I am a statistician and applied mathematician with broad interests in statistical methodology and computing in the physical sciences. My primary interest is modeling complicated dependence structure in real-life temporal/spatial/spatio-temporal processes, and I'm particularly interested in theoretical questions that are motivated by computationally scalable methods and approximations.

I am currently a PhD student in the Department of Statistics at Rutgers University working with Michael Stein. Since August 2016, I have worked at Argonne National Laboratory under the supervision of Mihai Anitescu.

Here is a list of some research interests that I have worked on with some level of specificity and purpose, although not all of those projects have led to publishable work.

• Statistical computing and algorithms
• Spatio-temporal processes, especially spectral domain representations of multidimensional and nonstationary processes
• Nonstationarity, nonlinearity, and non-Gaussianity in time-dependent processes
• Applications in the physical sciences
• More abstract stochastic processes, like combinatorial stochastic processes
• Matrix computations, especially hierarchical matrices and other methods for scalable dense linear algebra
• Applied functional and harmonic analysis
• Irregular/nonuniform Fourier-type methods
• Inverse problems and data assimilation

Publications:

• P.G. Beckman, C.J. Geoga, M.L. Stein, and M. Anitescu. Scalable Computations for Nonstationary Gaussian Processes (ArXiv soon). Submitted.
• C.J. Geoga, O. Marin, M. Schanen, and M.L. Stein. Fitting Matern smoothness parameters using automatic differentation (ArXiv v3). Submitted.
• C.J. Geoga, M. Anitescu, and M.L. Stein. Flexible nonstationary spatio-temporal modeling of high-frequency monitoring data (ArXiv v1). Environmetrics. DOI:https://doi.org/10.1002/env.2670
• C.J. Geoga, M. Anitescu, and M.L. Stein. Scalable Gaussian process computations using hierarchical matrices. Journal of Computational and Graphical Statistics. DOI:https://doi.org/10.1080/10618600.2019.1652616
• C.J. Geoga, C.L. Haley, A. Siegel, and M. Anitescu. Frequency-wavenumber spectral analysis of spatiotemporal flows. Journal of Fluid Mechanics. DOI:https://doi.org/10.1017/jfm.2018.366

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.

• KernelMatrices.jl, (INACTIVE) a software companion to "Scalable Gaussian process computations using hierarchical matrices" in the Julia programming language. It is reasonably efficient and easy to use for workstation-level problems, up to perhaps a few million points if you have time or a few hundred thousand if you'd like to just run something over your lunch break. It is not sufficiently tuned to be a good choice for clusters, unfortunately. If you have any interest and/or experience in bringing Julia software up to that level, though, please do reach out, as I (and I hope other people) still actively develop and use this package.
• SMultitaper.jl, a simple 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.
• 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. Perhaps more importantly, it provides a slightly tuned but very flexible trust region optimization method, which for whatever reason doesn't seem to be all that easy to find in canned software despite the fact that it clearly works better than line search methods for maximum likelihood problems.
• 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 and perform pretty competent optimization with the trust region method in GPMaxlik.jl.
• 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 threads. I can confirm more or less perfect scaling up to at least 8 threads on an 8-core machine, which in practice can be a serious performance improvement. Gradients and true Hessians are available using automatic differentiation, and are very fast. Sparse approximations to precision matrices induced by conditioning sets are also provided.
• 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...

Gratitude:

A short and incomplete list.

• Mihai Anitescu was the best boss I'll ever have. I took two of his classes as an undergraduate that I wasn't entirely ready for and he was patient and encouraging, and he took a huge chance on me when he hired me at ANL. He has been a huge influence on my academic interests and on how I approach problems in general. If he hadn't given me such a huge opportunity and been so supportive throughout, I probably would not have become a scientist at all. I really can't say enough about what he's done for me and how grateful I am.
• Rong Chen has been incredibly generous with his time and thoughts. I have done a lot of exploring in the Rutgers PhD program and Professor Chen has consistently been patient and supportive beyond what anybody could reasonably expect.
• Charlotte Haley taught me basically everything I know about spectral domain representations of stochastic processes, and was incredibly supportive and generous with her time when I started at ANL.
• Wenjia Jing 's introductory real analysis class was my first serious exposure to the subject, and the two quarters that I had with him really cemented my love for analysis.
• Paytsar Muradyan Was _incredibly_ helpful as I tried to work with the Doppler LIDAR data for the "Flexible nonstationary..." paper. Taking that data and the relevant physical properties of the process seriously would have been effectively impossible without her help. It's hard to overstate how helpful and informative my conversations with her were.
• Michael Stein 's introductory course (STAT 244) made me change my undergraduate plans and try to take statistics seriously. Despite me being pretty annoying, he's also been consistently patient, helpful, and supportive for over five years now. He has been incredibly influential on my interests and approach.
• Amie Wilkinson taught my favorite course that I took as an undergraduate---complex analysis---and has been incredibly generous with her time as I've asked her to write way too many recommendation letters for me.
• Lydia Zoells Is my partner and my best friend. She painted the portrait displayed above and copyedits all of my boring papers. I couldn't imagine life without her.
• The entire spatial statistics community has been incredibly warm and welcoming.

Contact:

I do not use any social media or internet networking websites. If you see any account with my name on it, please assume that it is not really me. Please contact me by email at one of these addresses:

• cgeoga $at anl $dot gov
• christopher.geoga $at $dot rutgers $dot edu