Birth-death processes with mass annihilation and state-dependent immigration

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate αj. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of existence and recurrence properties. However, results developed to date are generally opaque, and so the primary motivation of this paper is to construct conditions that are far easier to apply in practice. These turn out to be identical to the conditions for positive recurrence, which are very easy to check. We obtain, as a consequence, the surprising result that any MBPII that exists is ergodic, and so must possess an equilibrium distribution. These results are then extended to more general MBPII, and we show how to construct the associated equilibrium distributions.

Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

A class of generalized Lévy Laplacians in infinite dimensional calculus

A class of generalized Lévy Laplacians which contain as a special case the ordinary Lévy Laplacian are considered. Topics such as limit average of the second order functional derivative with respect to a certain equally dense (uniformly bounded) orthonormal base, the relations with Kuo’s Fourier transform and other infinite dimensional Laplacians are studied.

Birth-death processes with an instantaneous reflection barrier

A new structure with the special property that an instantaneous reflection barrier is imposed on the ordinary birth-death processes is considered. An easy-checking criterion for the existence of such Markov processes is first obtained. The uniqueness criterion is then established. In the nonunique case, all the honest processes are explicitly constructed. Ergodicity properties for these processes are investigated. It is proved that honest processes are always ergodic without necessarily imposing any extra conditions. Equilibrium distributions for all these ergodic processes are established. Several examples are provided to illustrate our results.

[Reviews] Super crunchers

Review of 'Super Crunchers: How Anything Can Be Predicted' by Ian Ayres, published by John Murray, 2007 (ISBN 0-719-564638)

A case study of the effectiveness of the electronic survey as a research tool for measuring students' experience of e-learning

This paper uses a case study approach to consider the effectiveness of the electronic survey as a research tool to measure the learner voice about experiences of e-learning in a particular institutional case. Two large scale electronic surveys were carried out for the Student Experience of e-Learning (SEEL) project at the University of Greenwich in 2007 and 2008, funded by the UK Higher Education Academy (HEA). The paper considers this case to argue that, although the electronic web-based survey is a convenient method of quantitative and qualitative data collection, enabling higher education institutions swiftly to capture multiple views of large numbers of students regarding experiences of e-learning, for more robust analysis, electronic survey research is best combined with other methods of in-depth qualitative data collection. The advantages and disadvantages of the electronic survey as a research method to capture student experiences of e-learning are the focus of analysis in this short paper, which reports an overview of large-scale data collection (1,000+ responses) from two electronic surveys administered to students using surveymonkey as a web-based survey tool as part of the SEEL research project. Advantages of web-based electronic survey design include flexibility, ease of design, high degree of designer control, convenience, low costs, data security, ease of access and guarantee of confidentiality combined with researcher ability to identify users through email addresses. Disadvantages of electronic survey design include the self-selecting nature of web-enabled respondent participation, which tends to skew data collection towards students who respond effectively to email invitations. The relative inadequacy of electronic surveys to capture in-depth qualitative views of students is discussed with regard to prior recommendations from the JISC-funded Learners' Experiences of e-Learning (LEX) project, in consideration of the results from SEEL in-depth interviews with students. The paper considers the literature on web-based and email electronic survey design, summing up the relative advantages and disadvantages of electronic surveys as a tool for student experience of e-learning research. The paper concludes with a range of recommendations for designing future electronic surveys to capture the learner voice on e-learning, contributing to evidence-based learning technology research development in higher education.

AASK - Aircraft accident statistics and knowledge: A database of human experience in evacuation, derived from aviation accident reports

Computer based mathematical models describing the aircraft evacuation process have a vital role to play in aviation safety. However such models have a heavy dependency on real evacuation data in order to (a) identify the key processes and factors associated with evacuation, (b) quantify variables and parameters associated with the identified factors/processes and finally (c) validate the models. The Fire Safety Engineering Group of the University of Greenwich is undertaking a large data extraction exercise from three major data sources in order to address these issues. This paper describes the extraction and application of data from one of these sources - aviation accident reports. To aid in the storage and analysis of the raw data, a computer database known as AASK (aircraft accident statistics and knowledge) is under development. AASK is being developed to store human observational and anecdotal data contained in accident reports and interview transcripts. AASK comprises four component sub-databases. These consist of the ACCIDENT (crash details), FLIGHT ATTENDANT (observations and actions of the flight attendants), FATALS (details concerning passenger fatalities) and PAX (observations and accounts from individual passengers) databases. AASK currently contains information from 25 survivable aviation accidents covering the period 4 April 1977 to 6 August 1995, involving some 2415 passengers, 2210 survivors, 205 fatalities and accounts from 669 people. In addition to aiding the development of aircraft evacuation models, AASK is also being used to challenge some of the myths which proliferate in the aviation safety industry such as, passenger exit selection during evacuation, nature and frequency of seat jumping, speed of passenger response and group dynamics. AASK can also be used to aid in the development of a more comprehensive approach to conducting post accident interviews, and will eventually be used to store the data directly.

The AASK database V4.0: aircraft accident statistics and knowledge. A database to record human experience of evacuation in aviation accidents

This paper describes the AASK database. The AASK database is unique as it is a record of human behaviour during survivable aviation accidents. The AASK database is compiled from interview data compiled by agencies such as the NTSB and the AAIB. The database can be found on the website http://fseg.gre.ac.uk

Aircraft accident statistics and knowledge database: analyzing passenger behavior in aviation accidents

The Aircraft Accident Statistics and Knowledge (AASK) database is a repository of passenger accounts from survivable aviation accidents/incidents compiled from interview data collected by agencies such as the US NTSB. Its main purpose is to store observational and anecdotal data from the actual interviews of the occupants involved in aircraft accidents. The database has wide application to aviation safety analysis, being a source of factual data regarding the evacuation process. It also plays a significant role in the development of the airEXODUS aircraft evacuation model, where insight into how people actually behave during evacuation from survivable aircraft crashes is required. This paper describes the latest version of the database (Version 4.0) and includes some analysis of passenger behavior during actual accidents/incidents.

CAA paper 2006/01: a database to record human experience of evacuation in aviation accidents: the aircraft accident statistics and knowledge database (AASK)

This report concerns the development of the AASK V4.0 database (CAA Project 560/SRG/R+AD). AASK is the Aircraft Accident Statistics and Knowledge database, which is a repository of survivor accounts from aviation accidents. Its main purpose is to store observational and anecdotal data from interviews of the occupants involved in aircraft accidents. The AASK database has wide application to aviation safety analysis, being a source of factual data regarding the evacuation process. It is also key to the development of aircraft evacuation models such as airEXODUS, where insight into how people actually behave during evacuation from survivable aircraft crashes is required. With support from the UK CAA (Project 277/SRG/R&AD), AASK V3.0 was developed. This was an on-line prototype system available over the internet to selected users and included a significantly increased number of passenger accounts compared with earlier versions, the introduction of cabin crew accounts, the introduction of fatality information and improved functionality through the seat plan viewer utility. The most recently completed AASK project (Project 560/SRG/R+AD) involved four main components: a) analysis of the data collected in V3.0; b) continued collection and entry of data into AASK; c) maintenance and functional development of the AASK database; and d) user feedback survey. All four components have been pursued and completed in this two-year project. The current version developed in the last year of the project is referred to as AASK V4.0. This report provides summaries of the work done and the results obtained in relation to the project deliverables.

The role of Minitab in teaching and learning statistics

This paper describes how the statistical package Minitab is used in teaching statistics in our undergraduate programmes in Mathematics and Statistics to enhance student learning. How the sophisticated recent versions of Minitab can be used to help students understand statistical concepts, develop their statistical thinking and gain valuable skills in performing statistical analysis are discussed.

Some issues on assessment methods and learning in mathematics and statistics

This paper looks at the application of some of the assessment methods in practice with the view to enhance students’ learning in mathematics and statistics. It explores the effective application of assessment methods and highlights the issues or problems, and ways of avoiding them, related to some of the common methods of assessing mathematical and statistical learning. Some observations made by the author on good assessment practice and useful approaches employed at his institution in designing and applying assessment methods are discussed. Successful strategies in implementing assessment methods at different levels are described.