A Python package for Bayesian estimation using Markov Chain Monte Carlo

Markov chain Monte Carlo (MCMC) estimation provides a solution to the complex integration problems that are faced in the Bayesian analysis of statistical problems. The implementation of MCMC algorithms is, however, code intensive and time consuming. We have developed a Python package, which is called PyMCMC, that aids in the construction of MCMC samplers and helps to substantially reduce the likelihood of coding error, as well as aid in the minimisation of repetitive code. PyMCMC contains classes for Gibbs, Metropolis Hastings, independent Metropolis Hastings, random walk Metropolis Hastings, orientational bias Monte Carlo and slice samplers as well as specific modules for common models such as a module for Bayesian regression analysis. PyMCMC is straightforward to optimise, taking advantage of the Python libraries Numpy and Scipy, as well as being readily extensible with C or Fortran.

Investigating child participation in the everyday talk of teacher and children in a preparatory year

In early years research, policy and education, a democratic perspective that positions children as participants and citizens is increasingly emphasized. These ideas take seriously listening to children’s opinions and respecting children’s influence over their everyday affairs. While much political and social investment has been paid to the inclusion of participatory approaches little has been reported on the practical achievement of such an approach in the day to day of early childhood education within school settings. This paper investigates talk and interaction in the everyday activities of a teacher and children in an Australian preparatory class (for children age 4-6 years) to see how ideas of child participation are experienced. We use an interactional analytic approach to demonstrate how participatory methods are employed in practical ways to manage routine interactions. Analysis shows that whilst the teacher seeks the children’s opinion and involves them in decision-making, child participation is at times constrained by the context and institutional categories of “teacher” and “student” that are jointly produced in their talk. The paper highlights tensions that arise for teachers as they balance a pedagogical intent of “teaching” and the associated institutional expectations, with efforts to engage children in decision-making. Recommendations include adopting a variety of conversational styles when engaging with children; consideration of temporal concerns and the need to acknowledge the culture of the school.

“What’s going on here?” The pedagogy of a data analysis session

Data analysis sessions are a common feature of discourse analytic communities, often involving participants with varying levels of expertise to those with significant expertise. Learning how to do data analysis and working with transcripts, however, are often new experiences for doctoral candidates within the social sciences. While many guides to doctoral education focus on procedures associated with data analysis (Heath, Hindmarsh, & Luff, 2010; McHoul & Rapley, 2001; Silverman, 2011; Wetherall, Taylor, & Yates, 2001), the in situ practices of doing data analysis are relatively undocumented. This chapter has been collaboratively written by members of a special interest research group, the Transcript Analysis Group (TAG), who meet regularly to examine transcripts representing audio- and video-recorded interactional data. Here, we investigate our own actual interactional practices and participation in this group where each member is both analyst and participant. We particularly focus on the pedagogic practices enacted in the group through investigating how members engage in the scholarly practice of data analysis. A key feature of talk within the data sessions is that members work collaboratively to identify and discuss ‘noticings’ from the audio-recorded and transcribed talk being examined, produce candidate analytic observations based on these discussions, and evaluate these observations. Our investigation of how talk constructs social practices in these sessions shows that participants move fluidly between actions that demonstrate pedagogic practices and expertise. Within any one session, members can display their expertise as analysts and, at the same time, display that they have gained an understanding that they did not have before. We take an ethnomethodological position that asks, ‘what’s going on here?’ in the data analysis session. By observing the in situ practices in fine-grained detail, we show how members participate in the data analysis sessions and make sense of a transcript.

Children’s strategies for making friends when starting school

Starting school is a critical and potentially stressful time for many young children, and having supportive relationships with parents, teachers and peers and friends offer better outcomes for school adjustment and social relationships. This paper explores matters of friendship when young children are starting school, and how they initiate friendships. In audio-recorded conversations with a researcher and their peers, the children proposed a number of strategies, including making requests, initiating clubs and teams, and peer intervention to support a friend. Their accounts drew on social knowledge and relational understandings, and showed that having someone, a friend, to play with was important for starting school. Children gave serious attention to developing strategies to initiate friendships.

Investigation of the effect of organics on the water uptake of marine aerosols

Water uptake refers to the ability of atmospheric particles to take up water vapour from the surrounding atmosphere. This is an important property that affects particle size and phase and therefore influences many characteristics of aerosols relevant to air quality and climate. However, the water uptake properties of many important atmospheric aerosol systems, including those related to the oceans, are still not fully understood. Therefore, the primary aim of this PhD research program was to investigate the water uptake properties of marine aerosols. In particular, the effect of organics on marine aerosol water uptake was investigated. Field campaigns were conducted at remote coastal sites on the east coast of Australia (Agnes Water; March-April 2007) and west coast of Ireland (Mace Head; June 2007), and laboratory measurements were performed on bubble-generated sea spray aerosols. A combined Volatility-Hygroscopicity-Tandem Differential Mobility Analyser (VH-TDMA) was employed in all experiments. This system probes the changes in the hygroscopic properties of nanoparticles as volatile organic components are progressively evaporated. It also allows particle composition to be inferred from combined volatility-hygroscopicity measurements. Frequent new particle formation and growth events were observed during the Agnes Water campaign. The VH-TDMA was used to investigate freshly nucleated particles (17-22.5 nm) and it was found that the condensation of sulphate and/or organic vapours was responsible for driving particle growth during the events. Aitken mode particles (~40 nm) were also measured with the VH-TDMA. In 3 out of 18 VH-TDMA scans evaporation of a volatile, organic component caused a very large increase in hygroscopicity that could only be explained by an increase in the absolute water uptake of the particle residuals, and not merely an increase in their relative hygroscopicity. This indicated the presence of organic components that were suppressing the hygroscopic growth of mixed particles on the timescale of humidification in the VH-TDMA (6.5 secs). It was suggested that the suppression of water uptake was caused by either a reduced rate of hygroscopic growth due to the presence of organic films, or organic-inorganic interactions in solution droplets that had a negative effect on hygroscopicity. Mixed organic-inorganic particles were rarely observed by the VH-TDMA during the summer campaign conducted at Mace Head. The majority of particles below 100 nm in clean, marine air appeared to be sulphates neutralised to varying degrees by ammonia. On one unique day, 26 June 2007, particularly large concentrations of sulphate aerosol were observed and identified as volcanic emissions from Iceland. The degree of neutralisation of the sulphate aerosol by ammonia was calculated by the VH-TDMA and found to compare well with the same quantity measured by an aerosol mass spectrometer. This was an important verification of the VH-TMDA‘s ability to identify ammoniated sulphate aerosols based on the simultaneous measurement of aerosol volatility and hygroscopicity. A series of measurements were also conducted on sea spray aerosols generated from Moreton Bay seawater samples in a laboratory-based bubble chamber. Accumulation mode sea spray particles (38-173 nm) were found to contain only a minor organic fraction (< 10%) that had little effect on particle hygroscopicity. These results are important because previous studies have observed that accumulation mode sea spray particles are predominantly organic (~80% organic mass fraction). The work presented here suggests that this is not always the case, and that there may be currently unknown factors that are controlling the transfer of organics to the aerosol phase during the bubble bursting process. Taken together, the results of this research program have significantly improved our understanding of organic-containing marine aerosols and the way they interact with water vapour in the atmosphere.

Using Bayesian methods for the estimation of uncertainty in complex statistical models

The research objectives of this thesis were to contribute to Bayesian statistical methodology by contributing to risk assessment statistical methodology, and to spatial and spatio-temporal methodology, by modelling error structures using complex hierarchical models. Specifically, I hoped to consider two applied areas, and use these applications as a springboard for developing new statistical methods as well as undertaking analyses which might give answers to particular applied questions. Thus, this thesis considers a series of models, firstly in the context of risk assessments for recycled water, and secondly in the context of water usage by crops. The research objective was to model error structures using hierarchical models in two problems, namely risk assessment analyses for wastewater, and secondly, in a four dimensional dataset, assessing differences between cropping systems over time and over three spatial dimensions. The aim was to use the simplicity and insight afforded by Bayesian networks to develop appropriate models for risk scenarios, and again to use Bayesian hierarchical models to explore the necessarily complex modelling of four dimensional agricultural data. The specific objectives of the research were to develop a method for the calculation of credible intervals for the point estimates of Bayesian networks; to develop a model structure to incorporate all the experimental uncertainty associated with various constants thereby allowing the calculation of more credible credible intervals for a risk assessment; to model a single day’s data from the agricultural dataset which satisfactorily captured the complexities of the data; to build a model for several days’ data, in order to consider how the full data might be modelled; and finally to build a model for the full four dimensional dataset and to consider the timevarying nature of the contrast of interest, having satisfactorily accounted for possible spatial and temporal autocorrelations. This work forms five papers, two of which have been published, with two submitted, and the final paper still in draft. The first two objectives were met by recasting the risk assessments as directed, acyclic graphs (DAGs). In the first case, we elicited uncertainty for the conditional probabilities needed by the Bayesian net, incorporated these into a corresponding DAG, and used Markov chain Monte Carlo (MCMC) to find credible intervals, for all the scenarios and outcomes of interest. In the second case, we incorporated the experimental data underlying the risk assessment constants into the DAG, and also treated some of that data as needing to be modelled as an ‘errors-invariables’ problem [Fuller, 1987]. This illustrated a simple method for the incorporation of experimental error into risk assessments. In considering one day of the three-dimensional agricultural data, it became clear that geostatistical models or conditional autoregressive (CAR) models over the three dimensions were not the best way to approach the data. Instead CAR models are used with neighbours only in the same depth layer. This gave flexibility to the model, allowing both the spatially structured and non-structured variances to differ at all depths. We call this model the CAR layered model. Given the experimental design, the fixed part of the model could have been modelled as a set of means by treatment and by depth, but doing so allows little insight into how the treatment effects vary with depth. Hence, a number of essentially non-parametric approaches were taken to see the effects of depth on treatment, with the model of choice incorporating an errors-in-variables approach for depth in addition to a non-parametric smooth. The statistical contribution here was the introduction of the CAR layered model, the applied contribution the analysis of moisture over depth and estimation of the contrast of interest together with its credible intervals. These models were fitted using WinBUGS [Lunn et al., 2000]. The work in the fifth paper deals with the fact that with large datasets, the use of WinBUGS becomes more problematic because of its highly correlated term by term updating. In this work, we introduce a Gibbs sampler with block updating for the CAR layered model. The Gibbs sampler was implemented by Chris Strickland using pyMCMC [Strickland, 2010]. This framework is then used to consider five days data, and we show that moisture in the soil for all the various treatments reaches levels particular to each treatment at a depth of 200 cm and thereafter stays constant, albeit with increasing variances with depth. In an analysis across three spatial dimensions and across time, there are many interactions of time and the spatial dimensions to be considered. Hence, we chose to use a daily model and to repeat the analysis at all time points, effectively creating an interaction model of time by the daily model. Such an approach allows great flexibility. However, this approach does not allow insight into the way in which the parameter of interest varies over time. Hence, a two-stage approach was also used, with estimates from the first-stage being analysed as a set of time series. We see this spatio-temporal interaction model as being a useful approach to data measured across three spatial dimensions and time, since it does not assume additivity of the random spatial or temporal effects.

Comparison of three-dimensional profiles over time

In this paper, we describe an analysis for data collected on a three-dimensional spatial lattice with treatments applied at the horizontal lattice points. Spatial correlation is accounted for using a conditional autoregressive model. Observations are defined as neighbours only if they are at the same depth. This allows the corresponding variance components to vary by depth. We use the Markov chain Monte Carlo method with block updating, together with Krylov subspace methods, for efficient estimation of the model. The method is applicable to both regular and irregular horizontal lattices and hence to data collected at any set of horizontal sites for a set of depths or heights, for example, water column or soil profile data. The model for the three-dimensional data is applied to agricultural trial data for five separate days taken roughly six months apart in order to determine possible relationships over time. The purpose of the trial is to determine a form of cropping that leads to less moist soils in the root zone and beyond.We estimate moisture for each date, depth and treatment accounting for spatial correlation and determine relationships of these and other parameters over time.

PySSM : a Python module for Bayesian inference of linear Gaussian state space models

PySSM is a Python package that has been developed for the analysis of time series using linear Gaussian state space models (SSM). PySSM is easy to use; models can be set up quickly and efficiently and a variety of different settings are available to the user. It also takes advantage of scientific libraries Numpy and Scipy and other high level features of the Python language. PySSM is also used as a platform for interfacing between optimised and parallelised Fortran routines. These Fortran routines heavily utilise Basic Linear Algebra (BLAS) and Linear Algebra Package (LAPACK) functions for maximum performance. PySSM contains classes for filtering, classical smoothing as well as simulation smoothing.

A practical approach for identifying expected solution performance and robustness in operations research applications

A practical approach for identifying solution robustness is proposed for situations where parameters are uncertain. The approach is based upon the interpretation of a probability density function (pdf) and the definition of three parameters that describe how significant changes in the performance of a solution are deemed to be. The pdf is constructed by interpreting the results of simulations. A minimum number of simulations are achieved by updating the mean, variance, skewness and kurtosis of the sample using computationally efficient recursive equations. When these criterions have converged then no further simulations are needed. A case study involving several no-intermediate storage flow shop scheduling problems demonstrates the effectiveness of the approach.

“A problem of versions” : laying down the law in the school playground

Purpose This chapter investigates an episode where a supervising teacher on playground duty asks two boys to each give an account of their actions over an incident that had just occurred on some climbing equipment in the playground. Methodology This paper employs an ethnomethodological approach using conversation analysis. The data are taken from a corpus of video recorded interactions of children, aged 7-9 years, and the teacher, in school playgrounds during the lunch recess. Findings The findings show the ways that children work up accounts of their playground practices when asked by the teacher. The teacher initially provided interactional space for each child to give their version of the events. Ultimately, the teacher’s version of how to act in the playground became the sanctioned one. The children and the teacher formulated particular social orders of behavior in the playground through multi-modal devices, direct reported speech and scripts. Such public displays of talk work as socialization practices that frame teacher-sanctioned morally appropriate actions in the playground. Value of paper This chapter shows the pervasiveness of the teacher’s social order, as she presented an institutional social order of how to interact in the playground, showing clearly the disjunction of adult-child orders between the teacher and children.

Disputes in Everyday Life : Social and Moral Orders of Children and Young People

"The research presented in this volume has been undertaken in a range of settings and across ages, to display the rich, varied, and complex aspects of children and young people's everyday lives. The papers contribute to understanding children's disputes, framed as forms of social practice, by closely examining children's talk and interaction in disputes to offer insight into how they arrange their social lives within the context of school, home, neighborhood, correctional, and cafe settings. As such, this volume contributes to an emerging body of edited volumes that investigate children and young people's everyday interactions (Cromdal, 2009; Cromdal & Tholander, in press; Gardner & Forrester, 2010; Goodwin & Kyratzis, 2007; Hutchby & Moran-Ellis, 1998). Each paper has been peer reviewed, by respected researchers of the field, in some cases authors of this volume, and revised. We also thank Charlotte Cobb-Moore who so ably assisted in the final preparation of the manuscripts."---publisher website