# Melvin M. Varughese

Email: melvin.varughese@uct.ac.za

**Research Interests:** Stochastic Processes; Ecological modelling; Astrostatistics

**Position:** Adjunct Senior lecturer

**Biographical Information**

I grew up in Zambia before moving to South Africa at the age of 10. I did my undergrad at Wits and taught there for a number of years. In 2008, I joined UCT as a lecturer. In addition to being a member of the South African Statistical Association, I have also been a reviewer for both the “Journal of the Franklin Institute” and “Ecological Modelling”.

**Research Interests**

**1. Stochastic Processes**

Interested in the analysis of nonlinear diffusion processes for which analytical solutions are often unavailable.

**2. Ecological Modelling**

Interested in modelling the sources of population stochasticity and their consequent impact on populations.

**3. Astrostatistics**

Interested in the intersection between astronomy and/or cosmology and statistics. Projects include supernova classification and cosmological model fitting.

**Publications**

- Hlozek, R., Kunz, M., Bassett, B., Smith, M., Newling, J., Varughese, M., Kessler, R., Bernstein, J., Campbell, H., Dilday, B., Falck, B., Frieman, J., Kulhmann, S., Lampeitl, H., Marriner, J., Nichol, R., Riess, A., Sako, M., Schneider, D. 2012. Photometric Supernova Cosmology with BEAMS and SDSS-II, Astrophysical Journal 752:79.
- Newling, J., Bassett, B., Hlozek, R., Kunz, M., Smith, M., Varughese, M. 2012. Parameter estimation with Bayesian estimation applied to multiple species in the presence of biases and correlations. Monthly Notices of the Royal Astronomical Society. Monthly Notices of the Royal Astronomical Society 421:913-925.
- Varughese, M.M. 2011. A framework for modelling ecological communities and their interactions with the environment. Ecological Complexity 8:105-112.
- Kessler, R., Bassett, B., Belov, P., Bhatnagar, V., Campbell, H., Conley, A., Frieman, J.A., Glazov, A., González-Gaitán, S., Hlozek, R., Jha, S., Kuhlmann, S., Kunz, M., Lampeitl, H., Mahabal, A., Newling, J., Nichol, R.C., Parkinson, D., Philip, N.S., Poznanski, D., Richards, J.W., Rodney, S.A., Sako, M., Schneider, D.P., Smith, M., Stritzinger, M., Varughese, M. 2010. Results from the Supernova Photometric Classification Challenge. Publications of the Astronomical Society of the Pacific 122:1415-1431.
- Varughese, M.M., 2010. A framework for modelling ecological communities and their interactions with the environment. Ecol. Complex. (accepted)
- Varughese, M.M., 2009. On the accuracy of a diffusion approximation to a discrete state-space Markovian model of a population. Theor. Popul. Biol. 76, 241-247.
- Varughese, M.M. 2009. On the accuracy of a diffusion approximation to a discrete state-space Markovian model of a population. Theoretical Population Biology 76:241-247.
- Varughese, M.M., Fatti, L.P. 2008. Incorporating environmental stochasticity within a biological population model. Theoretical Population Biology 74:115-129.
- Varughese, M.M., Fatti, L.P., 2008. Incorporating environmental stochasticity within a biological population model. Theor. Popul. Biol. 74, 115-129.
- Newling, J., Varughese, M., Bassett, B., Campbell, H., Hlozek, R., Kunz, M., Lampeitl, H., Martin, B., Nichol, R., Parkinson, D., Smith, M. 2011. Statistical Classification Techniques for Photometric Supernova Typing. Monthly Notices of the Royal Astronomical Society 414:1987-2004.
- Newling, J., Varughese, M., Bassett, B.A., Campbell, H., Hlozek, R., Kunz, M., Lampeitl, H., Martin, B., Nichol, R., Parkinson, D., Smith, M., Statistical Classification Techniques for Photometric Supernova Typing. Submitted to Mon. Not. R. Astron. Soc.
- Kessler, R., Bassett, B., Belov, P., Bhatnagar, V., Campbell, C., Conley, A., Frieman, J.A., Glazov, A., Gonzalez-Gaitan, S., Hlozek, R., Jha, S., Kuhlmann, S., Kunz, M., Lampeitl, H., Mahabal, A., Newling, J., Nichol, R.C., Parkinson, D., Philip, N.S., Poznanski, D., Richards, J.W., Rodney, S.A., Sako, M., Schneider, D.P., Smith, M., Stritzinger, M., Varughese, M., 2010. Results from the Supernova Photometric Classification Challenge. Submitted to Publ. Astron. Soc. Pac.
- Varughese, M.M., Parameter Estimation for a Multivariate, Coupled Diffusion System. (under revision)
- Varughese, M.M. Parameter Estimation for Multivariate Diffusion Systems, Computational Statistics and Data Analysis. Revision submitted.

**Postgraduate Projects**

**1. Analysing the Risk of Extinction for Wildlife Populations**

Diffusion processes provide a powerful framework for the modelling of wildlife populations. Many ecological mechanisms - such as the Allee effect, environmental stochasticity and crowding - may be naturally included within a diffusion model. The aim of this project would be to derive the mean stopping time for a nonlinear diffusion process. This may be applied to quantify the impact that various ecological mechanisms have upon the risk of extinction.

**2. Model selection for Stochastic Differential Equations**

Stochastic Differential Equations (SDEs) are continuous-time, continuous-space processes. In contrast, real-world phenomena are rarely observed continuously. Given, a finite set of observations, the aim of this project would be to develop and apply a model selection procedure to find a parsimonious SDE for discretely observed data.

**3. Incorporating model error when Classifying Sparse functional data**

Classification algorithms are typically applied to a homogenous set of data that originates from multiple distinct classes. Functional data samples the relationship between two or more variables for multiple classes. An example of functional data would be a study of height vs age for male and female children. Typically functional data is highly heterogeneous: the sampling points and the measurement errors can vary greatly from one data point to another. The data is often standardised by fitting a model to each data-point and subsequently applying a classification algorithm to the estimated model parameters. However, no account is taken of how well the model fits the observed functional data. The aim of this project will be to explore methods of incorporating the model error within a classification algorithm.

**4. Modelling Financial markets**

Diffusion models are prevalent in finance. The most well known financial models have analytical expressions for their probability distributions. The aim of this project would be to take advantage of recent approximation schemes to model non-linear financial processes. Such methods may also be used to study the stopping times of a diffusion process and hence may be applied to option pricing as well as to calculate the probability of ruin.