Research

My google scholar page | arXiv

My research lies at the interface of applied probability, computational methods, and experimentation. My current research is inspired by ideas in algorithmic fairness, reinforcement learning and sequential decision making and their connections to Markov Chain Monte Carlo (MCMC) methods. I also have an active interest in using ML/statistical modeling to address problems in climate science. Below is a selected bibliography.

Design and Analysis of Markov Chains

I study Markov chains both in discrete and continuous state spaces. For discrete state space Markov chains, I am interested in studying their mixing times often via elegant coupling techniques. In continuous state spaces, mixing times do not always give meaningful answers. Instead, I use scaling methods and diffusion limits to obtain practical guidelines for implementing them.

1. Pillai N.S., Stuart A.M. and Thiery, A.H. Optimal Scaling and Diffusion Limits for the Langevin Algorithm in High Dimensions. The Annals of Applied Probability, 22 (6) , 2320-2356, 2012. [AOAP]
2. Beskos A., Pillai N.S., Roberts G.O., Sanz-serna J.M. and Stuart A.M. Optimal tuning of the Hybrid Monte Carlo Algorithm. Bernoulli, 19, 5(A), 1501-1534, 2013. [Bernoulli]
3. Pillai N.S. and Smith A. Kac’s walk on n-sphere mixes in nlog(n) steps. Annals of Applied Probability, 27 (1), 631-650, 2017. [AOAP]
4. Pillai N.S. and Smith A. On the Mixing Time of Kac’s Walk and Other High Dimensional Gibbs Samplers with Constraints. The Annals of Probability, 46 (4), 2345-2399, 2018. [AOP]

Statistical methods grounded in theory

I am interested in developing statistical methods with a solid theoretical backing. This philosophy has often led me to unexpected discoveries and finding connections between disparate areas of research. I maintain an active interest in Bayesian methodology.

1. Pillai N.S. and Meng, X-L. An unexpected encounter with Cauchy and Levy. The Annals of Statistics 44 (5), 2089-97, 2017. [AOS]
2. Robert C.P., Cornuet J.M., Marin J.M. and Pillai N.S. Lack of trust in (Approximate Bayes Computation) ABC model choice. Proceedings of the National Academy of Sciences (PNAS), 108 (37), 15112-15117, 2011. See also blog entry HERE, HERE, HERE and HERE . [PNAS]
3. Bhattacharya A., Pati D., Pillai N.S. and Dunson, D.B. Dirichlet-Laplace priors for optimal shrinkage. Journal of the American Statistical Association, 110 (52), 1479-1490, 2015. This paper contains some ideas from an older paper titled Bayesian Shrinkage. Also see here. [JASA]
4. Pillai N.S., Wu Q., Liang F., Mukherjee S. and Wolpert R.L. Characterizing the Function Space for Bayesian Kernel Models. Journal of Machine Learning, 8, 1769-1797, 2007. [JMLR]

Experimentation and causal Inference

I was exposed to causal methods and experimentation at Harvard. In recent years, especially because of my work in the industry, I am drawn to research problems that require application of causal methods in new application domains.

1. Jagadeesan R., Pillai N.S. and Volfovsky A. Designs for estimating the treatment effects in networks with interference. The Annals of Statistics, 48 (2), 679-712, 2020. [AOS]
2. Dasgupta, T., Pillai N.S. and Rubin D.B. Causal inference from 2^k factorial designs using the potential outcomes. Journal of the Royal Statistical Society, Series-B, 77 (4), 727-753, 2015. [JRSSB]

Climate modeling

I am an affiliate member of HUCE and keenly follow various climate related research at Harvard and beyond. I am interested in addressing issues due to poor data quality, synthesizing different sources of data, spatial modeling and relating climate and health. 

1. Rigden A.J., Mueller N.D., Holbrook N.M., Pillai N.S. and Huybers P. Combined influence of soil moisture and atmospheric evaporative demand is important for accurately predicting US maize yields. Nature (food), 1, 127–133, 2020. [Nature]
2. Dai C., Chan D., Huybers P. and Pillai N.S. Late 19th-Century Navigational Uncertainties and Their Influence on Sea Surface Temperature Estimates. The Annals of Applied Statistics, 15 (1), 22-40, 2021. [AOAS]