Efficient implementation of Markov chain Monte Carlo when using an unbiased likelihood estimator

When an unbiased estimator of the likelihood is used within a Metropolis--Hastings chain, it is necessary to trade off the number of Monte Carlo samples used to construct this estimator against the asymptotic variances of averages computed under this chain. Many Monte Carlo samples will typically result in Metropolis--Hastings averages with lower asymptotic variances than the corresponding Metropolis--Hastings averages using fewer samples. However, the computing time required to construct the likelihood estimator increases with the number of Monte Carlo samples. Under the assumption that the distribution of the additive noise introduced by the log-likelihood estimator is Gaussian with variance inversely proportional to the number of Monte Carlo samples and independent of the parameter value at which it is evaluated, we provide guidelines on the number of samples to select. We demonstrate our results by considering a stochastic volatility model applied to stock index returns.Comment: 34 pages, 9 figures, 3 table

Who are the Open Learners? A Comparative Study Profiling non-Formal Users of Open Educational Resources

Open educational resources (OER) have been identified as having the potential to extend opportunities for learning to non-formal learners. However, little research has been conducted into the impact of OER on non-formal learners. This paper presents the results of a systematic survey of more than 3,000 users of open educational resources (OER). Data was collected between 2013 and 2014 on the demographics, attitudes and behaviours of users of three repositories. Questions included a particular focus on the behaviours of non-formal learners and the relationship between formal and non-formal study. Frequency analysis shows that there are marked differences in patterns of use, user profiles, attitudes towards OER, types of materials used and popularity of different subjects. The experience of using OER is fairly consistent across platforms in terms of satisfaction and impact on future behaviour. On the whole, non-formal learners surveyed were highly positive about their use of OER and believe they will continue to use them. With regards to this making formal study more likely some degree of polarization was observed: some believed formal study was now more likely, while others felt it made this less likely. On the whole, while non-formal learners are enthusiastic about using free and online resources, the language and concept of OER does not seem to be well understood in the groups surveyed. A range of findings relating to OER selection and use as well as differences between repositories are explored in the discussion