THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

Although uncertainty about structures of environmental models (conceptual uncertainty) is often acknowledged to be the main source of uncertainty in model predictions, it is rarely considered in environmental modelling. Rather, formal uncertainty analyses have traditionally focused on model parameters and input data as the principal source of uncertainty in model predictions. The traditional approach to model uncertainty analysis, which considers only a single conceptual model, may fail to adequately sample the relevant space of plausible conceptual models. As such, it is prone to modelling bias and underestimation of predictive uncertainty. In this paper we review a range of strategies for assessing structural uncertainties in models. The existing strategies fall into two categories depending on whether field data are available for the predicted variable of interest. To date, most research has focussed on situations where inferences on the accuracy of a model structure can be made directly on the basis of field data. This corresponds to a situation of ‘interpolation’. However, in many cases environmental models are used for ‘extrapolation’; that is, beyond the situation and the field data available for calibration. In the present paper, a framework is presented for assessing the predictive uncertainties of environmental models used for extrapolation. It involves the use of multiple conceptual models, assessment of their pedigree and reflection on the extent to which the sampled models adequately represent the space of plausible models. � 2005 Elsevier Ltd. All rights reserved.

A Framework for Dealing With Uncertainty due to Model Structure Error

The biodegradability and bioavailability of hydrolysis-limited substrates under anaerobic (and aerobic) conditions can be represented by two key parameters--degradability (f(d)), or the percentage that can be effectively be destroyed during digestion, and first order hydrolysis coefficient (k(hyd)), or the speed at which material breaks down. Biochemical methane potential (BMP) testing uses a batch test (in triplicate), and by fitting against a first order model, can fit both parameters in the same test. BMP testing is now being widely used for anaerobic process feasibility and design purposes, and standardisation efforts are ongoing. In this paper, we address a number of key issues relating to the test method and its analysis. This includes proposal of a new fitting and parameter estimation method, evaluation of the impact of inoculum to substrate ratio on fitted parameters, and comparison to performance in continuous systems. The new parameter estimation technique provides an estimate of parameter uncertainty and correlation, and is clearly more suitable than model transformation and linear regression. An inoculum volume ratio of at least 50% (2:1 on VS basis) was required on a cellulose substrate to use methane production as primary indicator, as found by comparing methane production and solubilisation of cellulose. Finally, on a typical material, waste activated sludge, the batch test was slightly conservative in terms of degradability and rate, indicating a bias in the BMP test. The test is a cost-effective and capable method to evaluate potential substrates, but it should be noted that it is generally conservative, especially if sub-optimal inoculum is used.

Assessing the role of biochemical methane potential tests in determining anaerobic degradability rate and extent

Sriniketh Srinivasan

Papers

Variant and invariant states for chemical reaction systems

Data reconciliation for chemical reaction systems using vessel extents and shape constraints

Extent-based incremental identification of reaction systems using concentration and calorimetric measurements

Extent-based Kinetic Identification using Spectroscopic Measurements and Multivariate Calibration

Variant and Invariant States for Reaction Systems