STAT0007: Introduction to Applied Probability (Level 5) or Stochastic Processes (Level 6)
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STAT0007: Introduction to Applied Probability (Level 5) or Stochastic Processes (Level 6)
Chapter 1 Overview of STAT0007
1.1 Content of the course
This module aims to provide an introduction to the study of systems which change state stochastically with time and to facilitate the development of skills in the application of probabilistic ideas. It is primarily intended for second and third year students registered on the undergraduate degree programmes offered by the Department of Statistical Science, or jointly with other departments.
On successful completion of the module a student should understand the Markov property in discrete and continuous time; for discrete-time Markov chains, be able to find and classify the irreducible classes of intercommunicating states, calculate absorption or first passage times and probabilities, assess the equilibrium behaviour; for simple examples of continuous-time Markov chains, be able to write down the forward equations, find and interpret the equilibrium distribution.
Stochastic processes are vital to applications in finance and insurance, and have many applications in biology and medicine, and in the social sciences. They also play a fundamental role in areas such as queueing theory and the study of system reliability. The material in this module can be applied to simplified real-world situations, and provides the foundations for further study of more complex systems.
The course will start by briefly revising of conditional probability (however you are expected to be well-versed in this before starting the course). We’ll then move on to look at Markov chains (discrete time and states), and in particular long-run behaviour. The second half of the course
looks at Markov processes in continuous time, but still discrete state space, and again our ultimate aim is to study the long-run behaviour of these processes. We’ll look at two very special types of continuous time processes: Poisson processes and birth-death processes.
1.2 How this course will be run
1.2.1 Course leader
The course will be led by Dr. Elinor Jones, Associate Professor (Teaching) in the Department of Statistical Science.
1.2.2 Level 5 and 6 versions of the course
The course is offered at two levels, but the chances are you won’t be able to choose which level (this generally depends on your year of study etc).
The content and teaching is identical between the two levels, but in the main exam period level 6 students will complete a more challenging paper.
1.2.3 How you’ll learn
You will work on the material in your own time with live sessions to complement your learning. A typical weekly schedule will look like the following:
Batch of work uploaded to Moodle each Monday at 9am.
Finish the work by the following Monday.
Each week, work will include:
Watch videos;
Read course notes;
Complete guided exercises;
Complete and submit homework each week (not in the first week);
Quizzes;
Other activities, as required.
You will also attend about three live sessions a week (exact number depends on which week we’re in).
ONLINE large group sessions (all students attend):
Tuesday 9- 10am UK time.
Friday 9- 10am UK time.
These sessions typically include:
Overview of material;
Time for questions;
Going through unseen questions.
FACE-TO-FACE small group sessions:
Tutorial (attendance is monitored).
All students must attend their allocated session
1.2.4 Weekly exercises
On Friday each week I will release an exercise sheet. Note: the exercise sheet is not released at the start of the week.
Submit by the following Thursday 10am UK time.
Solutions will be available at 9am each Friday.
Those with a SoRA will have until 12:01am on Friday (i.e. an additional 14 hours according to UCL guidelines) to submit.
NO LATE SUBMISSIONS. This rule will be strictly adhered to: no exceptions (but see
note above for students with a SoRA).
Your work will be marked and individual feedback provided for SOME questions.
These weekly exercises will feed into the weekly tutorial (tutorials start in the third week).
You should have been allocated to a tutorial group.
You cannot move tutorial group unless you have a timetable clash.
If you need to change your tutorial group, please email Ms Karen Leport.
Please don’t email me: I’ve no control over tutorial allocation.
During the tutorial, your tutor will go through the questions that were not marked. You should ‘mark’ your own work while they do this.
You will then discuss an unseen question which is connected to the work you’ve been doing. The question will be more involved than a typical homework question. You may be asked to do short tasks connected to the question, e.g.
Discuss in small groups;
Respond to live quiz questions.
Please take part: the tutorials are designed to benefit your learning.
1.2.5 Weekly structure in more depth
Just to make sure you are clear on how the weekly workload will be managed:
Week 1
Material released on Monday 10th Jan.
Live session Tuesday 11th Jan (welcome session only).
Live session Friday 14th Jan (Q&A for week 1 material).
Exercise sheet 1 released Friday 14th Jan.
Week 2
Material released on Monday 17th Jan.
Live session Tuesday 18th Jan (Q&A for week 1 material, continued).
Submit exercise sheet 1 by 10am on Thursday 20th Jan (unless you have a SoRA). Live session Friday 21st Jan (Q&A for week 1 and 2 material).
Exercise sheet 2 released Friday 21st Jan.
Week 3
Material released on Monday 24th Jan.
Live session Tuesday 25th Jan (Q&A for week 2 material, continued).
Attend your allocated tutorial.
Submit exercise sheet 2 by 10am on Thursday 27th Jan (unless you have a SoRA). Live session Friday 28th Jan (Q&A for week 2 and 3 material).
Exercise sheet 3 released Friday 28th Jan.
And so on, and so forth. There will be some exceptions to this, e.g. when you sit an ICA for the course.
1.2.6 Getting help
You can get help in the following ways:
Post to the Forum.
Book an office hour slot.
If your question is connected to the tutorial material, then ask your tutor during the
tutorial. Your tutor will not answer questions outside of your tutorial slot.
Please note that I won’t answer questions by email (the exception to this is if your question is more personal, e.g. organising additional time for your ICA).
1.2.7 Assessment
Assessment is split into four components:
ICA 1: Tuesday 8th February (7.5% weight)
Short Moodle quiz.
Takes place instead of Tuesday live session.
Mixture of MCQs and calculation questions.
ICA 2: Tuesday 22nd March (7.5% weight)
Short Moodle quiz
Takes place instead of Tuesday live session.
Mixture of MCQs and calculation questions.
Participation (10% weight)
Acceptable quality of weekly exercise submission.
Peer exercise.
Open book exam (75% weight)
Sometime in main exam period.
No choice of questions.
Level 6 students will have more challenging questions.
1.3 Useful books
Introduction to Probability Models by S. Ross;
Probability and Random Processes by Grimmett and Stirzaker (more mathematical … be
warned).
2022-03-17