List of mathematicians in probability and statistics

Craig L. Zirbel is a mathematician whose research connects probability theory with applications including RNA geometry and stochastic fluid motion. Bowling Green State University's faculty page identifies him as professor emeritus in mathematics and statistics and lists random measures, mass transport, and RNA structure and sequence variability among his interests.^[ref]

With Jesse Stombaugh, Eric Westhof and Neocles B. Leontis, he coauthored the 2009 study Frequency and isostericity of RNA base pairs by Jesse Stombaugh and others. It introduces the RNA IsoDiscrepancy Index and uses structural comparisons to investigate which base-pair substitutions preserve local geometry. This connects geometric annotation with comparisons of sequence variation, rather than treating nucleotide identities alone as a complete structural description.^[ref]

One mathematical task in that study is choosing an observed representative from several instances of a base-pair type. The authors compare instances and select the row with the smallest sum of discrepancies. An original miniature example uses the symmetric comparison-cost matrixIts row sums are 5, 4 and 7, so the second instance is the representative minimizing total comparison cost. These are chosen teaching values, not reported measurements of an RNA structure. The rule selects an observed instance; it does not require constructing an average set of atomic coordinates.^[ref]

Such a geometric representative is not necessarily the lowest-free energy structure, nor does a small discrepancy prove identical biological function. The example shows how an explicit comparison rule turns structural data into a reproducible choice, while leaving the physical interpretation to the measurement and molecular context.

Elena Yudovina is a mathematician whose work includes the theory of stochastic networks. With Frank Kelly, she wrote Stochastic Networks by Frank Kelly and Elena Yudovina, connecting queueing theory, loss networks, congestion control and distributed optimization. The author's book page verifies the joint authorship and 2014 publication.^[ref]

A central question is how local service or routing rules affect an entire network. The book's M/M/1 queue illustrates the danger of operating near capacity: with arrival rate $\lambda$, service rate $\mu$ and $\rho =\lambda /\mu <1$, mean queue population is $\rho /(1-\rho )$. Modest changes in load can therefore cause large changes in delay.^[ref]

Frank Kelly works on probability theory, stochastic networks and the mathematical organization of shared resources. His research connects queueing theory with optimization: local decisions about service, admission or price can determine a network's aggregate performance. His institutional research record describes these interests.^[ref]

With Elena Yudovina, Kelly wrote Stochastic Networks by Frank Kelly and Elena Yudovina. Its treatment of loss networks shows how detailed balance can produce an explicit equilibrium occupancy law, while congestion control uses resource prices to coordinate competing demands. These are complementary uses of mathematics: predicting congestion and designing rules that improve it.^[ref]

Wendelin Werner studies random geometric objects arising in probability theory and statistical physics, especially planar paths and their behavior under conformal maps. His work connects Brownian motion and Schramm–Loewner evolution with the geometry of random curves. His personal page identifies him at the University of Cambridge.^[ref]

With Gregory F. Lawler, Werner constructed the Brownian loop soup from a measure on unrooted planar Brownian loops. Sampling loops by a Poisson point process turns an invariant measure into a random collection of paths. The construction provides a way to add Brownian loops to a simple curve and study conformally invariant random geometry.^[ref]

Gregory F. Lawler studies random walks, Brownian motion and Schramm–Loewner evolution, with connections to statistical physics and complex analysis. His University of Chicago research profile emphasizes paths such as loop-erased random walks and their relation to uniform spanning trees.^[ref]

Lawler and Wendelin Werner developed the Brownian loop soup, using a conformally invariant measure on planar Brownian loops to build a Poisson point process of loops.^[ref] His Notes on the Bessel Process by Gregory F. Lawler provide another route from paths to geometry: a Bessel process describes radial diffusion, with its dimension parameter controlling whether the origin is reached. The boundary behavior matters when extending the process beyond its first zero.^[ref]

Fabrice Baudoin studies stochastic calculus and differential geometry, using diffusion processes and heat kernels to obtain functional inequalities. His Aarhus University research profile describes this exchange: geometric information can bound a diffusion, while probabilistic methods can reveal properties of the underlying space.^[ref]

His lecture Itō's representation theorem by Fabrice Baudoin illustrates the role of a precise information structure. For the completed natural filtration of Brownian motion, a square-integrable terminal random variable can be written as its expected value plus a stochastic integral. This yields a continuous version of each square-integrable martingale in that filtration. His exposition develops the Brownian martingale representation theorem through its filtration and square-integrability assumptions.^[ref]

Terry Therneau is a statistician working on survival analysis and statistical software. His Mayo Clinic profile identifies continuous-time multi-state models for time-to-event data as a focus, connecting statistical methods with the analysis of transitions between observed states.^[ref]

His A package for survival analysis in R by Terry Therneau documents tools for Cox proportional-hazards models and the handling of censoring. A censored observation still conveys information: a subject observed without an event through time $t$ contributes a survival probability through $t$, rather than being discarded. The software's treatment of risk sets and tied event times makes the statistical model's assumptions part of the computation.^[ref]

Germán Rodríguez works on statistical methods for population research. His Princeton teaching and research site connects generalized linear models, survival analysis and demographic questions about event timing. The site's biographical note identifies his training in biostatistics and his work in population research.^[ref]

His Survival Models by Germán Rodríguez explains how survival functions and hazard functions encode the same event-time distribution in different ways. With right censoring, an event observed at $t$ contributes density $f(t)$, whereas an observation ending without an event contributes $S(t)$. Writing the contribution as $S(t)h(t{)}^{\delta }$, with event indicator $\delta \in \{0,1\}$, makes that distinction explicit. These likelihood conventions let incomplete follow-up inform estimation without treating a censored time as an observed failure.^[ref]

Peter Bartlett studies the foundations of machine learning, statistical learning theory and reinforcement learning. His Berkeley research description emphasizes the joint demands of computational efficiency and statistical performance, including prediction with complex outputs and sequential decisions.^[ref]

His Introduction to Time Series Analysis, Lecture 20 by Peter Bartlett gives a concrete lesson about estimation. The raw periodogram can have an approximately correct expected value while its variance remains substantial as the sample grows. For Gaussian white noise, an interior-frequency periodogram ordinate is distributed as a scaled chi-squared distribution with two degrees of freedom. Spectral smoothing is therefore doing statistical work, rather than merely making a graph look smoother.^[ref]

Bruce W. Turnbull works on survival analysis and the statistical monitoring of clinical trials. His Cornell profile connects research on statistical methods with the practical problem of deciding what accumulating trial data justify.^[ref]

His 1974 paper studied nonparametric estimation when event times are subject to both left censoring and right censoring. A time known only to precede a threshold and one known only to exceed a threshold convey different information about the same survival function. Retaining those inequalities makes incomplete observations useful without substituting an invented event time.^[ref]

Ron Reeder coauthored Estimation of the Mean of Functional Time Series and a Two-Sample Problem by Lajos Horváth and others with Lajos Horváth and Piotr Kokoszka. Their problem treats successive daily curves as observations of a functional time series. The paper develops a normal approximation for their mean and a comparison of two mean curves that allows dependence across days.^[ref]

Piotr Kokoszka studies functional data analysis, time series and spatial statistical methods. His Colorado State University homepage describes inference for observations that can themselves be curves.^[ref]

With Lajos Horváth and Ron Reeder, he developed estimation and statistical hypothesis testing for mean curves under temporal dependence. Averaging many curves requires a covariance accounting for correlation between successive observations; treating the curves as independent can misstate uncertainty.^[ref]

Lajos Horváth works on mathematical statistics, time series and econometrics. His University of Utah profile identifies these research interests.^[ref]

His joint paper with Piotr Kokoszka and Ron Reeder studies comparisons of mean curves in a functional time series. Its Hilbert space formulation yields Gaussian limits and a test based on the distance between two estimated mean functions, retaining dependence within each sample.^[ref]

Nathaniel E. Helwig develops statistical methods at the intersection of psychology and computational statistics. His University of Minnesota research biography emphasizes multivariate and nonparametric statistics for complex observations.^[ref]

His Generalized Linear Models in R by Nathaniel E. Helwig explains how a link function connects a response's conditional expected value with a linear predictor. For logistic regression, the predictor represents log odds; for Poisson regression, a logarithmic link ensures a positive fitted mean. This separates the model for the mean from the response's probability distribution, while making deviance and dispersion part of model assessment.^[ref]

Lie Wang coauthored the Square-root Lasso paper with Alexandre Belloni and Victor Chernozhukov. Their estimator combines a root-mean-square residual loss with an ${\ell }^1$ penalty. Its tuning rule avoids requiring advance knowledge of the noise standard deviation, making sparse linear regression feasible when the number of candidate predictors exceeds the number of observations.^[ref]

Victor Chernozhukov works on econometrics and statistical inference with machine learning. With Alexandre Belloni and Lie Wang, he developed the Square-root Lasso, whose penalty calibration does not require knowing the noise scale.^[ref]

He also coauthored work on double machine learning. Predicting an outcome accurately does not by itself estimate a causal effect accurately: errors in fitted nuisance functions can bias the target parameter. An orthogonal estimating equation reduces first-order sensitivity to those errors, while cross-fitting separates training observations from score evaluation. Valid confidence intervals still require the paper's identification and convergence assumptions.^[ref]

Alexandre Belloni works across optimization, econometrics and high-dimensional statistics. His Chicago Booth profile describes research connecting statistical inference with decisions under limited information.^[ref]

With Victor Chernozhukov and Lie Wang, he formulated the Square-root Lasso as a convex conic optimization problem. This connects a statistically pivotal tuning rule with algorithms for convex optimization, giving a computable sparse regression estimator without a preliminary estimate of noise scale.^[ref]

Sara van de Geer develops the mathematical theory of high-dimensional statistics. Her Statistical Theory for High-Dimensional Models by Sara van de Geer studies prediction bounds for the Lasso and Square-root Lasso, and inference after correcting shrinkage bias.^[ref]

The distinction is useful: an estimator that predicts well may still bias an individual coefficient toward zero. A de-sparsified estimator adds a correction whose leading error can have an approximately normal distribution. Bounds on the remaining error, together with sparsity and design assumptions, then justify confidence intervals. The same notes connect generic chaining and concentration inequalities with control of random-process suprema.^[ref]

Steffen Rohde works where complex analysis meets probability theory. His University of Washington profile also identifies interests in numerical analysis.^[ref]

With Oded Schramm, he established basic geometric properties of Schramm–Loewner evolution, in which a Brownian motion drives a conformal growth equation. Their paper proves a change in path behavior with the parameter: simple curves for $0\le \kappa \le 4$, self-intersections for $4<\kappa <8$, and space-filling paths for $\kappa >8$. These regimes connect an analytic differential equation with the geometry of random interfaces.^[ref]

P. H. Peskun authored the 1973 paper underlying Peskun ordering, a comparison of the efficiency of Markov chain Monte Carlo algorithms with the same stationary target.^[ref]

For finite reversible Markov chains, increasing every off-diagonal transition probability while preserving the stationary law cannot increase the asymptotic variance of time averages. The comparison formalizes why spending less time repeating the current state can help statistical estimation, provided the ordering's hypotheses hold. It compares the variance of estimators, not merely their one-step acceptance rates.^[ref]

Gareth Roberts studies Markov chain Monte Carlo and the mathematical efficiency of Bayesian computation. With Giacomo Zanella, he developed importance tempering for high-dimensional sampling.^[ref]

Their Tempered Gibbs sampler changes how coordinates are selected. Its invariant law differs from the intended target, so importance sampling weights correct the averages. This trades easier movement through the state space against the variability of the correcting weights, with explicit theoretical comparisons to ordinary sampling methods.^[ref]

Giacomo Zanella develops methods in computational statistics, applied probability theory and machine learning, especially Bayesian computation. His research statement identifies Markov chain Monte Carlo, random measures and variable selection among these interests.^[ref]

With Gareth Roberts, he proposed the Tempered Gibbs sampler. A modified coordinate-selection rule can explore difficult high-dimensional targets more effectively; importance sampling weights then recover averages under the desired probability distribution. Their analysis includes applications to Bayesian variable selection.^[ref]

Radford M. Neal works on Bayesian inference, machine learning and computational methods for complex probability distributions. His research page lists neural networks, Gaussian processes and Markov chain Monte Carlo.^[ref]

His MCMC Using Hamiltonian Dynamics by Radford M. Neal develops Hamiltonian Monte Carlo: introduce auxiliary momenta, simulate approximately energy-preserving motion and correct discretization error with a Metropolis–Hastings algorithm. Longer, directed proposals can explore a target more effectively than a diffusive random walk. The combination of volume preservation, reversibility and an acceptance correction explains why an approximate numerical trajectory can still produce the intended invariant distribution.^[ref]

Thomas S. Ferguson works on statistics, probability theory and game theory. His UCLA page documents research on statistical decisions, stopping problems and games.^[ref]

His 1973 paper introduced a Bayesian framework built on the Dirichlet process, a probability distribution over probability measures. If the prior parameter measure is $\alpha$, observing $x_1,\dots ,x_n$ changes it to $\alpha +{\sum }_i{\delta }_{x_i}$. This conjugate update extends the familiar idea of adding category counts to inference about an entire unknown distribution, providing a foundation for Bayesian nonparametric statistics.^[ref]

Jason Miller (mathematician) studies random planar geometry, including Schramm–Loewner evolution, the Gaussian free field, Liouville quantum gravity and random planar maps. His Cambridge research profile verifies these interests.^[ref]

His Random Planar Geometry by Jason Miller (2020) develops discrete-to-continuum connections through trees, maps and random curves. The trivial bijection between planar maps and quadrangulations is a concrete example: vertices of one type encode original map vertices and the other type encodes faces. Recovering the map from this bipartition explains why the correspondence is reversible.^[ref]

David Bruce Wilson developed an exact sampling algorithm for uniform spanning trees. Wilson's algorithm grows a tree by adding loop-erased random walks, each stopped on first reaching the tree already constructed.^[ref]

Erasing loops ensures that an added path creates no cycle. The more surprising assertion is distributional: the resulting tree is uniform among spanning trees, despite the sequential construction and the choice of starting vertices. The algorithm makes a global random combinatorial object accessible through local walk operations.^[ref]

David Aldous studies probability theory and random combinatorial structures. His random-walk construction of a uniform spanning tree keeps the first-entrance edge for each newly visited vertex of a finite connected graph.^[ref]

Those edges necessarily form a tree, but their uniform distribution requires a separate argument. The construction permits properties of random trees—degrees, leaves and diameter—to be studied through random walks. Its running time is tied to the walk's cover time, giving a direct link between a stochastic exploration process and a combinatorial sampling algorithm.^[ref]

Robin Pemantle studies probability theory and random combinatorial structures. With Robert Burton, he developed methods for computing local probabilities in uniform spanning trees using electrical transfer impedances.^[ref]

The probability that several specified edges occur is a determinant of a small transfer matrix. This avoids enumerating all trees and relates joint edge events to Green's functions and network currents. Their work also applies these methods to domino tilings and entropy.^[ref]

Robert Burton coauthored the transfer-impedance analysis of uniform spanning trees with Robin Pemantle. Their original paper verifies this byline.^[ref]

The method computes probabilities for small collections of edges from determinants, even when the graph is large. The relevant matrix entries depend on global electrical information, so a small determinant does not mean the problem is entirely local. This distinction is essential in extending the calculations to infinite periodic graphs.^[ref]

Russell Lyons studies probability theory on graphs. With Itai Benjamini, Yuval Peres and Oded Schramm, he developed the theory of uniform spanning forests on infinite graphs.^[ref]

Finite spanning-tree laws can approach different limits depending on whether the boundary is left free or wired together. Their work connects these limits with random walks, potential theory and harmonic functions. One result characterizes the number of wired-forest components through intersections of independent walks, showing that global connectivity is encoded in stochastic paths.^[ref]

Itai Benjamini studies random geometric and combinatorial structures. His joint work with Russell Lyons, Yuval Peres and Oded Schramm investigates uniform spanning forests as limits of finite uniform spanning trees.^[ref]

On an infinite graph, a limiting forest need not be a single tree. Free and wired boundary conditions can lead to different laws. The paper relates this distinction and the number of connected components to random walks and harmonic functions, making infinite-volume geometry accessible through probabilistic tests.^[ref]

J. Gil-Pelaez authored the 1951 Note on the inversion theorem by J. Gil-Pelaez, giving a way to recover a distribution function from its characteristic function. The primary journal byline supplies the verified initials.^[ref]

The inversion integrates an oscillatory expression involving the characteristic function. At a discontinuity, the formula naturally returns the midpoint of the two one-sided distribution values. Keeping this convention explicit matters for discrete laws as well as continuous ones: an inversion formula is not automatically a pointwise identity at every jump.^[ref]

Sutton Monro coauthored the 1951 stochastic approximation paper with Herbert Robbins. The original title page verifies both full names and their joint contribution.^[ref]

The problem is to find where an unknown mean response $M(x)$ reaches a target $\alpha$ when only noisy observations are available. An update $x_{n+1}=x_n-a_n(Y_n-\alpha )$ moves according to the observed error. Positive step sizes with $\sum a_n=\infty$ and $\sum a_n^2<\infty$, together with suitable response and noise hypotheses, balance continued movement against accumulated noise. The method replaces exact root evaluation by a convergent statistical procedure.^[ref]