Design flood estimation is often required in hydrologic practice. For catchments with sufficient streamflow data, design floods can be obtained using flood frequency analysis. For catchments with no or little streamflow data (ungauged catchments), design flood estimation is a difficult task. The currently recommended method in Australia for design flood estimation in ungauged catchments is known as the Probabilistic Rational Method. There are alternatives to this method such as Quantile Regression Technique or Index Flood Method. All these methods give the flood peak estimate but the full streamflow hydrograph is required for many applications. The currently recommended rainfall based flood estimation method in Australia that can estimate full streamflow hydrograph is known as the Design Event Approach. This considers the probabilistic nature of rainfall depth but ignores the probabilistic behavior of other flood producing variables such as rainfall temporal pattern and initial loss, and thus this is likely to produce probability bias in final flood estimates. Joint Probability Approach is a superior method of design flood estimation which considers the probabilistic nature of the input variables (such as rainfall temporal pattern and initial loss) in the rainfall-runoff modelling. Rahman et al. (2002) developed a simple Monte Carlo Simulation technique based on the principles of joint probability, which is applicable to gauged catchments. This thesis extends the Monte Carlo Simulation technique to ungauged catchments. The Joint Probability Approach/ Monte Carlo Simulation Technique requires identification of the distributions of the input variables to the rainfall-runoff model e.g. rainfall duration, rainfall intensity, rainfall temporal pattern, and initial loss. For gauged catchments, these probability distributions are identified from observed rainfall and/or streamflow data. For application of the Joint Probability Approach to ungauged catchments, the distributions of the input variables need to be regionalised. This thesis, in particular, investigates the regionalisation of the distribution of rainfall duration and intensity. In this thesis, it is hypothesised that the distribution of storm duration can be described by Exponential distribution. The developed new technique of design flood estimation can provide the full hydrograph rather than only peak value as with the Probabilistic Rational Method and Quantile Regression Technique. The developed new technique can further be improved by addition of new and improved regional estimation equations for the initial loss, continuing loss and storage delay parameter (k) as and when these are available. / (M. Eng.) (Hons)

This study aimed to investigate students' models of probability in a modern physics context. The study was divided into three phases. The first phase explored student pre-knowledge about probability before modem physics instruction. The second phase investigated student understanding of concepts related to probability such as wave-particle behavior, the uncertainty principle, and localization. The third phase probed how students used the wave function to interpret probability in potential energy problems. The participants were students taking modem physics at Oregon State University. In the first phase, we developed a diagnostic test to probe mathematical probability misconceptions and probability in a classical physics content. For the mathematical probability misconceptions part, we found that students often used a randomly distributed expectancy resource to predict an outcome of a random event. For classical probability, we found that students often employed an object's speed to predict the probability of locating it in a certain region, which we call a classical probability reasoning resource. In the second and the third phases, we interviewed students in order to get more in-depth data. We also report the findings from Fall 03 preliminary interviews which indicated the need for a more detail theoretical framework to analyze student reasoning. Therefore, we employed the framework proposed by Redish (2003) to analyze the interview data into two perspectives - reasoning resources and epistemic resources. We found that most students used a classical probability resource to interpret the probability from the wave function. Additionally, we identified two associated patterns that students used to describe the traveling wave function in the potential step and barrier. Finally, we discuss some teaching implications and future research that the findings suggested. / Graduation date: 2005

Logic Sampling, Likelihood Weighting and AIS-BN are three variants of stochastic sampling, one class of approximate inference for Bayesian networks. We summarize the ideas underlying each algorithm and the relationship among them. The results from a set of empirical experiments comparing Logic Sampling, Likelihood Weighting and AIS-BN are presented. We also test the impact of each of the proposed heuristics and learning method separately and in combination in order to give a deeper look into AIS-BN, and see how the heuristics and learning method contribute to the power of the algorithm. Key words: belief network, probability inference, Logic Sampling, Likelihood Weighting, Importance Sampling, Adaptive Importance Sampling Algorithm for Evidential Reasoning in Large Bayesian Networks(AIS-BN), Mean Percentage Error (MPE), Mean Square Error (MSE), Convergence Rate, heuristic, learning method. / Graduation date: 2002

As a result of the calls for reform in mathematics education and the ever-changing nature of mathematics, today's teachers face the challenge of teaching unfamiliar content in ways that are equally unfamiliar. In view of this challenge, the purpose of this study was to investigate middle school teachers' subject matter and pedagogical content knowledge of probability and its relationship to the teaching of probability. The study also explored the nature of the instructional tasks and classroom discourse during probability instruction. Case study methodology was used to examine the knowledge and practice of 4 middle school teachers. A pre-observation interview assessed the teachers' subject matter knowledge of probability. The teachers were then observed as they taught probability. Post-observation interviews further explored teacher knowledge and its relationship to teaching practice. Data sources included interview transcripts, observational field notes, video and audiotapes of classroom instruction, and written instructional documents. Individual case studies were written describing the teachers' background and probability instruction. Cross-case analyses compared and contrasted the cases in response to the research questions. The results of this study indicate the teachers generally (a) lacked an explicit and connected knowledge of probability content, (b) held traditional views about mathematics and the learning and teaching of mathematics, (c) lacked an understanding of the "big ideas" to be emphasized in probability instruction, (d) lacked knowledge of students' possible conceptions and misconceptions, (e) lacked the knowledge and skills needed to orchestrate discourse in ways that promoted students' higher level learning, and (f) lacked an integrated understanding of the nature of the reform. One teacher captured the essence of the reform effort in her probability instruction; the other 3 teachers generally fell short of the goal despite their efforts to implement aspects of the reform. Although students were actively involved in exploring probability content through the use of games, simulations, and other hands-on instructional tasks, the cognitive level of the tasks and discourse was limited by the nature of instruction. The findings of this study have implications for mathematics education reform, preservice teacher preparation, staff development, and curriculum development. / Graduation date: 1998

No description available.

Jack Hilibrand. / "September 7, 1956." "This report is based on a thesis that was submitted to the Department of Electrical Engineering, August 1956, in partial fulfillment of the requirements for the degree of Doctor of Science, Massachusetts Institute of Technology." / Bibliography: p. 50-51. / Army Signal Corps Contract DA36-039-sc-64637 Dept. of the Army Task 3-99-06-108 Project 3-99-00-100

The CWB has the stated objective of increasing producer returns through maximizing sales revenue and minimizing operating costs. To maximize producer returns the CWB derives value from single-desk selling, price pooling and the initial price guarantee.<p> The initial price allows the CWB to offer a price floor to producers which is guaranteed by the Federal government. This guarantee has come under review in recent World Trade Organization (WTO) negotiations with opponents stating that the Federal government is unfairly subsidizing producers. Therefore developing methods to hedge the initial payment and remove the CWB dependency on the Federal government guarantee has taken on considerable importance.<p> Hedging the initial price has two components, the first is commodity risk, and the second is currency risk. Commodity risk basically consists of the risk that wheat prices decrease significantly from the announcement of the initial payment resulting in a wheat pool account deficit. Currency risk relates to the risk of the Canadian dollar (CAD) increasing vis-à-vis the United States dollar (USD) resulting in lower wheat prices. This is due to the fact most sales are made in USD, necessitating the conversion of USD for CAD in order to pay Canadian producers. Given recent increases in exchange rate volatility this later risk is important. <p> The goal of this study is to evaluate the currency risk present in the initial payment and to examine alternate means of mitigating this risk. A number of call option strategies will be evaluated to determine its ability to reduce the probability of a wheat pool account deficit by offsetting the effect of a rising CAD.<p> The policy variables analyzed in the thesis are the initial payment as a percentage of the Pool Return Outlook for wheat and the strike price of the call options purchased. Therefore the study will examine the effect of inputting varying initial payment levels and different strike prices for the call options in the model. This will allow for quantifiable insight into cost versus risk reduction comparisons. These comparisons will be useful in determining the most efficient mode of action for the CWB.

The CWB has the stated objective of increasing producer returns through maximizing sales revenue and minimizing operating costs. To maximize producer returns the CWB derives value from single-desk selling, price pooling and the initial price guarantee.<p> The initial price allows the CWB to offer a price floor to producers which is guaranteed by the Federal government. This guarantee has come under review in recent World Trade Organization (WTO) negotiations with opponents stating that the Federal government is unfairly subsidizing producers. Therefore developing methods to hedge the initial payment and remove the CWB dependency on the Federal government guarantee has taken on considerable importance.<p> Hedging the initial price has two components, the first is commodity risk, and the second is currency risk. Commodity risk basically consists of the risk that wheat prices decrease significantly from the announcement of the initial payment resulting in a wheat pool account deficit. Currency risk relates to the risk of the Canadian dollar (CAD) increasing vis-à-vis the United States dollar (USD) resulting in lower wheat prices. This is due to the fact most sales are made in USD, necessitating the conversion of USD for CAD in order to pay Canadian producers. Given recent increases in exchange rate volatility this later risk is important. <p> The goal of this study is to evaluate the currency risk present in the initial payment and to examine alternate means of mitigating this risk. A number of call option strategies will be evaluated to determine its ability to reduce the probability of a wheat pool account deficit by offsetting the effect of a rising CAD.<p> The policy variables analyzed in the thesis are the initial payment as a percentage of the Pool Return Outlook for wheat and the strike price of the call options purchased. Therefore the study will examine the effect of inputting varying initial payment levels and different strike prices for the call options in the model. This will allow for quantifiable insight into cost versus risk reduction comparisons. These comparisons will be useful in determining the most efficient mode of action for the CWB.

Zugl.: @Delft, Techn. University, Diss., 2006.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 132-137). Also available on the Internet.