About

Frederi Viens is a full professor in the Department of Statistics at Rice University, pursuing a long-standing research agenda in probability theory, stochastic processes, mathematical statistics, and applied probability for insurance mathematics and quantitative finance. Over the past 15 years, he has developed a robust applied statistics research program utilizing computational Bayesian statistics, collaborating on significant projects across diverse fields such as climate science, agro-ecology, agricultural economics, development economics, nuclear physics, and human health management. Prior to his current position, Viens served as a full professor at Michigan State University from 2016 to 2022, where he was Department Chair, Director of Actuarial Science, and adjunct director of the Center for Statistical Training and Consulting. He also contributed to the creation of a new Data Science master's program at MSU. His academic career includes positions at Purdue University, where he directed the Computational Finance program, and roles at the National Science Foundation, the U.S. State Department, and faculty positions in Spain, France, Texas, and Chile. His distinctions include being a Fellow of the Institute of Mathematical Statistics, a Franklin Fellow of the U.S. State Department, and a Fulbright Research Scholar. Viens is actively involved in the academic community as the long-term moderator of the Seminar on Stochastic Processes, serving on editorial boards, and organizing international conferences. His research is supported by agencies such as the NSF, USDA, and the Office of Naval Research. He holds advanced degrees in mathematics from the University of California, Irvine, and the Université de Paris 7.

Research topics

• Physics
• Machine Learning
• Artificial Intelligence
• Computer Science
• Statistical physics
• Nuclear physics
• Theoretical physics
• Mathematics
• Particle physics
• Quantum mechanics
• Algorithm

Selected publications

• Asymptotics of Yule's nonsense correlation for Ornstein-Uhlenbeck paths: The correlated case

  ArXiv.org · 2025-04-24

  preprintOpen accessSenior author

  We study the continuous-time version of the empirical correlation coefficient between the paths of two possibly correlated Ornstein-Uhlenbeck processes, known as Yule's nonsense correlation for these paths. Using sharp tools from the analysis on Wiener chaos, we establish the asymptotic normality of the fluctuations of this correlation coefficient around its long-time limit, which is the mathematical correlation coefficient between the two processes. This asymptotic normality is quantified in Kolmogorov distance, which allows us to establish speeds of convergence in the Type-II error for two simple tests of independence of the paths, based on the empirical correlation, and based on its numerator. An application to independence of two observations of solutions to the stochastic heat equation is given, with excellent asymptotic power properties using merely a small number of the solutions' Fourier modes.

  PublisherOA PDFDOI

• Temporal Comparisons Involving Paleoclimate Data Assimilation: Challenges and Remedies

  Journal of Climate · 2024-12-12 · 2 citations

  article

  Abstract Paleoclimate reconstructions are increasingly central to climate assessments, placing recent and future variability in a broader historical context. Several estimation methods produce plumes of climate trajectories that practitioners often want to compare to other reconstruction ensembles or to deterministic trajectories produced by other means, such as global climate models. Of particular interest are “offline” data assimilation (DA) methods, which have recently been adapted to paleoclimatology. Offline DA lacks an explicit model connecting time instants, so its ensemble members are not true system trajectories. This obscures quantitative comparisons, particularly when considering the ensemble mean in isolation. We propose several resampling methods to introduce a priori constraints on temporal behavior, as well as a general notion, called plume distance, to carry out quantitative comparisons between collections of climate trajectories (“plumes”). The plume distance provides a norm in the same physical units as the variable of interest (e.g., °C for temperature) and lends itself to assessments of statistical significance. We apply these tools to four paleoclimate comparisons: 1) global mean surface temperature (GMST) in the online and offline versions of the Last Millennium Reanalysis (v2.1); 2) GMST from these two ensembles to simulations of the Paleoclimate Modelling Intercomparison Project past1000 ensemble; 3) Last Millennium Reanalysis, version 2.1 (LMRv2.1), to the PAGES 2k Consortium ensemble of GMST; and 4) the Northern Hemisphere mean surface temperature from LMRv2.1 to the Büntgen et al. ensemble. Results generally show more compatibility between these ensembles than is visually apparent. The proposed methodology is implemented in an open-source Python package, and we discuss the possible applications of the plume distance framework beyond paleoclimatology. Significance Statement Paleoclimate data assimilation is an emerging technique to reconstruct past climate variations. The currently dominant approximation, offline data assimilation, lacks the ability to connect information across time. This work proposes open-source solutions to this problem and applies them to three paleoclimate questions, before discussing broader implications.

  PublisherDOI

• Diversified crop rotations mitigate agricultural losses from dry weather.

  2024-04-19 · 1 citations

  article

  As changing climates create drought conditions with increasing frequency and severity, there is an urgent need for farmers to adopt agricultural systems that lower the risk of losses during drought. Diverse crop rotations have long been associated with a wide array of economic and environmental benefits, yet cropping systems in the US Midwest and across the world have been simplifying for over a century. Long-term experiments have shown potential for diverse rotations to avoid yield losses under dry conditions, and could be an impactful target in a region overwhelmingly dominated by corn-soy rotation. Here we use Bayesian modeling to show spatial patterns of yield benefits that result from increasing rotational diversity in a range of weather conditions. Data from over 2.2 million field-years reveal that diverse rotations decrease the risk of corn yield losses in dry years in areas that experience these conditions more frequently, while simultaneously increasing yields under favorable conditions across the region. The potential for yield risk mitigation described in the current analysis underscores the critical need for crop rotation adoption as changing climates threaten yield stability in the US and across the globe. We highlight areas where diverse rotations are most likely to improve yields and mitigate risk, amidst spatial heterogeneity in the magnitude of these benefits.

  PublisherDOI

• A Bayesian mixture model approach to quantifying the empirical nuclear saturation point

  arXiv (Cornell University) · 2024-05-04

  preprintOpen accessSenior author

  The equation of state (EOS) in the limit of infinite symmetric nuclear matter exhibits an equilibrium density, $n_0 \approx 0.16 \, \mathrm{fm}^{-3}$, at which the pressure vanishes and the energy per particle attains its minimum, $E_0 \approx -16 \, \mathrm{MeV}$. Although not directly measurable, the saturation point $(n_0,E_0)$ can be extrapolated by density functional theory (DFT), providing tight constraints for microscopic interactions derived from chiral effective field theory (EFT). However, when considering several DFT predictions for $(n_0,E_0)$ from Skyrme and Relativistic Mean Field models together, a discrepancy between these model classes emerges at high confidence levels that each model prediction's uncertainty cannot explain. How can we leverage these DFT constraints to rigorously benchmark saturation properties of chiral interactions? To address this question, we present a Bayesian mixture model that combines multiple DFT predictions for $(n_0,E_0)$ using an efficient conjugate prior approach. The inferred posterior for the saturation point's mean and covariance matrix follows a Normal-inverse-Wishart class, resulting in posterior predictives in the form of correlated, bivariate $t$-distributions. The DFT uncertainty reports are then used to mix these posteriors using an ordinary Monte Carlo approach. At the 95\% credibility level, we estimate $n_0 \approx 0.157 \pm 0.010 \, \mathrm{fm}^{-3}$ and $E_0 \approx -15.97 \pm 0.40 \, \mathrm{MeV}$ for the marginal (univariate) $t$-distributions. Combined with chiral EFT calculations of the pure neutron matter EOS, we obtain bivariate normal distributions for the symmetry energy and its slope parameter at $n_0$: $S_v \approx 32.0 \pm 1.1 \, \mathrm{MeV}$ and $L\approx 52.6\pm 8.1 \, \mathrm{MeV}$ (95\%), respectively. Our Bayesian framework is publicly available, so practitioners can readily use and extend our results.

  PublisherOA PDFDOI

• Deriving general principles of agroecosystem multifunctionality with the Diverse Rotations Improve Valuable Ecosystem Services (DRIVES) network

  Agronomy Journal · 2024-10-17 · 3 citations

  articleOpen accessSenior author

  Abstract Long‐term agricultural field experiments (LTFEs) have been conducted for nearly 150 years. Yet lack of coordination means that synthesis across such experiments remains rare, constituting a missed opportunity for deriving general principles of agroecosystem structure and function. Here, we introduce the Diverse Rotations Improve Valuable Ecosystem Services (DRIVES) project, which uses legacy data from North American LTFEs to address research questions about the multifunctionality of agriculture. The DRIVES Project is a network of researchers who have compiled a database of primary (i.e., observations) and secondary (i.e., transformed observations or modeling results) data from participating sites. It comprises 21 LTFEs that evaluate how crop rotational diversity impacts cropping system performance. The Network consists of United States Department of Agriculture, university, and International Maize and Wheat Improvement Center scientists (20 people) who manage and collect primary data from LTFEs and a core team (nine people) who organize the network, curate network data, and synthesize cross‐network findings. As of 2024, the DRIVES Project database contains 495 site‐years of crop yields, daily weather, soil analysis, and management information. The DRIVES database is findable, accessible, interoperable, and reusable, which allows integration with other public datasets. Initial research has focused on how rotational diversity impacts resilience in the face of adverse weather, nutritional quality, and economic feasibility. Our collaborative approach in handling LTFE data has established a model for data organization that facilitates broader synthesis studies. We openly invite other sites to join the DRIVES network and share their data.

  PublisherDOI

• Bayesian mixture model approach to quantifying the empirical nuclear saturation point

  Physical review. C · 2024-10-25 · 12 citations

  articleOpen accessSenior author

  The equation of state (EOS) in the limit of infinite symmetric nuclear matter exhibits an equilibrium density, ${n}_{0}\ensuremath{\approx}0.16\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$, at which the pressure vanishes and the energy per particle attains its minimum, ${E}_{0}\ensuremath{\approx}\ensuremath{-}16\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$. Although not directly measurable, the nuclear saturation point $({n}_{0},{E}_{0})$ can be extrapolated by density-functional theory (DFT), providing tight constraints for microscopic interactions derived from chiral effective-field theory (EFT). However, when considering several DFT predictions for $({n}_{0},{E}_{0})$ from Skyrme and relativistic mean field (RMF) models together, a discrepancy between these model classes emerges at high confidence levels that each model prediction's uncertainty cannot explain. How can we leverage these DFT constraints to rigorously benchmark nuclear saturation properties of chiral interactions? To address this question, we present a Bayesian mixture model that combines multiple DFT predictions for $({n}_{0},{E}_{0})$ using an efficient conjugate prior approach. The inferred posterior distribution for the saturation point's mean and covariance matrix follows a normal-inverse-Wishart (NIW) class, resulting in posterior predictives in the form of correlated, bivariate $t$ distributions. The DFT uncertainty reports are then used to mix these posteriors using an ordinary Monte Carlo approach. At the 95% credibility level, we estimate ${n}_{0}\ensuremath{\approx}0.157\ifmmode\pm\else\textpm\fi{}0.010\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$ and ${E}_{0}\ensuremath{\approx}\ensuremath{-}15.97\ifmmode\pm\else\textpm\fi{}0.40\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ for the marginal (univariate) $t$ distributions. Combined with chiral EFT calculations of the pure neutron matter equation of state, we obtain bivariate normal distributions for the nuclear symmetry energy and its slope parameter evaluated at ${n}_{0}$: ${S}_{v}\ensuremath{\approx}32.0\ifmmode\pm\else\textpm\fi{}1.1\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ and $L\ensuremath{\approx}52.6\ifmmode\pm\else\textpm\fi{}8.1\phantom{\rule{4pt}{0ex}}\mathrm{MeV}$ (95%), respectively. Our Bayesian framework is publicly available, so practitioners can readily use and extend our results.

  PublisherOA PDFDOI

• Rotational complexity increases cropping system output under poorer growing conditions

  One Earth · 2024-08-06 · 27 citations

  articleOpen access

  Growing multiple crops in rotation can increase the sustainability of agricultural systems and reduce risks from increasingly adverse weather. However, widespread adoption of diverse rotations is limited by economic uncertainty, lack of incentives, and limited information about long-term outcomes. Here, we combined 36,000 yield observations from 20 North American long-term cropping experiments (434 site-years) to assess how greater crop diversity impacts productivity of complete rotations and their component crops under varying growing conditions. Maize and soybean output increased as the number of species and rotation length increased, while results for complete rotations varied by site depending on which crops were present. Diverse rotations reduced rotation-level output at eight sites due to the addition of lower-output crops such as small grains, illustrating trade-offs. Diverse rotations positively impacted rotation-level output under poor growing conditions, which illustrates how diverse cropping systems can reduce the risk of crop loss in a changing climate.

  PublisherOA PDFDOI

• Temporal comparisons involving paleoclimate data assimilation: Challenges and remedies

  2024-02-14 · 1 citations

  preprintOpen access

  Paleoclimate reconstructions are increasingly central to climate assessments, placing recent and future variability in abroader historical context. Several estimation methods produce ensembles of climate trajectories that practitioners often want to compare to other ensembles, or to deterministic trajectories produced by other methods such as global climate models. Of particular interest are so-called “offline” data assimilation (DA) methods, which have recently been adapted to paleoclimatology, and lack an explicit estimate of reconstruction error covariability in time. As a result, offline DA ensemble members are not true system trajectories. We show that this atemporality obscures quantitative comparisons, particular when considering the ensemble mean in isolation. We propose several parametric resampling methods to introduce a priori constraints on temporal covariance among ensemble members. We also propose a general framework to carry out quantitative comparisons between ensembles using a “plume distance” framework, which provides a norm in the same physical units as the variable of interest. We apply these tools to three paleoclimate questions: (1) Comparing global mean surface temperature in the online and offline versions of the Last Millennium Reanalysis; (2) Comparing global mean surface temperature from these two ensembles to simulations of the Paleoclimate Model Intercomparison Project past1000 ensemble; and (3) Comparing northern hemisphere mean surface temperature from the offline DA ensemble to the Büntgen et al. (2021) ensemble. The proposed methodology is implemented in an open-source Python package, inviting re-use and extensions. We also discuss possible applications of the plume distance framework to a broad array of problems where ensemble comparisons arise.

  PublisherOA PDFDOI

• Pricing basket options with the first three moments of the basket: log-normal models and beyond

  arXiv (Cornell University) · 2023-02-16 · 1 citations

  preprintOpen accessSenior author

  Options on baskets (linear combinations) of assets are notoriously challenging to price using even the simplest log-normal continuous-time stochastic models for the individual assets. The paper [5] gives a closed form approximation formula for pricing basket options with potentially negative portfolio weights under log-normal models by moment matching. This approximation formula is conceptually simple, methodologically sound, and turns out to be highly accurate. However it involves solving a system of nonlinear equations which usually produces multiple solutions and which is sensitive to the selection of initial values in the numerical procedures, making the method computationally challenging. In the current paper, we take the moment-matching methodology in [5] a step further by obtaining a closed form solution for this non-linear system of equations, by identifying a unary cubic equation based solely on the basket's skewness, which parametrizes all model parameters, and we use it to express the approximation formula as an explicit function of the mean, variance, and skewness of the basket. Numerical comparisons with the baskets considered in [5] show a very high level of agreement, and thus of accuracy relative to the true basket option price.

  PublisherOA PDFDOI

• The isometry of symmetric-Stratonovich integrals w.r.t. Fractional Brownian motion $H< \frac{1}{2}$

  arXiv (Cornell University) · 2023-09-18

  preprintOpen accessSenior author

  In this work, we present a detailed analysis on the exact expression of the $L^2$-norm of the symmetric-Stratonovich stochastic integral driven by a multi-dimensional fractional Brownian motion $B$ with parameter $\frac{1}{4} < H < \frac{1}{2}$. Our main result is a complete description of a Hilbert space of integrand processes which realizes the $L^2$-isometry where none regularity condition in the sense of Malliavin calculus is imposed. The main idea is to exploit the regularity of the conditional expectation of the tensor product of the increments $B_{t-δ,t+δ}\otimes B_{s-ε,s+ε}$ onto the Gaussian space generated by $(B_s,B_t)$ as $(δ,ε)\downarrow 0$. The Hilbert space is characterized in terms of a random Radon $σ$-finite measure on $[0,T]^2$ off diagonal which can be characterized as a product of a non-Markovian version of the stochastic Nelson derivatives. As a by-product, we present the exact explicit expression of the $L^2$-norm of the pathwise rough integral in the sense of Gubinelli.

  PublisherOA PDFDOI

Recent grants

• Topics in stochastic analysis and Malliavin calculus

  NSF · $150k · 2014–2017

• Density and tail estimates via Malliavin calculus, and applications

  NSF · $231k · 2009–2013

• Applications of stochastic analysis to statistical inference for stationary and non-stationary Gaussian processes

  NSF · $250k · 2023–2026

• Topics in stochastic analysis and Malliavin calculus

  NSF · $56k · 2016–2019

• AMC-SS: Stochastic analysis and random medium in continuous space and time

  NSF · $375k · 2006–2010

Frequent coauthors

• Ciprian A. Tudor

  33 shared

• Martin P. Tingley

  31 shared

• Samy Tindel

  21 shared

• Alexandra Chronopoulou

  University of Illinois Urbana-Champaign

  19 shared

• Julien Emile‐Geay

  University of Southern California

  17 shared

• Daniel E. Amrhein

  NSF National Center for Atmospheric Research

  17 shared

• Gregory J. Hakim

  University of Washington

  17 shared

• Khalifa Es-Sebaiy

  Kuwait University

  15 shared

Awards & honors

• Fellow of the Institute of Mathematical Statistics (2012)
• Franklin Fellow of the U.S. State Department (2010)
• Purdue College of Science Research Award (2013)
• Purdue College of Science Team Award (2012)
• IMS Quadfect 23 (2021/2022)