Software:

I'd like to briefly point out an issue that I have experienced a few times. I think it's important for scientific practitioners to clean up and package code to the point where other people who are interested in the work have a fighting chance of actually running the code themselves. I do my best to meet that expectation. On the other hand, however, I am not a software engineer, and so my code is not always perfect in terms of steering users away from footguns or testing all edge cases. So if you try any of this code, which I sincerely hope you do, and experience something working way differently (often much worse) than a paper or figure or example file suggests, please reach out to me before writing off the code or method completely. There is a non-negligible chance that I just haven't enforced some aspect of proper usage that may be obvious to a practitioner in that field---such as sensibly enumerating the observations when assembling a hierarchical matrix approximation---but that may not occur to somebody who is just trying out the code or who isn't particularly familiar with the field. While I obviously do my best to try and enforce proper usage through the code design itself, it is challenging and I make mistakes. So please do reach out if you experience surprising things when trying any of these software packages. There might be an easy remedy, and you might save future users similar frustrations.

As a second small rant, if you use any of these packages in your own research in a way that substantively helped your project, *please* do cite them appropriately. Almost all of these packages are companions to a paper, or the README of the package will have citation instructions. As an example, please cite the "Fitting Matern..." paper if you use BesselK.jl to fit a full three-parameter Matern model. It may seem like sort of a trivial software dependency, but in this hypothetical you're really using that package to do something that for decades hasn't really been reliably possible. So please do acknowledge the work that did make your results possible.

I write all software using the GPLv2 license unless otherwise specified.

• SMultitaper.jl, a software package that provides a simple but efficient implementation of an adaptively weighted multitaper spectral density estimator. There is a lot of workspace and result caching, so even without careful pre-allocations repeated calls will be fast. You'll see that this package doesn't have many commits in the last few years, but that's because it's done and it has basically no dependencies that need to be bumped. The code still works well and I do still use it regularly. If you want to compute hundreds of adaptively weighted multitaper estimates for data of the same (padded) length, this package is probably a plenty good choice.
• GPMaxlik.jl, a simple software package that provides a reasonably tuned function for evaluating the exact log-likelihood for Gaussian processes and stochastic estimators for its first and second derivatives. It also now provides exact methods for the log-likelihood where I have added custom methods for the gradient and Hessian, so that you can call `ForwardDiff.hessian` on it and it will actually compute the Hessian using the analytical formula, thus using LAPACK and only operate on arrays of doubles, but it will still use ForwardDiff for the derivatives of the kernel function.
• HalfSpectral.jl, a sort of software companion to "Flexible nonstationary..." above, this small package provides a reasonably tuned method for conveniently working with half-spectral covariance functions for regular data completely in the time domain. The example files demonstrate how straightforward it is to build quite complicated models with very little code and then use automatic differentiation for the derivatives. Besides the recent re-write for complete AD compatibility, the example files also provide a demonstration of how to efficiently hook it in to `Vecchia.jl` so that you can fit your fancy half-spectral covariance function scalably and efficiently.
• Vecchia.jl, (MIT license) A very simple implementation of Vecchia's likelihood approximation applied to mean-zero Gaussian processes. The code is specifically optimized to have low allocations and perform well with multiple threads (in particular, by using aggressive pre-allocation to squeeze out all allocations from the section that spawns tasks to compute the small likelihood terms). Gradients and true Hessians are available using automatic differentiation (ForwardDiff and ReverseDiff), and are very fast. The package also offers the "reverse" Cholesky factor (a la Katzfuss and Guinness 2021), and also gives a convenient software implementation of the EM-based method for estimating parameters when you have measurement noise that was described in "A Scalable Method to Exploit Screening...". See the README for a few more tricks that it offers.
• BesselK.jl, (MIT license) An ostensibly simple package that implements the modified second-kind Bessel function $\mathcal{K}_\nu(x)$ natively in Julia for the purpose of using automatic differentiation to compute derivatives with respect to $\nu$. Which sounds very simple, but really isn't due to a variety of subtle but legitimately problematic issues. See the paper "Fitting Matern..." for details. The real point is to fit three-parameter Matern covariance functions. The example file gives a simple Matern covariance function that you can just drop in to your code (and your AD stack, assuming you use ForwardDiff.jl) and then just forget about. But please do cite the paper if you do that...