A sequential Monte Carlo algorithm to incorporate model uncertainty in Bayesian sequential design

Here we present a sequential Monte Carlo (SMC) algorithm that can be used for any one-at-a-time Bayesian sequential design problem in the presence of model uncertainty where discrete data are encountered. Our focus is on adaptive design for model discrimination but the methodology is applicable if one has a different design objective such as parameter estimation or prediction. An SMC algorithm is run in parallel for each model and the algorithm relies on a convenient estimator of the evidence of each model which is essentially a function of importance sampling weights. Other methods for this task such as quadrature, often used in design, suffer from the curse of dimensionality. Approximating posterior model probabilities in this way allows us to use model discrimination utility functions derived from information theory that were previously difficult to compute except for conjugate models. A major benefit of the algorithm is that it requires very little problem specific tuning. We demonstrate the methodology on three applications, including discriminating between models for decline in motor neuron numbers in patients suffering from neurological diseases such as Motor Neuron disease.

A sequential Monte Carlo approach to the sequential design for discriminating between rival continuous data models

Here we present a sequential Monte Carlo approach to Bayesian sequential design for the incorporation of model uncertainty. The methodology is demonstrated through the development and implementation of two model discrimination utilities; mutual information and total separation, but it can also be applied more generally if one has different experimental aims. A sequential Monte Carlo algorithm is run for each rival model (in parallel), and provides a convenient estimate of the marginal likelihood (of each model) given the data, which can be used for model comparison and in the evaluation of utility functions. A major benefit of this approach is that it requires very little problem specific tuning and is also computationally efficient when compared to full Markov chain Monte Carlo approaches. This research is motivated by applications in drug development and chemical engineering.

A pseudo-marginal sequential Monte Carlo algorithm for random effects models in Bayesian sequential design

A computationally efficient sequential Monte Carlo algorithm is proposed for the sequential design of experiments for the collection of block data described by mixed effects models. The difficulty in applying a sequential Monte Carlo algorithm in such settings is the need to evaluate the observed data likelihood, which is typically intractable for all but linear Gaussian models. To overcome this difficulty, we propose to unbiasedly estimate the likelihood, and perform inference and make decisions based on an exact-approximate algorithm. Two estimates are proposed: using Quasi Monte Carlo methods and using the Laplace approximation with importance sampling. Both of these approaches can be computationally expensive, so we propose exploiting parallel computational architectures to ensure designs can be derived in a timely manner. We also extend our approach to allow for model uncertainty. This research is motivated by important pharmacological studies related to the treatment of critically ill patients.

Sequential design of decentralized control systems

Our main result is a new sequential method for the design of decentralized control systems. Controller synthesis is conducted on a loop-by-loop basis, and at each step the designer obtains an explicit characterization of the class C of all compensators for the loop being closed that results in closed-loop system poles being in a specified closed region D of the s-plane, instead of merely stabilizing the closed-loop system. Since one of the primary goals of control system design is to satisfy basic performance requirements that are often directly related to closed-loop pole location (bandwidth, percentage overshoot, rise time, settling time), this approach immediately allows the designer to focus on other concerns such as robustness and sensitivity. By considering only compensators from class C and seeking the optimum member of that set with respect to sensitivity or robustness, the designer has a clearly-defined limited optimization problem to solve without concern for loss of performance. A solution to the decentralized tracking problem is also provided. This design approach has the attractive features of expandability, the use of only 'local models' for controller synthesis, and fault tolerance with respect to certain types of failure.

An adaptive group sequential design for phase II/III clinical trials that select a single treatment from several

There is increasing interest in combining Phases II and III of clinical development into a single trial in which one of a small number of competing experimental treatments is ultimately selected and where a valid comparison is made between this treatment and the control treatment. Such a trial usually proceeds in stages, with the least promising experimental treatments dropped as soon as possible. In this paper we present a highly flexible design that uses adaptive group sequential methodology to monitor an order statistic. By using this approach, it is possible to design a trial which can have any number of stages, begins with any number of experimental treatments, and permits any number of these to continue at any stage. The test statistic used is based upon efficient scores, so the method can be easily applied to binary, ordinal, failure time, or normally distributed outcomes. The method is illustrated with an example, and simulations are conducted to investigate its type I error rate and power under a range of scenarios.

How a sequential design would have affected the GAIN international study of Gavestinel in stroke

While planning the GAIN International Study of gavestinel in acute stroke, a sequential triangular test was proposed but not implemented. Before the trial commenced it was agreed to evaluate the sequential design retrospectively to evaluate the differences in the resulting analyses, trial durations and sample sizes in order to assess the potential of sequential procedures for future stroke trials. This paper presents four sequential reconstructions of the GAIN study made under various scenarios. For the data as observed, the sequential design would have reduced the trial sample size by 234 patients and shortened its duration by 3 or 4 months. Had the study not achieved a recruitment rate that far exceeded expectation, the advantages of the sequential design would have been much greater. Sequential designs appear to be an attractive option for trials in stroke. Copyright 2004 S. Karger AG, Basel

Adaptive and Maladaptive Correlates of Repetitive Behavior and Restricted Interests in Persons with Down Syndrome and Developmentally-Matched Typical Children: A Two-Year Longitudinal Sequential Design

We examined the course of repetitive behavior and restricted interests (RBRI) in children with and without Down syndrome (DS) over a two-year time period. Forty-two typically-developing children and 43 persons with DS represented two mental age (MA) levels: `` younger'' 2-4 years; `` older'' 5-11 years. For typically developing younger children some aspects of RBRI increased from Time 1 to Time 2. In older children, these aspects remained stable or decreased over the two-year period. For participants with DS, RBRI remained stable or increased over time. Time 1 RBRI predicted Time 2 adaptive behavior (measured by the Vineland Scales) in typically developing children, whereas for participants with DS, Time 1 RBRI predicted poor adaptive outcome (Child Behavior Checklist) at Time 2. The results add to the body of literature examining the adaptive and maladaptive nature of repetitive behavior.

Optimal static and sequential design : a critical review

The aim of this thesis is to review and augment the theory and methods of optimal experimental design. In Chapter I the scene is set by considering the possible aims of an experimenter prior to an experiment, the statistical methods one might use to achieve those aims and how experimental design might aid this procedure. It is indicated that, given a criterion for design, a priori optimal design will only be possible in certain instances and, otherwise, some form of sequential procedure would seem to be indicated. In Chapter 2 an exact experimental design problem is formulated mathematically and is compared with its continuous analogue. Motivation is provided for the solution of this continuous problem, and the remainder of the chapter concerns this problem. A necessary and sufficient condition for optimality of a design measure is given. Problems which might arise in testing this condition are discussed, in particular with respect to possible non-differentiability of the criterion function at the design being tested. Several examples are given of optimal designs which may be found analytically and which illustrate the points discussed earlier in the chapter. In Chapter 3 numerical methods of solution of the continuous optimal design problem are reviewed. A new algorithm is presented with illustrations of how it should be used in practice. It is shown that, for reasonably large sample size, continuously optimal designs may be approximated to well by an exact design. In situations where this is not satisfactory algorithms for improvement of this design are reviewed. Chapter 4 consists of a discussion of sequentially designed experiments, with regard to both the philosophies underlying, and the application of the methods of, statistical inference. In Chapter 5 we criticise constructively previous suggestions for fully sequential design procedures. Alternative suggestions are made along with conjectures as to how these might improve performance. Chapter 6 presents a simulation study, the aim of which is to investigate the conjectures of Chapter 5. The results of this study provide empirical support for these conjectures. In Chapter 7 examples are analysed. These suggest aids to sequential experimentation by means of reduction of the dimension of the design space and the possibility of experimenting semi-sequentially. Further examples are considered which stress the importance of the use of prior information in situations of this type. Finally we consider the design of experiments when semi-sequential experimentation is mandatory because of the necessity of taking batches of observations at the same time. In Chapter 8 we look at some of the assumptions which have been made and indicate what may go wrong where these assumptions no longer hold.

An analysis of holding cost impact on housing affordability in relation to midsized Greenfield residential property developments in South East Queensland

The position of housing demand and supply is not consistent. The Australian situation counters the experience demonstrated in many other parts of the world in the aftermath of the Global Financial Crisis, with residential housing prices proving particularly resilient. A seemingly inexorable housing demand remains a critical issue affecting the socio-economic landscape. Underpinned by high levels of population growth fuelled by immigration, and further buoyed by sustained historically low interest rates, increasing income levels, and increased government assistance for first home buyers, this strong housing demand level ensures problems related to housing affordability continue almost unabated. A significant, but less visible factor impacting housing affordability relates to holding costs. Although only one contributor in the housing affordability matrix, the nature and extent of holding cost impact requires elucidation: for example, the computation and methodology behind the calculation of holding costs varies widely - and in some instances completely ignored. In addition, ambiguity exists in terms of the inclusion of various elements that comprise holding costs, thereby affecting the assessment of their relative contribution. Such anomalies may be explained by considering that assessment is conducted over time in an ever-changing environment. A strong relationship with opportunity cost - in turn dependant inter alia upon prevailing inflation and / or interest rates - adds further complexity. By extending research in the general area of housing affordability, this thesis seeks to provide a detailed investigation of those elements related to holding costs specifically in the context of midsized (i.e. between 15-200 lots) greenfield residential property developments in South East Queensland. With the dimensions of holding costs and their influence over housing affordability determined, the null hypothesis H0 that holding costs are not passed on can be addressed. Arriving at these conclusions involves the development of robust economic and econometric models which seek to clarify the componentry impacts of holding cost elements. An explanatory sequential design research methodology has been adopted, whereby the compilation and analysis of quantitative data and the development of an economic model is informed by the subsequent collection and analysis of primarily qualitative data derived from surveying development related organisations. Ultimately, there are significant policy implications in relation to the framework used in Australian jurisdictions that promote, retain, or otherwise maximise, the opportunities for affordable housing.

Ist der Ernährungsführerschein eine geeignete Primärpräventionsmaßnahme, um die Ernährungssituation zu verbessern?

Das Ernährungsverhalten einer Bevölkerung hat einen wesentlichen Einfluss auf das Wohlbefinden, die Gesundheit und Leistungsfähigkeit der Menschen. Ernährungsbedingte, chronische Erkrankungen weisen in den westlichen Industrienationen eine hohe Inzidenz und Prävalenz auf. Präventionsmaßnahmen im Setting Schule sollen das Ernährungsverhalten der Kinder- und Jugendlichen positiv beeinflussen. Gerade in diesem Setting können Personen mit unterschiedlichem sozioökonomischem Status, sowie Personen aus diversen Lebensbereichen angesprochen werden. Der Ernährungsführerschein (EFS) ist eine schulbasierte Primärpräventions-maßnahme, der in der 3. Jahrgangsstufe/Grundschule durchgeführt wird. In 6 – 7 Unterrichtseinheiten erfolgt eine praxisnahe Vermittlung von Grundkenntnissen über Ernährung, Lebensmittel und deren Zubereitung. Der EFS möchte eine Verhaltensänderung der Schulkinder bewirken. Sie erlernen Kompetenzen, damit sie in der Lage sind, sich selbst eine gesunde Mahlzeit zubereiten zu können. Aber kann dieses Projekt eine nachhaltige Verhaltensänderung bewirken? Die folgende Studie mit Mixed-Methods-Ansatz im Explanatory-Sequential-Design versucht genau dieser Frage nachzugehen. Auf eine quantitative Prä- und Postbefragung in 16 Klassen an 12 Grundschulen im Landkreis Marburg Biedenkopf und insgesamt 992 Befragungen folgte eine qualitative Studie mit neun problemzentrierten, leitfadengestützten Interviews. Der EFS zeigt keinen signifikanten Einfluss auf die Veränderung des Ernährungsverhaltens. Positiv zu bewerten ist, dass durch den EFS Alltagskompetenzen bei der Nahrungszubereitung gefördert wurden. Dieser positive Einfluss muss jedoch differenziert betrachtet werden, denn die qualitativen Studie zeigt, dass der EFS sehr gut in Familien aufgenommen wird, die sich bereits mit Ernährungsfragen auseinandersetzen und darauf achten, einen ernährungsphysiologisch günstigen Ernährungsstil zu leben oder anzustreben. In Familien der Billig- und Fleischesser konnte der EFS die Türen nicht öffnen. Aber gerade in diesem Segment wäre eine Veränderung des Essverhaltens induziert. Die Untersuchung ergab, dass der EFS für sich alleine nicht den Anspruch erheben kann, die Ernährungssituation der Kinder und Familien zu verbessern. Aber er bietet ein methodisch-didaktisch gut ausgearbeitetes Konzept und könnte als Baustein in die Entwicklung eines praxisnahen, erlebnisorientierten und ganzheitlichen Ernährungsbildungskonzepts unter Berücksichtigung diverser Settings und Lebenswelten der Kinder und Familien einfließen.

Perceptions Surrounding the Implementation of Colorado Senate Bill 10-191's New Teacher Evaluations

In 2013, many public education reform efforts in the United States of America center on testing and accountability. Recent data revealed that teachers have the single greatest in-school impact on student learning; however, the methods to assess teacher effectiveness are widely criticized for not holding teachers accountable and, consequently, are experiencing significant legislative attention. In 2010, Colorado passed Senate Bill 10-191: The Great Teachers and Leaders Act to improve student learning by revising teacher and principal evaluations, including linking them to student learning data, and eradicating tenure. Teachers, administrators, and policymakers hold critical roles in the implementation of this bill, yet little is known about how members of each group perceive their respective roles in the implementation. This explanatory sequential mixed methods study was designed to gather perception data from these three groups, through surveys and interviews. Data revealed that teachers and administrators do not have similar perceptions of many matters related to teacher evaluations, education reform, and the implementation of Senate Bill 10-191 (SB 191). The data also revealed that teachers and administrators expected they would agree on these matters. These collective findings led to multiple recommendations, such as the need for increased dialogue between teachers and administrators about their own perceptions of education reforms.