Models

Question 0

Processes with discrete space and continuous time

Answer 0

• Markov jump processes (Poisson process)

- Counting processes with continuous time sets

Question 1

Processes with discrete space and discrete time

Answer 1

• Markov chains
• Simple random walks
• Counting processes with discrete time sets

Question 2

Processes with continuous space and discreet time

Answer 2

• General random walks and time series

Question 3

Processes with continuous space and continuous time

Answer 3

• Brownian motion
• Diffusion process
• Compound Poisson process with continuous space

Question 4

What is a model?

Answer 4

Imitation of a real world system or process

Question 5

Why to choose a model?

Answer 5

Real experiment can be:

• too risky
• too expensive
• too slow

Question 6

What is the framework for representation of a model?

Answer 6

A set of mathematical or logical assumption about how it works

Question 7

How to determine values for the parameters in a model?

Answer 7

To determine suitable parameters data need to be considered and decided on relevance to the future environment, such data can be from past observations, from current observations and from expectations of future changes

Question 8

Two criteria used to determine is a simple model is likely to be satisfactory

Answer 8

Before finalising the choice of the model, one need to consider:

• the objectives for creation
• the use of the model

Question 9

List steps of construction and use of a model

Answer 9

1. Develop objectives which model need to meet
2. Plan the modelling process and how model will be validated
3. Collect and analyse necessary data
4. Define the parameters for the model and their appropriate values
5. Define the model initially by capturing the essence of the real world system
6. Involve experts on the real world system to be imitated and get feedback on the validity of the model
7. Decide whether a simulation package or a general purpose language is appropriate for the implementation of the model. Choose the appropriate random number generator in the context of complexity of the model
8. Write the computer programme for the model
9. Debug the program to make sure it performs the intended operations in the model definition
10. Test reasonableness of the output of the model
11. Review and carefully consider the appropriateness of the model in light of small changes in input parameters
12. Analyse the output from the model
13. Ensure compliance with professional guidenace
14. Communicate and document the result and the model