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A report on DST sponsored two weeks training programme on Stochastic Process Modelling [Dec. 2-15, 2006 ]

Sat, Dec 30 2006 
 

A report on

Training Programme on

Stochastic Process Modelling: Concepts, Theory and Applications

(sponsored by Department of Science & Technology, Govt. of India, New Delhi)

(December 2-15, 2006)

 1. Objective: The applications of stochastic modelling encompass such a big spectrum that the research demand can never be fulfilled. However, as it seems, though mathematical models in terms of differential equations involving deterministic state variables are used rather widely the mathematical background is not very strong. There is a need to ensure that researchers have adequate background in the basics of probability theory e.g. limit theorems, Markov chains in discrete and continuous time and martingales in discrete time. Applications like signal decoding, image processing and weather prediction have yet to be taken up.

The present training program was organized with an objective to acquaint the young women researchers from the state of Rajasthan with the subject of Stochastic Modelling and its different interesting facets of applications to solve real life problems.

The program was also aimed at contributing to bridge the gender gap in higher studies in Mathematical Sciences.

2.  Program: The program was scheduled to have two hours of lectures by an expert in the   forenoon, two hours of post lunch sessions on Hands on Computers and statistical packages and one hour of interactive session with the experts.  The contents of the program were chosen to be

    1.   Basics of Probability Theory

    2.   Markov Chains (Discrete & Continuous time)

2.1         Poisson Process

2.2         Markov Decision Process

2.3         Hidden Markov Models

     3.  Renewal Theory

3.1   Renewal Reward Process

3.2   Semi-Markov Renewal Process

       4.   Stochastic Modeling in Time Series Data

5.      Perturbation Analysis

6.        Applications of Stochastic Modelling

 6.1. Marketing & Finance

        6.2. Biology and Genetics

        6.3. Adaptive Filtering

        6.4. Optimization in Networks

 

  3.  Faculty: A number of experts from the field were contacted out of which the following four faculty from ISI, Kolkata consented to be the visiting faculty in the program.

  • Prof. B. V. Rao                                    Probability & set theory, Stochastic Process    
  • Prof. Krishanu Maulik                           Stochastic Processes, Internet traffic Modeling 
  •  Prof. Dev Priya Sen Gupta                   Time series stochastic modeling, Bayesian Inference 

  •  Prof Alok Goswami                       Stochastic Processes 

 

In addition Prof. G.N.Purohit, Banasthali Vidyapith, Jaipur Campus volunteered to deliver a talk on ‘Application of Stochastic Modeling in Medical Sciences’.

4. Participants:

The training program was focused towards research orientation and participation was limited to women only PG, M. Phil., or research students of Mathematics/statistics from the state of Rajasthan and in addition the faculty of Banasthali Vidyapith.

The participants were invited through sending letters to the Mathematical Sciences and  almost all the institutes of Higher Education in Computer Science and Bio Informatics faculty from Rajasthan and also by floating the announcement on official website of Banasthali Vidyapith www.banasthali.org

A total of 53 applications were received and scrutinized by the Advisory Committee and short listed based on relevance of the topic of the program with their research. Twenty nine candidates were shortlisted, 12 from University of Rajasthan, 8 from Govt.college, Ajmer and 6 from M.D.S. University, Ajmer. Finally twenty-seven candidates participated. The candidates attended were either pursuing research in operations research or completed their M.Phil/MSc in Statistics. Twenty-four faculty members of Banasthali Vidyapith also participated in the program.

A total of 53 applications were received and scrutinized by the Advisory Committee and short listed based on relevance of the topic of the program with their research. Twenty nine candidates were shortlisted, 12 from University of Rajasthan, 8 from Govt.college, Ajmer and 6 from M.D.S. University, Ajmer. Finally twenty-seven candidates participated. The candidates attended were either pursuing research in operations research or completed their M.Phil/MSc in Statistics. Twenty-four faculty members of Banasthali Vidyapith also participated in the program.

5. Sessions:

(i) Inauguration: The Program was inaugurated by Prof. Diwakar Shastri, President Banasthali Vidyapith. He expressed his satisfaction over the fact that in Banasthali Vidyapith, an institution for women, the participation in Computing and Mathematical Sciences is increasing steadily and Apaji Institute now has capability to emerge as a center for research in Mathematical Sciences. He welcomed Prof. B.V.Rao and thanked DST for facilitating this program.

(ii)   Lecture Sessions: These sessions were held as per the schedule in Table 1.

(iii)  Hands -on –Sessions were conducted by the internal faculty of Apaji Institute on the software packages SPSS, Statistica and MATLAB with an objective to acquaint the trainees with the use of these packages which is very important in simulating the models.

(iv)  Valedictory Session & Certification: This session was the last on Dec 15,2006 attended by Prof. Chitra Purohit, Secretary and Treasurer of Banasthali Vidyapith and Prof. Alok Goswami.Beginning with a brief of the proceedings of  the training program the session had expressions and feelings from both the expert and the participants. Prof. Alok Goswami was very much impressed by the five fold educational philosophy of the Vidyapith. He also expressed his views that Vidyapith should hold more activities and experts would definitely like to visit the Vidyapith for it. One of the participants presented her views on behalf of all, where she expressed that the quality of all the sessions was par excellence. Prof. Chitra Purohit, Secretary, Banasthali Vidyapith gave her blessings to all the participants to carry out research in the field and Prof. Rekha Govil, Program Coordinator on behalf of organizing committee thanked the Vidyapith staff, DST and the support system for making the organisation of seminar smooth, a key factor in the success of the event. 

 6.  Feedback: A formal feedback was obtained from each participant. Every one appreciated the content delivery from the experts  especially the interactive sessions. However, the trainees found the time for Hands on sessions to be very short.

7.   Course Material: The participants were initially provided a book ‘A course on Applied Stochastic Processes’ by Prof. Alok Goswami and Prof. B.V.Rao along with registration material. The lecture notes by the experts were compiled by the faculty members of Statistics from the Vidyapith attending the training program. These handwritten notes were compiled and copies distributed to the participants. It is proposed to bring out a published volume on the lectures in the form of a book. The experts have voluntarily taken the responsibility of word processing and editing the volume.