Posts filed under ‘Statistics’

Software for Flexible Bayesian Modeling – New release

I’ve released a new version of my Software for Flexible Bayesian Modeling and Markov Chain Sampling (FBM). This is the first public release since 2004, with the first release of the precursor software being in 1995. There was a version mostly completed in 2007 that never got released (due to my not getting around to checking that I’d fixed up everything). The new version has the changes from 2007 plus some more recent updates, including new features used for the tests in this paper.

FBM implements several general-purpose Markov chain sampling methods, such as Metropolis updates, Hamiltonian (Hybrid) Monte Carlo, and slice sampling. These methods can be applied to distributions defined by simple formulas, including posterior distributions for simple Bayesian models. Several more specialized modules have been written that implement posterior distributions for more complex models, including Bayesian neural networks, Gaussian process models, and mixture models (including Dirichlet process mixture models).

2020-02-17 at 4:06 pm Leave a comment

Automatic differentiation in pqR

I’ve released a version of my pqR implementation of R that has extensions for automatic differentiation. This is not a stable release, but it can be downloaded from — look for the test version at the bottom — and installed the same as other pqR versions (from source, so you’ll need C and Fortran compilers).

Note that this version very likely has various bugs — mostly showing up only if you use automatic differentiation, I hope.

You can read about the automatic differentation facilities here, or with help(Gradient) after installing the test version. Below are a few examples to show a bit of what you can do.

2019-07-06 at 5:39 pm 1 comment

Faster garbage collection in pqR

The latest version of pqR and the version before as well use a new garbage collector, and new memory layouts for R objects, which both reduce memory usage and considerably speed up garbage collection.


2018-11-29 at 7:45 pm Leave a comment

The new pqR parser, and R’s “else” problem

The latest version of pqR (mostly) solves R’s “else” problem, by modifying the new parser previously introduced in pqR.  I’ll explain the “else” problem and solution here, and also present other advantages of pqR’s parser over the R Core parser, including a big speed advantage in one context.


2018-11-27 at 8:33 pm 1 comment

New version of pqR, with major speed improvements

I’ve released pqR-2018-11-18, a new version of my variant implementation of R.  You can install it on Linux, Windows, or Mac as described at Installation must currently be from source, similarly to source installs of R Core versions of R.

This version has some major speed improvements, as well as some new features. I’ll details some of these improvements in future posts. Here, I’ll just mention a few things to show the flavour of the improvements in this release, and why you might be interested in pqR as an alternative to the R Core implementation.

Performance improvements

One landmark reached in this release is that it is no longer advisable to use the byte-code compiler in pqR. The speed of direct interpretation of R code has now been improved to the point where it is about as fast at executing simple scalar code as the byte-code interpreter. Eliminating the byte-code compiler simplifies the overall implementation, and avoids possible semantic differences between interpreted and byte-compiled code. It is also important for pqR because some pqR optimizations and some new pqR features are not implemented in byte-code. For example, only the interpreter does optimizations such as deferring vector operations so that they may automatically be merged with other operations or be done in parallel when multiple cores are available.

Some vector operations have been substantially sped up compared to the previous release of pqR-2017-06-09. The improvement compared to R-3.5.1 can be even greater. Here is an example of replacing a subset of vector elements, benchmarked on an Intel “Skylake” processor, with both pqR-2018-11-18 and R-3.5.1 compiled from source with gcc 8.2.0 at optimization level -O3:

Here’s R-3.5.1:

> a <- numeric(20000)
> system.time(for (i in 1:100000) a[2:19999] <- 3.1)
   user  system elapsed 
  4.211   0.148   4.360 

And here’s pqR-2018-11-18:

> a <- numeric(20000)
> system.time(for (i in 1:100000) a[2:19999] <- 3.1)
   user  system elapsed 
  0.256   0.000   0.257 

So the current R Core implementation is 17 times slower than pqR for this replacement operation.

The advantage of pqR isn’t always this large, but many vector operations are sped up by smaller but still significant factors. An example:

With R-3.5.1:

> a <- seq(0,1,length=2000); b <- seq(1,0,length=2000)
> system.time (for (i in 1:100000) {
+       d <- abs(a-b); r <- sum (d>0.4 & d<0.7) })
   user  system elapsed 
  1.215   0.015   1.231 

With pqR-2018-11-18:

> a <- seq(0,1,length=2000); b <- seq(1,0,length=2000)
> system.time (for (i in 1:100000) {
+       d <- abs(a-b); r <- sum (d>0.4 & d<0.7) })
   user  system elapsed 
  0.654   0.008   0.662 

So for this example, pqR is almost twice as fast.

For some operations, pqR’s implementation has lower asymptotic time complexity, and so can be enormously faster. An example is the following convenient coding pattern that R programmers are currently warned to avoid:

With R-3.5.1:

> n <- 200000; a <- numeric(0);
> system.time (for (i in 1:n) a <- c(a,(i+1)^2))
   user  system elapsed 
 30.387   0.223  30.612 

With pqR-2018-11-18:

> n <- 200000; a <- numeric(0);
> system.time (for (i in 1:n) a <- c(a,(i+1)^2))
   user  system elapsed 
  0.040   0.004   0.045 

In R-3.5.1, extending a vector one element at a time with “c” takes time growing as n2, as a new vector is allocated when each element is appended. With the latest version of pqR, the time grows only as n log n. In this example, that leads to pqR being 680 times faster, but the ratio could be made arbitrarily large by increasing n.

It’s still faster in pqR to preallocate a vector of length n, but only by about a factor of three, which would often be tolerable when writing one-off code if using “c” is more convenient.

New features

The latest version of pqR has some new features. As for earlier pqR versions, some new features are aimed at addressing design flaws in R that lead to unreliable code, and others are aimed at making R more convenient for programming and scripting.

One new convenience feature is that the paste and paste0 operations can now be written with new !! and ! operators. For example,

> city <- "Toronto"; province <- "Ontario"
> city ! "," !! province
[1] "Toronto, Ontario"

The !! operator pastes strings together with space separation; the ! operator pastes with no separation. Of course, ! retains its meaning of “not” when used as a unary operator; there is no ambiguity.

What next?

I’ll be writing some more blog posts regarding improvements in pqR-2018-11-18, and regarding some improvements in earlier pqR versions that I haven’t already blogged about. Of course, you can read about these now in the pqR NEWS file.

The main disadvantage of pqR is that it is not fully compatible with the current R Core version. It is a fork of R-2.15.0, with many, but not all, later changes incorporated. This affects what packages will work with pqR.

Addressing this compatibility issue is one thing that needs to be done going forward. I’ll discuss this and other plans — notably implementing automatic differentiation — in another future blog post.

I’m open to other people getting involved in this project. Of course, you can contribute now by trying out pqR and reporting any problems in the comments here or at the pqR issues page. Performance comparisons, especially on real-world applications, are also welcome.

Finally, for the paranoid, here are the shasum values for the compressed and uncompressed tar files that you can download from

89216dc76be23b3928c26561acc155b6e5ad32f3  pqR-2018-11-18.tar.gz
f0ee8a37198b7e078fa1aec7dd5cda762f1a7799  pqR-2018-11-18.tar

2018-11-25 at 5:45 pm 5 comments

New release of pqR — faster, and now compatible with R-2.15.1

I have released a new version of my “pretty quick” R interpreter, pqR-2016-10-05.

One major change with this version is that pqR, which was based on R-2.15.0, is now compatible with R-2.15.1.  This allows for an increased number of packages in the pqR repository.

This release also has some significant speed improvements, a new form of the “for” statement, for conveniently iterating across columns or down rows of a matrix, and a new, less error-prone way for C functions to “protect” objects from garbage collection. There are also a few bug fixes (including fixes for some bugs that are also in the current R core release).

You can read more in the NEWS file, and get it from

Currently, pqR is distributed in source form only, and so you need to be comfortable compiling it yourself. It has been tested on Linux/Unix systems (with Intel/AMD, ARM, PowerPC, and SPARC processors), on Mac OS X (including macOS Sierra), and on Microsoft Windows (XP, 7, 8, 10) systems.

I plan to soon put up posts with more details on some of the features of this and the previous pqR release, as well as a post describing some of my future plans for pqR.

2016-10-08 at 9:01 pm Leave a comment

Fixing R’s design flaws in a new version of pqR

I’ve released a new version of my pqR implementation of R. This version introduces extensions to the R language that fix some long-standing design flaws that were inherited from S.

These language extensions make it easier to write reliable programs, that work even in edge cases, such as data sets with one observation.

In particular, the extensions fix the problems that 1:n doesn’t work as intended when n is zero, and that M[1:n,] is a vector rather than a matrix when n is one, or when M has only one column. Since changing the “:” operator would cause too many problems with existing programs, pqR introduces a new “..” operator for generating increasing sequences.  Unwanted dimension dropping is also addressed in ways that have minimal effects on existing code.

The new release, pqR-2016-06-24, is available at pqR-project-org. The NEWS file for this release also documents some other language extensions, as well as fixes for various bugs (some of which are also in R-3.3.1).

2016-06-25 at 8:46 pm 13 comments

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