packages. - In a model with stochastic indices, those indices should have
`inits`values. - When using
`nimbleMCMC`or`runMCMC`,`inits`can be a function, as in R packages for calling WinBUGS, OpenBUGS or JAGS. Alternatively, it can be a list. - When you build a model with
`nimbleModel`for more control than`nimbleMCMC`, you can provide`inits`as a list. This sets defaults that can be over-ridden with the`inits`argument to`runMCMC`.

- In some cases, NIMBLE likes to have more complete

# NIMBLE workshop in Switzerland, 23-25 April

There will be a three-day NIMBLE workshop in Sempach, Switzerland, 23-25 April, hosted at the Swiss Ornithological Institute. More information can be found here: http://www.phidot.org/forum/viewtopic.php?f=8&t=3586. Examples will be oriented towards ecological applications, but otherwise the workshop content will be general.

# Writing reversible jump MCMC in NIMBLE

# Writing reversible jump MCMC samplers in NIMBLE

## Introduction

Reversible jump Markov chain Monte Carlo (RJMCMC) is a powerful method for drawing posterior samples over multiple models by jumping between models as part of the sampling. For a simple example that I’ll use below, think about a regression model where we don’t know which explanatory variables to include, so we want to do variable selection. There may be a huge number of possible combinations of variables, so it would be nice to explore the combinations as part of one MCMC run rather than running many different MCMCs on some chosen combinations of variables. To do it in one MCMC, one sets up a model that includes all possible variables and coefficients. Then “removing” a variable from the model is equivalent to setting its coefficient to zero, and “adding” it back into the model requires a valid move to a non-zero coefficient. Reversible jump MCMC methods provide a way to do that.

Reversible jump is different enough from other MCMC situations that packages like WinBUGS, OpenBUGS, JAGS, and Stan don’t do it. An alternative way to set up the problem, which does not involve the technicality of changing model dimension, is to use indicator variables. An indicator variable is either zero or one and is multiplied by another parameter. Thus when the indicator is 0, the parameter that is multipled by 0 is effectively removed from the model. Darren Wilkinson has a nice old blog post on using indicator variables for Bayesian variable selection in BUGS code. The problem with using indicator variables is that they can create a lot of extra MCMC work and the samplers operating on them may not be well designed for their situation.

NIMBLE lets one program model-generic algorithms to use with models written in the BUGS language. The MCMC system works by first making a configuration in R, which can be modified by a user or a program, and then building and compiling the MCMC. The nimbleFunction programming system makes it easy to write new kinds of samplers.

The aim of this blog post is to illustrate how one can write reversible jump MCMC in NIMBLE. A variant of this may be incorporated into a later version of NIMBLE.

## Example model

For illustration, I’ll use an extremely simple model: linear regression with two candidate explanatory variables. I’ll assume the first, x1, should definitely be included. But the analyst is not sure about the second, x2, and wants to use reversible jump to include it or exclude it from the model. I won’t deal with the issue of choosing the prior probability that it should be in the model. Instead I’ll just pick a simple choice and stay focused on the reversible jump aspect of the example. The methods below could be applied en masse to large models.

Here I’ll simulate data to use:

N <- 20 x1 <- runif(N, -1, 1) x2 <- runif(N, -1, 1) Y <- rnorm(N, 1.5 + 0.5 * x1, sd = 1)

I’ll take two approaches to implementing RJ sampling. In the first, I’ll use a traditional indicator variable and write the RJMCMC sampler to use it. In the second, I’ll write the RJMCMC sampler to incorporate the prior probability of inclusion for the coefficient it is sampling, so the indicator variable won’t be needed in the model.

First we’ll need nimble:

library(nimble)

## RJMCMC implementation 1, with indicator variable included

Here is BUGS code for the first method, with an indicator variable written into the model, and the creation of a NIMBLE model object from it. Note that although RJMCMC technically jumps between models of different dimensions, we still start by creating the largest model so that changes of dimension can occur by setting some parameters to zero (or, in the second method, possibly another fixed value).

simpleCode1 <- nimbleCode({ beta0 ~ dnorm(0, sd = 100) beta1 ~ dnorm(0, sd = 100) beta2 ~ dnorm(0, sd = 100) sigma ~ dunif(0, 100) z2 ~ dbern(0.8) ## indicator variable for including beta2 beta2z2 <- beta2 * z2 for(i in 1:N) { Ypred[i] <- beta0 + beta1 * x1[i] + beta2z2 * x2[i] Y[i] ~ dnorm(Ypred[i], sd = sigma) } }) simpleModel1 <- nimbleModel(simpleCode1, data = list(Y = Y, x1 = x1, x2 = x2), constants = list(N = N), inits = list(beta0 = 0, beta1 = 0, beta2 = 0, sigma = sd(Y), z2 = 1))

Now here are two custom samplers. The first one will sample beta2 *only* if the indicator variable z2 is 1 (meaning that beta2 is included in the model). It does this by containing a regular random walk sampler but only calling it when the indicator is 1 (we could perhaps set it up to contain *any* sampler to be used when z2 is 1, but for now it’s a random walk sampler). The second sampler makes reversible jump proposals to move beta2 in and out of the model. When it is out of the model, both beta2 and z2 are set to zero. Since beta2 will be zero every time z2 is zero, we don’t really need beta2z2, but it ensures correct behavior in other cases, like if someone runs default samplers on the model and expects the indicator variable to do its job correctly. For use in reversible jump, z2’s role is really to trigger the prior probability (set to 0.8 in this example) of being in the model.

*Don’t worry about the warning message emitted by NIMBLE.* They are there because when a nimbleFunction is defined it tries to make sure the user knows anything else that needs to be defined.

RW_sampler_nonzero_indicator <- nimbleFunction( contains = sampler_BASE, setup = function(model, mvSaved, target, control) { regular_RW_sampler <- sampler_RW(model, mvSaved, target = target, control = control$RWcontrol) indicatorNode <- control$indicator }, run = function() { if(model[[indicatorNode]] == 1) regular_RW_sampler$run() }, methods = list( reset = function() {regular_RW_sampler$reset()} ))

## Warning in nf_checkDSLcode(code): For this nimbleFunction to compile, these ## functions must be defined as nimbleFunctions or nimbleFunction methods: ## reset.

RJindicatorSampler <- nimbleFunction( contains = sampler_BASE, setup = function( model, mvSaved, target, control ) { ## target should be the name of the indicator node, 'z2' above ## control should have an element called coef for the name of the corresponding coefficient, 'beta2' above. coefNode <- control$coef scale <- control$scale calcNodes <- model$getDependencies(c(coefNode, target)) }, run = function( ) { ## The reversible-jump updates happen here. currentIndicator <- model[[target]] currentLogProb <- model$getLogProb(calcNodes) if(currentIndicator == 1) { ## propose removing it currentCoef <- model[[coefNode]] logProbReverseProposal <- dnorm(0, currentCoef, sd = scale, log = TRUE) model[[target]] <<- 0 model[[coefNode]] <<- 0 proposalLogProb <- model$calculate(calcNodes) log_accept_prob <- proposalLogProb - currentLogProb + logProbReverseProposal } else { ## propose adding it proposalCoef <- rnorm(1, 0, sd = scale) model[[target]] <<- 1 model[[coefNode]] <<- proposalCoef logProbForwardProposal <- dnorm(0, proposalCoef, sd = scale, log = TRUE) proposalLogProb <- model$calculate(calcNodes) log_accept_prob <- proposalLogProb - currentLogProb - logProbForwardProposal } accept <- decide(log_accept_prob) if(accept) { copy(from = model, to = mvSaved, row = 1, nodes = calcNodes, logProb = TRUE) } else { copy(from = mvSaved, to = model, row = 1, nodes = calcNodes, logProb = TRUE) } }, methods = list(reset = function() { }) )

Now we’ll set up and run the samplers:

mcmcConf1 <- configureMCMC(simpleModel1) mcmcConf1$removeSamplers('z2') mcmcConf1$addSampler(target = 'z2', type = RJindicatorSampler, control = list(scale = 1, coef = 'beta2')) mcmcConf1$removeSamplers('beta2') mcmcConf1$addSampler(target = 'beta2', type = 'RW_sampler_nonzero_indicator', control = list(indicator = 'z2', RWcontrol = list(adaptive = TRUE, adaptInterval = 100, scale = 1, log = FALSE, reflective = FALSE))) mcmc1 <- buildMCMC(mcmcConf1) compiled1 <- compileNimble(simpleModel1, mcmc1) compiled1$mcmc1$run(10000)

## |-------------|-------------|-------------|-------------| ## |-------------------------------------------------------|

## NULL

samples1 <- as.matrix(compiled1$mcmc1$mvSamples)

Here is a trace plot of the beta2 (slope) samples. The thick line at zero corresponds to having beta2 removed from the model.

plot(samples1[,'beta2'])

And here is a trace plot of the z2 (indicator variable) samples.

plot(samples1[,'z2'])

The chains look reasonable.

As a quick check of reasonableness, let’s compare the beta2 samples to what we’d get if it was always included in the model. I’ll do that by setting up default samplers and then removing the sampler for z2 (and z2 should be 1).

mcmcConf1b <- configureMCMC(simpleModel1) mcmcConf1b$removeSamplers('z2') mcmc1b <- buildMCMC(mcmcConf1b) compiled1b <- compileNimble(simpleModel1, mcmc1b) compiled1b$mcmc1b$run(10000)

## |-------------|-------------|-------------|-------------| ## |-------------------------------------------------------|

## NULL

samples1b <- as.matrix(compiled1b$mcmc1b$mvSamples) plot(samples1b[,'beta2'])

That looks correct, in the sense that the distribution of beta2 given that it’s in the model (using reversible jump) should match the distribution of beta2 when it is

always in the model.

## RJ implementation 2, without indicator variables

Now I’ll set up the second version of the model and samplers. I won’t include the indicator variable in the model but will instead include the prior probability for inclusion in the sampler. One added bit of generality is that being “out of the model” will be defined as taking some fixedValue, to be provided, which will typically but not necessarily be zero. These functions are very similar to the ones above.

Here is the code to define and build a model without the indicator variable:

simpleCode2 <- nimbleCode({ beta0 ~ dnorm(0, sd = 100) beta1 ~ dnorm(0, sd = 100) beta2 ~ dnorm(0, sd = 100) sigma ~ dunif(0, 100) for(i in 1:N) { Ypred[i] <- beta0 + beta1 * x1[i] + beta2 * x2[i] Y[i] ~ dnorm(Ypred[i], sd = sigma) } }) simpleModel2 <- nimbleModel(simpleCode2, data = list(Y = Y, x1 = x1, x2 = x2), constants = list(N = N), inits = list(beta0 = 0, beta1 = 0, beta2 = 0, sigma = sd(Y)))

And here are the samplers (again, ignore the warning):

RW_sampler_nonzero <- nimbleFunction( ## "nonzero" is a misnomer because it can check whether it sits at any fixedValue, not just 0 contains = sampler_BASE, setup = function(model, mvSaved, target, control) { regular_RW_sampler <- sampler_RW(model, mvSaved, target = target, control = control$RWcontrol) fixedValue <- control$fixedValue }, run = function() { ## Now there is no indicator variable, so check if the target node is exactly ## equal to the fixedValue representing "not in the model". if(model[[target]] != fixedValue) regular_RW_sampler$run() }, methods = list( reset = function() {regular_RW_sampler$reset()} ))

## Warning in nf_checkDSLcode(code): For this nimbleFunction to compile, these ## functions must be defined as nimbleFunctions or nimbleFunction methods: ## reset.

RJsampler <- nimbleFunction( contains = sampler_BASE, setup = function( model, mvSaved, target, control ) { ## target should be a coefficient to be set to a fixed value (usually zero) or not ## control should have an element called fixedValue (usually 0), ## a scale for jumps to and from the fixedValue, ## and a prior prob of taking its fixedValue fixedValue <- control$fixedValue scale <- control$scale ## The control list contains the prior probability of inclusion, and we can pre-calculate ## this log ratio because it's what we'll need later. logRatioProbFixedOverProbNotFixed <- log(control$prior) - log(1-control$prior) calcNodes <- model$getDependencies(target) }, run = function( ) { ## The reversible-jump moves happen here currentValue <- model[[target]] currentLogProb <- model$getLogProb(calcNodes) if(currentValue != fixedValue) { ## There is no indicator variable, so check if current value matches fixedValue ## propose removing it (setting it to fixedValue) logProbReverseProposal <- dnorm(fixedValue, currentValue, sd = scale, log = TRUE) model[[target]] <<- fixedValue proposalLogProb <- model$calculate(calcNodes) log_accept_prob <- proposalLogProb - currentLogProb - logRatioProbFixedOverProbNotFixed + logProbReverseProposal } else { ## propose adding it proposalValue <- rnorm(1, fixedValue, sd = scale) model[[target]] <<- proposalValue logProbForwardProposal <- dnorm(fixedValue, proposalValue, sd = scale, log = TRUE) proposalLogProb <- model$calculate(calcNodes) log_accept_prob <- proposalLogProb - currentLogProb + logRatioProbFixedOverProbNotFixed - logProbForwardProposal } accept <- decide(log_accept_prob) if(accept) { copy(from = model, to = mvSaved, row = 1, nodes = calcNodes, logProb = TRUE) } else { copy(from = mvSaved, to = model, row = 1, nodes = calcNodes, logProb = TRUE) } }, methods = list(reset = function() { }) )

Now let’s set up and use the samplers

mcmcConf2 <- configureMCMC(simpleModel2) mcmcConf2$removeSamplers('beta2') mcmcConf2$addSampler(target = 'beta2', type = 'RJsampler', control = list(fixedValue = 0, prior = 0.8, scale = 1)) mcmcConf2$addSampler(target = 'beta2', type = 'RW_sampler_nonzero', control = list(fixedValue = 0, RWcontrol = list(adaptive = TRUE, adaptInterval = 100, scale = 1, log = FALSE, reflective = FALSE))) mcmc2 <- buildMCMC(mcmcConf2) compiled2 <- compileNimble(simpleModel2, mcmc2) compiled2$mcmc2$run(10000)

## NULL

samples2 <- as.matrix(compiled2$mcmc2$mvSamples)

And again let’s look at the samples. As above, the horizontal line at 0 represents having beta2 removed from the model.

plot(samples2[,'beta2'])

### How to apply this for larger models.

The samplers above could be assigned to arbitrary nodes in a model. The only additional code would arise from adding more samplers to an MCMC configuration. It would also be possible to refine the reversible-jump step to adapt the scale of its jumps in order to achieve better mixing. For example, one could try this method by Ehlers and Brooks. We’re interested in hearing from you if you plan to try using RJMCMC on your own models.

# Building Particle Filters and Particle MCMC in NIMBLE

This example shows how to construct and conduct inference on a state space model using particle filtering algorithms. `nimble`

currently has versions of the bootstrap filter, the auxiliary particle filter, the ensemble Kalman filter, and the Liu and West filter implemented. Additionally, particle MCMC samplers are available and can be specified for both univariate and multivariate parameters.

# Model Creation

Assume is the latent state and is the observation at time for . We define our state space model as

with initial states

and prior distributions

where denotes a normal distribution with mean and standard deviation , and is a shifted, scaled -distribution with center parameter , scale parameter , and degrees of freedom.

We specify and build our state space model below, using time points:

## load the nimble library and set seed library('nimble') set.seed(1) ## define the model stateSpaceCode <- nimbleCode({ a ~ dunif(-0.9999, 0.9999) b ~ dnorm(0, sd = 1000) sigPN ~ dunif(1e-04, 1) sigOE ~ dunif(1e-04, 1) x[1] ~ dnorm(b/(1 - a), sd = sigPN/sqrt((1-a*a))) y[1] ~ dt(mu = x[1], sigma = sigOE, df = 5) for (i in 2:t) { x[i] ~ dnorm(a * x[i - 1] + b, sd = sigPN) y[i] ~ dt(mu = x[i], sigma = sigOE, df = 5) } }) ## define data, constants, and initial values data <- list( y = c(0.213, 1.025, 0.314, 0.521, 0.895, 1.74, 0.078, 0.474, 0.656, 0.802) ) constants <- list( t = 10 ) inits <- list( a = 0, b = .5, sigPN = .1, sigOE = .05 ) ## build the model stateSpaceModel <- nimbleModel(stateSpaceCode, data = data, constants = constants, inits = inits, check = FALSE)

# Construct and run a bootstrap filter

We next construct a bootstrap filter to conduct inference on the latent states of our state space model. Note that the bootstrap filter, along with the auxiliary particle filter and the ensemble Kalman filter, treat the top-level parameters `a, b, sigPN`

, and `sigOE`

as fixed. Therefore, the bootstrap filter below will proceed as though `a = 0, b = .5, sigPN = .1`

, and `sigOE = .05`

, which are the initial values that were assigned to the top-level parameters.

The bootstrap filter takes as arguments the name of the model and the name of the latent state variable within the model. The filter can also take a control list that can be used to fine-tune the algorithm’s configuration.

## build bootstrap filter and compile model and filter bootstrapFilter <- buildBootstrapFilter(stateSpaceModel, nodes = 'x') compiledList <- compileNimble(stateSpaceModel, bootstrapFilter)

## run compiled filter with 10,000 particles. ## note that the bootstrap filter returns an estimate of the log-likelihood of the model. compiledList$bootstrapFilter$run(10000)

## [1] -28.13009

Particle filtering algorithms in `nimble`

store weighted samples of the filtering distribution of the latent states in the `mvSamples`

modelValues object. Equally weighted samples are stored in the `mvEWSamples`

object. By default, `nimble`

only stores samples from the final time point.

## extract equally weighted posterior samples of x[10] and create a histogram posteriorSamples <- as.matrix(compiledList$bootstrapFilter$mvEWSamples) hist(posteriorSamples)

The auxiliary particle filter and ensemble Kalman filter can be constructed and run in the same manner as the bootstrap filter.

# Conduct inference on top-level parameters using particle MCMC

Particle MCMC can be used to conduct inference on the posterior distribution of both the latent states and any top-level parameters of interest in a state space model. The particle marginal Metropolis-Hastings sampler can be specified to jointly sample the `a, b, sigPN`

, and `sigOE`

top level parameters within `nimble`

‘s MCMC framework as follows:

## create MCMC specification for the state space model stateSpaceMCMCconf <- configureMCMC(stateSpaceModel, nodes = NULL) ## add a block pMCMC sampler for a, b, sigPN, and sigOE stateSpaceMCMCconf$addSampler(target = c('a', 'b', 'sigPN', 'sigOE'), type = 'RW_PF_block', control = list(latents = 'x')) ## build and compile pMCMC sampler stateSpaceMCMC <- buildMCMC(stateSpaceMCMCconf) compiledList <- compileNimble(stateSpaceModel, stateSpaceMCMC, resetFunctions = TRUE)

## run compiled sampler for 5000 iterations compiledList$stateSpaceMCMC$run(5000)

## NULL

## create trace plots for each parameter library('coda')

par(mfrow = c(2,2)) posteriorSamps <- as.mcmc(as.matrix(compiledList$stateSpaceMCMC$mvSamples)) traceplot(posteriorSamps[,'a'], ylab = 'a') traceplot(posteriorSamps[,'b'], ylab = 'b') traceplot(posteriorSamps[,'sigPN'], ylab = 'sigPN') traceplot(posteriorSamps[,'sigOE'], ylab = 'sigOE')

The above `RW_PF_block`

sampler uses a multivariate normal proposal distribution to sample vectors of top-level parameters. To sample a scalar top-level parameter, use the `RW_PF`

sampler instead.

# NIMBLE package for hierarchical modeling (MCMC and more) faster and more flexible in version 0.6-1

NIMBLE version 0.6-1 has been released on CRAN and at r-nimble.org.

NIMBLE is a system that allows you to:

- Write general hierarchical statistical models in BUGS code and create a corresponding model object to use in R.
- Build Markov chain Monte Carlo (MCMC), particle filters, Monte Carlo Expectation Maximization (MCEM), or write generic algorithms that can be applied to any model.
- Compile models and algorithms via problem-specific generated C++ that NIMBLE interfaces to R for you.

Most people associate BUGS with MCMC, but NIMBLE is about much more than that. It implements and extends the BUGS language as a flexible system for model declaration and lets you do what you want with the resulting models. Some of the cool things you can do with NIMBLE include:

- Extend BUGS with functions and distributions you write in R as nimbleFunctions, which will be automatically turned into C++ and compiled into your model.
- Program with models written in BUGS code: get and set values of variables, control model calculations, simulate new values, use different data sets in the same model, and more.
- Write your own MCMC samplers as nimbleFunctions and use them in combination with NIMBLE’s samplers.
- Write functions that use MCMC as one step of a larger algorithm.
- Use standard particle filter methods or write your own.
- Combine particle filters with MCMC as Particle MCMC methods.
- Write other kinds of model-generic algorithms as nimbleFunctions.
- Compile a subset of R’s math syntax to C++ automatically, without writing any C++ yourself.

Some early versions of NIMBLE were not on CRAN because NIMBLE’s system for on-the-fly compilation via generating and compiling C++ from R required some extra work for CRAN packaging, but now it’s there. Compared to earlier versions, the new version is faster and more flexible in a lot of ways. Building and compiling models and algorithms could sometimes get bogged down for large models, so we streamlined those steps quite a lot. We’ve generally increased the efficiency of C++ generated by the NIMBLE compiler. We’ve added functionality to what can be compiled to C++ from nimbleFunctions. And we’ve added a bunch of better error-trapping and informative messages, although there is still a good way to go on that. Give us a holler on the nimble-users list if you run into questions.

# NIMBLE: A new way to do MCMC (and more) from BUGS code in R

Yesterday we released version 0.5 of NIMBLE on our web site, r-nimble.org. (We’ll get it onto CRAN soon, but it has some special needs to work out.) NIMBLE tries to fill a gap in what R programmers and analysts can do with general hierarchical models. Packages like WinBUGS, OpenBUGS, JAGS and Stan provide a language for writing a model flexibly, and then they provide one flavor of MCMC. These have been workhorses of the Bayesian revolution, but they don’t provide much control over how the MCMC works (what samplers are used) or let one do anything else with the model (though Stan provides some additional fitting methods).

The idea of NIMBLE has been to provide a layer of programmability for algorithms that use models written in BUGS. We adopted BUGS as a model declaration language because these is so much BUGS code out there and so many books that use BUGS for teaching Bayesian statistics. Our implementation processes BUGS code in R and creates a model object that you can program with. For MCMC, we provide a default set of samplers, but these choices can be modified. It is easy to write your own sampler and add it to the MCMC. And it is easy to add new distributions and functions for use in BUGS code, something that hasn’t been possible (in any easy way) before. These features can allow big gains in MCMC efficiency.

MCMCs are heavily computational, so NIMBLE includes a compiler that generates C++ specific to a model and algorithm (MCMC samplers or otherwise), compiles it, loads it into R and gives you an interface to it. To be able to compile an algorithm, you need to write it as a nimbleFunction rather than a regular R function. nimbleFunctions can interact with model objects, and they can use a subset of R for math and flow-control. Among other things, the NIMBLE compiler automatically generates code for the Eigen C++ linear algebra library and manages all the necessary interfaces.

Actually, NIMBLE is not specific to MCMC or to Bayesian methods. You can write other algorithms to use whatever model you write in BUGS code. Here’s one simple example: in the past if you wanted to do a simulation study for a model written in BUGS code, you had to re-write the model in R just to simulate from it. With NIMBLE you can simulate from the model as written in BUGS and have complete control over what parts of the model you use. You can also query the model about how nodes are related so that you can make an algorithm adapt to what it finds in a model. We have a set of sequential Monte Carlo (particle filter) methods in development that we’ll release soon. But the idea is that NIMBLE provides a platform for others to develop and disseminate model-generic algorithms.

NIMBLE also extends BUGS in a bunch of ways that I won’t go into here. And it has one major limitation right now: it doesn’t handle models with stochastic indices, like latent class membership models.

Here is a toy example of what it looks like to set up and run an MCMC using NIMBLE.

library(nimble) myBUGScode <- nimbleCode({ mu ~ dnorm(0, sd = 100) ## uninformative prior sigma ~ dunif(0, 100) for(i in 1:10) y[i] ~ dnorm(mu, sd = sigma) }) myModel <- nimbleModel(myBUGScode)

myData <- rnorm(10, mean = 2, sd = 5) myModel$setData(list(y = myData)) myModel$setInits(list(mu = 0, sigma = 1)) myMCMC <- buildMCMC(myModel) compiled <- compileNimble(myModel, myMCMC) compiled$myMCMC$run(10000)

samples <- as.matrix(compiled$myMCMC$mvSamples) plot(density(samples[,'mu']))

plot(density(samples[,'sigma']))

# NIMBLE paper in Journal of Computational and Graphical Statistics

Our paper giving an overview on the rationale and design of NIMBLE has appeared online in accepted manuscript form at the Journal of Computational and Graphical Statistics. You can get it here.

# We have a post-doc opening.

We have a 1-year opening for a post-doc interested in developing statistical methods in NIMBLE.

Here is the official, approved job advertisement:

POSTDOCTORAL SCHOLAR POSITION AVAILABLE IN COMPUTATIONAL STATISTICS – UNIVERSITY OF CALIFORNIA, BERKELEY

The Departments of Statistics and Environmental Science Policy, and Management have an opening for a Postdoctoral Scholar – Employee to develop and apply statistical algorithms as part of the NIMBLE software development team. NIMBLE is a NSF-funded framework for programming computational methods for general hierarchical models such as Markov chain Monte Carlo, sequential Monte Carlo, and numerical integration and approximation. More information is available at R-nimble.org. The post- doc will be supervised by co-PIs Perry de Valpine and Chris Paciorek. We seek a candidate who will build out NIMBLE’s algorithm library, which includes using it as a platform for methodological and applied research. The successful candidate will be expected to author peer-reviewed publications and contribute to software development.

BASIC QUALIFICATIONS

Candidates must have completed all degree requirements except the dissertation or be enrolled in an accredited PhD or equivalent degree in a statistical field such as Statistics or Computer Science or a field of statistical application at the time of application.

ADDITIONAL QUALIFICATIONS

Candidates must have a PhD or equivalent degree in a statistical field such as Statistics or Computer Science or in a field of statistical application such as biology, ecology, environmental science, political science, psychology, education, public health or related field by appointment start date.

PREFERRED QUALIFICATIONS

Demonstrated experience programming complex scientific computing applications using R and/or C++, Python or others. Demonstrated experience advancing computational statistical methodology by appointment start date.

APPOINTMENT

The position is available to start immediately but we seek the best candidate even if they cannot start until a later date. The initial appointment is for one-year, with renewal based on performance and funding. This is a full-time appointment.

SALARY AND BENEFITS

Salary will be commensurate with qualifications and experience. Generous benefits are included (http://vspa.berkeley.edu/postdocs)

TO APPLY

Visit: https://aprecruit.berkeley.edu/apply/JPF00860

Interested individuals should include a 1-2 page cover letter describing their research experience and publications along with a current CV and the names and contact information of three references. Letters of reference may be requested for finalists. It is optional to include a statement addressing past and/or potential contributions to diversity through research, teaching, and/or service.

This position will remain open until filled.

Questions regarding this recruitment can be directed to Maria P. Aranas, aranas4@berkeley.edu.

All letters will be treated as confidential per University of California policy and California state law. Please refer potential referees, including when letters are provided via a third party (i.e. dossier service or career center) to the UC Berkeley Statement of Confidentiality (http://apo.berkeley.edu/evalltr.html ) prior to submitting their letters.

The University of California is an Equal Opportunity/Affirmative Action Employer. All qualified applicants will receive consideration for employment without regard to race, color, religion, sex, sexual orientation, gender identity, national origin, disability, age or protected veteran status. For the complete University of California nondiscrimination and affirmative action policy see: http://policy.ucop.edu/doc/4000376/NondiscrimAffirmAct

The Department is interested in candidates who will contribute to diversity and equal opportunity in higher education through their research or teaching.

The University of California, Berkeley has an excellent benefits package as well as a number of policies and programs in place to support employees as they balance work and family.

# Version 0.4 released!

In late July we released a major new version of NIMBLE, 0.4. Ok, that’s still a low version number, indicating we have a lot we still want to build and improve, but this version can do a lot and is a huge step forward from 0.3. Almost everything runs faster, from model building to model and nimbleFunction compiling to compiled execution. New features include the ability to write your own functions and distributions for BUGS (as nimbleFunctions, of course) and an algorithm that automatically adapts blocks of correlated parameters for efficient joint sampling in MCMC. Read NEWS (link here) for more details. The same information is also on github (here).