Ongoing Ph.D. Work:

  • Data-Driven Selection of Fractional Differential Operator with Applications to Real Data.

  • Sampling from the posterior distribution using the Approximate Bayesian Computations (ABC) such as: ABC Rejection sampler, ABC Markov Chain Monte Carlo Algorithm (MCMC), ABC Sequential Monte Carlo Algorithm (SMC)

  • Model selection using RJMCMC for Intraguild predations (IGP).

  • Global sensitivity analysis of ordinary differential equation (ODE) model using the following methods: Morris’s screening Method and Sobol’s variance-based Method.

Masters Project:

Estimation of Nonlinear Models using Bayesian Statistics | Semester-III

  • Developed a program in R for fitting the simple linear regression model and generalized logistic model using the Bayesian method using simulated data.

  • Approximation of the posterior densities was carried out by Gibb’s sampling and grid approximation.

  • Convergence of the posterior samples was verified by different MCMC diagnostic tools (e.g., Gelman and Rubin diagnostic).

  • The robustness of our method by simulating 10 different time series and inference about the parameters of the generalized logistic model was performed by fixing population parameters. Also, by taking 4 different parameter configurations, we calculate the posterior estimates of parameters and 90% posterior credible interval.


Development of Bayesian methods for Predator-Prey system | Semester-IV

  • Developed programs for fitting two-dimensional nonlinear differential equation models for simulated data.

  • The posterior distribution of all the parameters was obtained by Gibb’s sampling and grid approximation.

  • Analysis of real data corresponding to Ursus Americanus species has been carried out from the Global Population Dynamics Database.

Internship:

Institute of Chemical Technology, Mumbai | May 2018 - July 2018

Guides: Dr. A. R. Bhowmick (ICT Mumbai), Dr. Abhishek Mukherjee (ISI, Kolkata)

  • Studied the principle of Bayesian Statistics: Prior, Posterior, and Likelihood, the conjugate prior distribution for exponential families, non-informative prior distribution, etc.

  • Studied different simulation algorithms: Accept/Reject, Metropolis algorithm, Gibbs, Slice sampling, etc.

  • Developed programs in R for all the simulation methods.


Institute of Chemical Technology, Mumbai (Funded by UDCT Alumni Association) |15 May 2019 - 30 June 2019

Guide: Dr. A. R. Bhowmick (ICT Mumbai)

  • Implemented R programs to analyze the time series from the Global Population Dynamics Database.

  • Implemented the program for fitting the theta-logistic model using Gibb’s sampling and grid approximation.

  • The goal of this study is to compare the estimates with the existing study and obtain improved (shorter) credible intervals for the parameters of the theta-logistic model.