Martin Lysy

Contact Information:
Martin Lysy

Research interests

I enjoy working on a variety of applied problems, for which statistical and computational methodologies fall under the three following themes.

1. Continuous stochastic processes. These processes are typically characterized by stochastic integro-differential equations, for which I am interested in efficient numerical solutions. Applications I am currently working on include simulating the output of an atomic-resolution microscope, inferring the reaction rates in an autoregulatory gene network, and assessing a stochastic volatility model's ability to describe stock market data.

2. Graphical and hierarchical modeling. This flexible modeling framework focus on the conditional dependence structure between all relevant random variables, included those which may not be observed. This typically leads to realistic models while avoiding over-parametrization. I am currently using this approach to combine two marginal models of lizard speciation, and to evaluate the effect of folate intake from different natural sources on the likelihood of colon cancer.
3. Mediation analysis. This type of analysis seeks to understand not only the causal relation between one variable and another, but more specifically, the mechanism through which it occurs. I am interested in formulating realistic modeling assumptions and experimental designs under which this causal mechanism might be convincingly inferred. An application of this work is to determine whether the change in size of lizard species A is due directly to fighting with species B, or merely whether competition for resources indirectly forces species A higher into the trees, where increased size offers a fitness advantage.

Education/biography

• BSc in Pure Mathematics (Honors), McGill University, 2006.
  • Title of thesis: "Sample Size Determination Under Length-Biased Sampling"
  • Advisor: Professor Masoud Asgharian
• MA in Statistics, Harvard University, 2007.
• PhD in Statistics, Harvard University, 2012.
  • Title of thesis: "The Method of Batch Inference for Multivariate Diffusions"
  • Advisor: Professor Samuel Kou

Selected publications

• Kou, S.C., Olding, B., Lysy, M., and Liu, J.S. (2012), "A Multiresolution Method for Parameter Estimation of Diffusion Processes", Journal of the American Statistical Association, 107(500), pp. 1558-1574.
• Labuda, A., Lysy, M., Paul, W., Miyahara, Y., Grütter, P., Bennewitz, R., and Sutton, M. (2012), "On Stochastic Noise in Atomic Force Microscopy", Physical Review E, 86(3), pp. 031104 1-18.
• Labuda, A., Lysy, M., and Grütter, P. (2012), "Stochastic Simulation of Tip-Sample Interactions in Atomic Force Microscopy", Applied Physics Letters, 101, pp. 113105 1-4.
• Morris, C.N. and Lysy, M. (2012), "Shrinkage Estimation in Multilevel Normal Models", Statistical Science, 27(1), pp. 115-134.