# Chapter 3 More introduction

Now that we have shown a brief example, we will introduce more about the concepts and design of NIMBLE.

One of the most important concepts behind NIMBLE is to allow a combination of high-level processing in R and low-level processing in C++. For example, when we write a Metropolis-Hastings MCMC sampler in the NIMBLE language, the inspection of the model structure related to one node is done in R, and the actual sampler calculations are done in C++. This separation between *setup* and *run* steps will become clearer as we go.

## 3.1 NIMBLE adopts and extends the BUGS language for specifying models

We adopted the BUGS language, and we have extended it to make it more flexible. The BUGS language became widely used in WinBUGS, then in OpenBUGS and JAGS. These systems all provide automatically-generated MCMC algorithms, but we have adopted only the language for describing models, not their systems for generating MCMCs.

NIMBLE extends BUGS by:

- allowing you to write new functions and distributions and use them in BUGS models;
- allowing you to define multiple models in the same code using conditionals evaluated when the BUGS code is processed;
- supporting a variety of more flexible syntax such as R-like named parameters and more general algebraic expressions.

By supporting new functions and distributions, NIMBLE makes BUGS an extensible language, which is a major departure from previous packages that implement BUGS.

We adopted BUGS because it has been so successful, with over 30,000 users by the time they stopped counting (Lunn et al. 2009). Many papers and books provide BUGS code as a way to document their statistical models. We describe NIMBLE’s version of BUGS later. The web sites for WinBUGS, OpenBUGS and JAGS provide other useful documntation on writing models in BUGS. For the most part, if you have BUGS code, you can try NIMBLE.

NIMBLE does several things with BUGS code:

- NIMBLE creates a
*model definition*object that knows everything about the variables and their relationships written in the BUGS code. Usually you’ll ignore the*model definition*and let NIMBLE’s default options take you directly to the next step. - NIMBLE creates a model object
^{6}. This can be used to manipulate variables and operate the model from R. Operating the model includes calculating, simulating, or querying the log probability value of model nodes. These basic capabilities, along with the tools to query model structure, allow one to write programs that use the model and adapt to its structure. - When you’re ready, NIMBLE can generate customized C++ code representing the model, compile the C++, load it back into R, and provide a new model object that uses the compiled model internally. We use the word ‘compile’ to refer to all of these steps together.

As an example of how radical a departure NIMBLE is from previous BUGS implementations, consider a situation where you want to simulate new data from a model written in BUGS code. Since NIMBLE creates model objects that you can control from R, simulating new data is trivial. With previous BUGS-based packages, this isn’t possible.

More information about specifying and manipulating models is in Chapters 6 and 13.

## 3.2 nimbleFunctions for writing algorithms

NIMBLE provides *nimbleFunction*s for writing functions that can (but don’t have to) use BUGS models. The main ways that nimbleFunctions can use BUGS models are:

- inspecting the structure of a model, such as determining the dependencies between variables, in order to do the right calculations with each model;
- accessing values of the model’s variables;
- controlling execution of the model’s probability calculations or corresponding simulations;
- managing
*modelValues*data structures for multiple sets of model values and probabilities.

In fact, the calculations of the model are themselves constructed as nimbleFunctions, as are the algorithms provided in NIMBLE’s algorithm library^{7}.

Programming with nimbleFunctions involves a fundamental distinction between two stages of processing:

A

*setup*function within a nimbleFunction gives the steps that need to happen only once for each new situation (e.g., for each new model). Typically such steps include inspecting the model’s variables and their relationships, such as determining which parts of a model will need to be calculated for a MCMC sampler. Setup functions are executed in R and never compiled.One or more

*run*functions within a nimbleFunction give steps that need to happen multiple times using the results of the setup function, such as the iterations of a MCMC sampler. Formally, run code is written in the NIMBLE language, which you can think of as a small subset of R along with features for operating models and related data structures. The NIMBLE language is what the NIMBLE compiler can automatically turn into C++ as part of a compiled nimbleFunction.

What NIMBLE does with a nimbleFunction is similar to what it does with a BUGS model:

- NIMBLE creates a working R version of the nimbleFunction. This is most useful for debugging (Section 15.7).
- When you are ready, NIMBLE can generate C++ code, compile it, load it back into R and give you new objects that use the compiled C++ internally. Again, we refer to these steps all together as ‘compilation’. The behavior of compiled nimbleFunctions is usually very similar, but not identical, to their uncompiled counterparts.

If you are familiar with object-oriented programming, you can think of a nimbleFunction as a class definition. The setup function initializes a new object and run functions are class methods. Member data are determined automatically as the objects from a setup function needed in run functions. If no setup function is provided, the nimbleFunction corresponds to a simple (compilable) function rather than a class.

More about writing algorithms is in Chapter 15.

## 3.3 The NIMBLE algorithm library

In Version 0.7.1, the NIMBLE algorithm library includes:

- MCMC with samplers including conjugate (Gibbs), slice, adaptive random walk (with options for reflection or sampling on a log scale), adaptive block random walk, and elliptical slice, among others. You can modify sampler choices and configurations from R before compiling the MCMC. You can also write new samplers as nimbleFunctions.
- WAIC calculation for model comparison after an MCMC algorithm has been run.
- A set of particle filter (sequential Monte Carlo) methods including a basic bootstrap filter, auxiliary particle filter, and Liu-West filter.
- An ascent-based Monte Carlo Expectation Maximization (MCEM) algorithm.
A variety of basic functions that can be used as programming tools for larger algorithms. These include:

- A likelihood function for arbitrary parts of any model.
- Functions to simulate one or many sets of values for arbitrary parts of any model.
- Functions to calculate the summed log probability (density) for one or many sets of values for arbitrary parts of any model along with stochastic dependencies in the model structure.

More about the NIMBLE algorithm library is in Chapter 8.

### References

Lunn, David, David Spiegelhalter, Andrew Thomas, and Nicky Best. 2009. “The BUGS Project: Evolution, Critique and Future Directions.” *Statistics in Medicine* 28 (25): 3049–67. doi:10.1002/sim.3680.