Enabling Active Learning in Large Classes Through the Use of Plickers

Class response systems allows for just-in-time teaching (JITT) assessments and quizzes. Unfortunately, most of them require students to have an electronic device and do not allow for students to participate and engage in critical thinking. Plickers, on the other hand, is an alternative class response system which does not suffer from the previous disadvantages and can stimulate debate and discussion during the class which as a result may enhance learner motivation. I assessed the effect of using Plickers on the engagement and participation of the students by having a questionnaire at the end of the course with questions related to the Plickers application and what students thought about it. Results were positive and it seems that students felt that the application enabled them to measure the understanding of the subject and they were more involved compared to courses that were not using Plickers. Overall, Plickers could be a potentially useful tool for classrooms, and it has yet to be evaluated in empirical research. The lack of research with this application leaves a potentially vital absence in the literature that may improve both learning and teaching with the use of this new technology

Bayesian mixture models for count data

Regression models for count data are usually based on the Poisson distribution. This thesis is concerned with Bayesian inference in more flexible models for count data. Two classes of models and algorithms are presented and studied in this thesis. The first employs a generalisation of the Poisson distribution called the COM-Poisson distribution, which can represent both overdispersed data and underdispersed data. We also propose a density regression technique for count data, which, albeit centered around the Poisson distribution, can represent arbitrary discrete distributions. The key contribution of this thesis are MCMC-based methods for posterior inference in these models. One key challenge in COM-Poisson-based models is the fact that the normalisation constant of the COM-Poisson distribution is not known in closed form. We propose two exact MCMC algorithms which address this problem. One is based on the idea of retrospective sampling; we sample the uniform random variable used to decide on the acceptance (or rejection) of the proposed new state of the unknown parameter first and then only evaluate bounds for the acceptance probability, in the hope that we will not need to know the acceptance probability exactly in order to come to a decision on whether to accept or reject the newly proposed value. This strategy is based on an efficient scheme for computing lower and upper bounds for the normalisation constant. This procedure can be applied to a number of discrete distributions, including the COM-Poisson distribution. The other MCMC algorithm proposed is based on an algorithm known as the exchange algorithm. The latter requires sampling from the COM-Poisson distribution and we will describe how this can be done efficiently using rejection sampling. We will also present simulation studies which show the advantages of using the COM-Poisson regression model compared to the alternative models commonly used in literature (Poisson and negative binomial). Three real world applications are presented: the number of emergency hospital admissions in Scotland in 2010, the number of papers published by Ph.D. students and fertility data from the second German Socio-Economic Panel. COM-Poisson distributions are also the cornerstone of the proposed density regression technique based on Dirichlet process mixture models. Density regression can be thought of as a competitor to quantile regression. Quantile regression estimates the quantiles of the conditional distribution of the response variable given the covariates. This is especially useful when the dispersion changes across the covariates. Instead of estimating the conditional mean , quantile regression estimates the conditional quantile function across different quantiles.As a result, quantile regression models both location and shape shifts of the conditional distribution. This allows for a better understanding of how the covariates affect the conditional distribution of the response variable. Almost all quantile regression techniques deal with a continuous response. Quantile regression models for count data have so far received little attention. A technique that has been suggested is adding uniform random noise (``jittering''), thus overcoming the problem that, for a discrete distribution, the conditional quantile function is not a continuous function of the parameters of interest. Even though this enables us to estimate the conditional quantiles of the response variable, it has disadvantages. For small values of the response variable Y, the added noise can have a large influence on the estimated quantiles. In addition, the problem of ``crossing quantiles'' still exists for the jittering method. We eliminate all the aforementioned problems by estimating the density of the data, rather than the quantiles. Simulation studies show that the proposed approach performs better than the already established jittering method. To illustrate the new method we analyse fertility data from the second German Socio-Economic Panel

Retrospective sampling in MCMC with an application to COM-Poisson regression

The normalization constant in the distribution of a discrete random variable may not be available in closed form; in such cases, the calculation of the likelihood can be computationally expensive. Approximations of the likelihood or approximate Bayesian computation methods can be used; but the resulting Markov chain Monte Carlo (MCMC) algorithm may not sample from the target of interest. In certain situations, one can efficiently compute lower and upper bounds on the likelihood. As a result, the target density and the acceptance probability of the Metropolis–Hastings algorithm can be bounded. We propose an efficient and exact MCMC algorithm based on the idea of retrospective sampling. This procedure can be applied to a number of discrete distributions, one of which is the Conway–Maxwell–Poisson distribution. In practice, the bounds on the acceptance probability do not need to be particularly tight in order to accept or reject a move. We demonstrate this method using data on the emergency hospital admissions in Scotland in 2010, where the main interest lies in the estimation of the variability of admissions, as it is considered as a proxy for health inequalities

Efficient Bayesian inference for COM-Poisson regression models

COM-Poisson regression is an increasingly popular model for count data. Its main advantage is that it permits to model separately the mean and the variance of the counts, thus allowing the same covariate to affect in different ways the average level and the variability of the response variable. A key limiting factor to the use of the COM-Poisson distribution is the calculation of the normalisation constant: its accurate evaluation can be time-consuming and is not always feasible. We circumvent this problem, in the context of estimating a Bayesian COM-Poisson regression, by resorting to the exchange algorithm, an MCMC method applicable to situations where the sampling model (likelihood) can only be computed up to a normalisation constant. The algorithm requires to draw from the sampling model, which in the case of the COM-Poisson distribution can be done efficiently using rejection sampling. We illustrate the method and the benefits of using a Bayesian COM-Poisson regression model, through a simulation and two real-world data sets with different levels of dispersion

The Use of Technology and Social Media in Teaching Statistics

When teaching an applied subject such as Statistics it is important to be up-to-date with modern teaching methods and take advantage of any available teaching "tools". Technology can play an important role in this, with the use of social media, interactive online applications and videos. The use of these tools allows the teacher to take advantage of flipped-classroom approaches and for the student to grasp difficult statistical concepts (e.g. regression, simulation, confidence intervals, etc) easier through visualisation and a hands-on approach. In this paper, I will present how a lecturer can take advantage of some of the available “tools” that I used (e.g. Shiny, R Markdown, Screencast-O-Matic, Twitter, etc) in such a way that class time could be spent in stimulating debate and discussion

The Use of Technology and Social Media in Teaching Statistics

When teaching an applied subject such as Statistics it is important to be up-to-date with modern teaching methods and take advantage of any available teaching "tools". Technology can play an important role in this, with the use of social media, interactive online applications and videos. The use of these tools allows the teacher to take advantage of flipped-classroom approaches and for the student to grasp difficult statistical concepts (e.g. regression, simulation, confidence intervals, etc) easier through visualisation and a hands-on approach. In this paper, I will present how a lecturer can take advantage of some of the available “tools” that I used (e.g. Shiny, R Markdown, Screencast-O-Matic, Twitter, etc) in such a way that class time could be spent in stimulating debate and discussion

The use of technology and social media in teaching Statistics

Slides from talk given at ICOTS10 in Kyoto, Japan

Evaluating Squat Performance With a Single Inertial Measurement Unit

Inertial measurement units (IMUs) may be used during exercise performance to assess form and technique. To maximise practicality and minimise cost a single-sensor system is most desirable. This study sought to investigate whether a single lumbar-worn IMU is capable of identifying seven commonly observed squatting deviations. Twenty-two volunteers (18 males, 4 females, age: 26.09±3.98 years, height: 1.75±0.14m, body mass: 75.2±14.2 kg) performed the squat exercise correctly and with 7 induced deviations. IMU signal features were extracted for each condition. Statistical analysis and leave one subject out classifier evaluation were used to assess the ability of a single sensor to evaluate performance. Binary level classification was able to distinguish between correct and incorrect squatting performance with a sensitivity of 64.41%, specificity of 88.01% and accuracy of 80.45%. Multi-label classification was able to distinguish between specific squat deviations with a sensitivity of 59.65%, specificity of 94.84% and accuracy of 56.55%. These results indicate that a single IMU can successfully discriminate between squatting deviations. A larger data set must be collected and more complex classification techniques developed in order to create a more robust exercise analysis IMU-based system

Evaluating Squat Performance with a Single Inertial Measurement Unit

2015 IEEE 12th International Conference on Wearable and Implantable Body Sensor Networks, MIT, Cambridge, Massachusetts, United States of America, 9-12 June 2015Inertial measurement units (IMUs) may be used during exercise performance to assess form and technique. To maximise practicality and minimise cost a single-sensor system is most desirable. This study sought to investigate whether a single lumbar-worn IMU is capable of identifying seven commonly observed squatting deviations. Twenty-two volunteers (18 males, 4 females, age: 26.09±3.98 years, height: 1.75±0.14m, body mass: 75.2±14.2 kg) performed the squat exercise correctly and with 7 induced deviations. IMU signal features were extracted for each condition. Statistical analysis and leave one subject out classifier evaluation were used to assess the ability of a single sensor to evaluate performance. Binary level classification was able to distinguish between correct and incorrect squatting performance with a sensitivity of 64.41%, specificity of 88.01% and accuracy of 80.45%. Multi-label classification was able to distinguish between specific squat deviations with a sensitivity of 59.65%, specificity of 94.84% and accuracy of 56.55%. These results indicate that a single IMU can successfully discriminate between squatting deviations. A larger data set must be collected and more complex classification techniques developed in order to create a more robust exercise analysis IMU-based system.Science Foundation Irelan