Projected sequential Gaussian processes:a C++ tool for interpolation of large datasets with heterogeneous noise

Heterogeneous datasets arise naturally in most applications due to the use of a variety of sensors and measuring platforms. Such datasets can be heterogeneous in terms of the error characteristics and sensor models. Treating such data is most naturally accomplished using a Bayesian or model-based geostatistical approach; however, such methods generally scale rather badly with the size of dataset, and require computationally expensive Monte Carlo based inference. Recently within the machine learning and spatial statistics communities many papers have explored the potential of reduced rank representations of the covariance matrix, often referred to as projected or fixed rank approaches. In such methods the covariance function of the posterior process is represented by a reduced rank approximation which is chosen such that there is minimal information loss. In this paper a sequential Bayesian framework for inference in such projected processes is presented. The observations are considered one at a time which avoids the need for high dimensional integrals typically required in a Bayesian approach. A C++ library, gptk, which is part of the INTAMAP web service, is introduced which implements projected, sequential estimation and adds several novel features. In particular the library includes the ability to use a generic observation operator, or sensor model, to permit data fusion. It is also possible to cope with a range of observation error characteristics, including non-Gaussian observation errors. Inference for the covariance parameters is explored, including the impact of the projected process approximation on likelihood profiles. We illustrate the projected sequential method in application to synthetic and real datasets. Limitations and extensions are discussed. © 2010 Elsevier Ltd.

Supporting learners’ agentic engagement with feedback:a systematic review and a taxonomy of recipience processes

Much has been written in the educational psychology literature about effective feedback and how to deliver it. However, it is equally important to understand how learners actively receive, engage with, and implement feedback. This article reports a systematic review of the research evidence pertaining to this issue. Through an analysis of 195 outputs published between 1985 and early 2014, we identified various factors that have been proposed to influence the likelihood of feedback being used. Furthermore, we identified diverse interventions with the common aim of supporting and promoting learners' agentic engagement with feedback processes. We outline the various components used in these interventions, and the reports of their successes and limitations. Moreover we propose a novel taxonomy of four recipience processes targeted by these interventions. This review and taxonomy provide a theoretical basis for conceptualizing learners' responsibility within feedback dialogues and for guiding the strategic design and evaluation of interventions. Receiving feedback on one's skills and understanding is an invaluable part of the learning process, benefiting learners far more than does simply receiving praise or punishment (Black & Wiliam, 1998 Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education: Principles, Policy & Practice, 5, 7–74. doi:10.1080/0969595980050102[Taylor & Francis Online]; Hattie & Timperley, 2007 Hattie, J., & Timperley, H. (2007). The power of feedback. Review of Educational Research, 77, 81–112. doi:10.3102/003465430298487[CrossRef], [Web of Science ®]). Inevitably, the benefits of receiving feedback are not uniform across all circumstances, and so it is imperative to understand how these gains can be maximized. There is increasing consensus that a critical determinant of feedback effectiveness is the quality of learners' engagement with, and use of, the feedback they receive. However, studies investigating this engagement are underrepresented in academic research (Bounds et al., 2013 Bounds, R., Bush, C., Aghera, A., Rodriguez, N., Stansfield, R. B., & Santeen, S. A. (2013). Emergency medicine residents' self-assessments play a critical role when receiving feedback. Academic Emergency Medicine, 20, 1055–1061. doi:10.1111/acem.12231[CrossRef], [PubMed], [Web of Science ®]), which leaves a “blind spot” in our understanding (Burke, 2009 Burke, D. (2009). Strategies for using feedback students bring to higher education. Assessment & Evaluation in Higher Education, 34, 41–50. doi:10.1080/02602930801895711[Taylor & Francis Online], [Web of Science ®]). With this blind spot in mind, the present work sets out to systematically map the research literature concerning learners' proactive recipience of feedback. We use the term “proactive recipience” here to connote a state or activity of engaging actively with feedback processes, thus emphasizing the fundamental contribution and responsibility of the learner (Winstone, Nash, Rowntree, & Parker, in press Winstone, N. E., Nash, R. A., Rowntree, J., & Parker, M. (in press). ‘It'd be useful, but I wouldn't use it’: Barriers to university students' feedback seeking and recipience. Studies in Higher Education. doi: 10.1080/03075079.2015.1130032[Taylor & Francis Online]). In other words, just as Reeve and Tseng (2011 Reeve, J., & Tseng, M. (2011). Agency as a fourth aspect of student engagement during learning activities. Contemporary Educational Psychology, 36, 257–267. doi:10.1016/j.cedpsych.2011.05.002[CrossRef], [Web of Science ®]) defined “agentic engagement” as a “student's constructive contribution into the flow of the instruction they receive” (p. 258), likewise proactive recipience is a form of agentic engagement that involves the learner sharing responsibility for making feedback processes effective.

Quantitative analysis of solid-state processes studied with isothermal microcalorimetry

Quantitative analysis of solid-state processes from isothermal microcalorimetric data is straightforward if data for the total process have been recorded and problematic (in the more likely case) when they have not. Data are usually plotted as a function of fraction reacted (α); for calorimetric data, this requires knowledge of the total heat change (Q) upon completion of the process. Determination of Q is difficult in cases where the process is fast (initial data missing) or slow (final data missing). Here we introduce several mathematical methods that allow the direct calculation of Q by selection of data points when only partial data are present, based on analysis with the Pérez-Maqueda model. All methods in addition allow direct determination of the reaction mechanism descriptors m and n and from this the rate constant, k. The validity of the methods is tested with the use of simulated calorimetric data, and we introduce a graphical method for generating solid-state power-time data. The methods are then applied to the crystallization of indomethacin from a glass. All methods correctly recovered the total reaction enthalpy (16.6 J) and suggested that the crystallization followed an Avrami model. The rate constants for crystallization were determined to be 3.98 × 10-6, 4.13 × 10-6, and 3.98 × 10 -6 s-1 with methods 1, 2, and 3, respectively. © 2010 American Chemical Society.