Environmental models are important tools; however uncertainty is pervasive in the modeling process.   Current research has shown that under­standing and representing these uncertainties is critical when decisions are expected to be made from the modeling results.  One critical question has become: how focused should uncertainty intervals be with consideration of characteristics of uncertain input data, model equation representations, and output observations?   This thesis delves into this issue with applied research in four independent studies.  These studies developed a diverse array of simply-structured process models (catchment hydrology, soil carbon dynamics, wetland P cycling, stream rating); employed field data observations with wide ranging characteristics (e.g., spatial variability, suspected systematic error); and explored several variations of probabilistic and non-probabilistic uncertainty schemes for model calibrations.  A key focus has been on how the design of various schemes impacted the resulting uncertainty intervals, and more importantly the ability to justify conclusions.  In general, some uncertainty in uncertainty (u2) resulted in all studies, in various degrees.  Subjectivity was intrinsic in the non-probabilistic results.  One study illustrated that such subjectivity could be partly mitigated using a “limits of acceptability” scheme with posterior validation of errors.  u2 was also a factor from probabilistic calibration algorithms, as residual errors were not wholly stochastic.  Overall however, u2 was not a deterrent to drawing conclusions from each study. One insight on the value of data for modeling was that there can be substantial redundant information in some hydrological time series.  Several process insights resulted: there can be substantial fractions of relatively inert soil carbon in agricultural systems; the lowest achievable outflow phosphorus concentration in an engineered wetland seemed partly controlled by rapid turnover and decomposition of the specific vegetation in that system.  Additionally, consideration of uncertainties in a stage-discharge rating model enabled more confident detection of change in long-term river flow patterns. / <p>QC 20121105</p>

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If there is currency substitution, the central bank will lose independence in monetary policy even if the flexible exchange rate system is adopted. In this paper, we investigate the existence of currency substitution between Taiwan and the United States in an open economy during the period of the managed floating exchange rate system, and examine the role of the factor influencing monetary policy and domestic money demand function derived from a small-country portfolio balance approach. To take account of currency substitution, we use quarterly data over 1981-2005 period on the demand for money and include data on the real exchange rate in addition to real income, domestic nominal interest rate and foreign nominal interest rate. The methodology is based on an application of the Johansen and Juselius¡]1990¡^cointegration technique. Also use error correction model to discuss short-run dynamic adjustment processes of these variables. Application of the Augmented Dickey-Fuller test and Phillips-Perron test indeed reveal that all variables are integrated of order one. The result from the Johansen¡¦s maximum likelihood mehtod reveal that there is only one cointegrating vector among the variables. This implies that there is long-run equilibrium relationship among the variables. There is clear evidence that demand for money is affected not only by changes in domestic variables such as real income, domestic nominal interest rate but also by fluctuations in foreign nominal interest rate and real exchange rate. And the coefficiect of the real exchange rate is negative and statistically significant. That means currency substitution is significant factor in the domestic money demand equation and currency substitution indeed exists in Taiwan. This paper successfully provides a consistent result, currency substitution indeed exists in Taiwan. Therefore, to have an effective monetary policy, the monetary authorities should take into account the international factors.

Small area estimation is an arena that has seen rapid development in the past 50 years, due to its widespread applicability in government projects, marketing research and many other areas. However, it is often difficult to obtain error-free data for this purpose. In this dissertation, each project describes a model used for small area estimation in which the covariates are measured with error. We applied different methods of bias correction to improve the estimates of the parameter of interest in the small areas. There is a variety of methods available for bias correction of estimates in the presence of measurement error. We applied the simulation extrapolation (SIMEX), ordinary corrected scores and Monte Carlo corrected scores methods of bias correction in the Fay-Herriot model, and investigated the performance of the bias-corrected estimators. The performance of the estimators in the presence of non-normal measurement error and of the SIMEX estimator in the presence of non-additive measurement error was also studied. For each of these situations, we presented simulation studies to observe the performance of the proposed correction procedures. In addition, we applied our proposed methodology to analyze a real life, nontrivial data set and present the results. We showed that the Lohr-Ybarra estimator is slightly inefficient and that applying methods of bias correction like SIMEX, corrected scores or Monte Carlo corrected scores (MCCS) increases the efficiency of the small area estimates. In particular, we showed that the simulation based bias correction methods like SIMEX and MCCS provide a greater gain in efficiency. We also showed that the SIMEX method of bias correction is robust with respect to departures from normality or additivity of measurement error. We showed that the MCCS method is robust with respect to departure from normality of measurement error.

In this thesis I study the German housing market and specifically the level of housing investment. First, a theoretical background to housing market dynamics is presented and then I test whether there is a relationship between housing investments and GDP, the size of the population, Tobin’s Q and construction costs. An Error Correction Model is estimated and the result is that the equilibrium level of housing investment is restored after less then two quarters after a change in one of the explainable variables. The estimation indicates that GDP, the size of the population and construction costs affect the level of construction in the short run. However, in the long run the only significant effect is changes in construction cost.

In wireless communication systems, transmitted signals are corrupted by fading as well as noise. The receiver can benefit from the estimates of fading channels to detect the transmitted symbols. However, in practical wireless systems channel information cannot be estimated perfectly at the receiver. Therefore, it is crucial to examine the effect of channel estimation error on the structure and performance of the receivers. In the first part of the thesis, we study single-user systems with single-antenna reception over fading channels in the presence of Gaussian-distributed channel estimation error. By using the statistical information of the channel estimation error, we will derive the structure of maximum-likelihood receivers for a number of different modulation formats and then analyze their performance over fading channels. In the second part of the thesis, we consider the uplink of multi-user wireless systems with multi-antenna reception. For conventional diversity combining techniques such as maximal ratio combining and optimum combining we analyze the performance degradation due to imperfect channel estimates in the presence of multiple interfering users for several fading channels. By investigating the probability density function of the output signal-to-interference ratio, we will derive analytical expressions for several performance measures such as the average signal-to-interference ratio, outage probability and average bit-error probability. These expressions quantify performance degradation due to channel estimation error.

In regression analysis, random errors in an explanatory variable cause the usual estimates of its regression coefficient to be biased. Although this problem has been studied for many years, routine methods have not emerged. This thesis investigates some aspects of this problem in the setting of analysis of epidemiological data. A major premise is that methods to cope with this problem must account for the shape of the frequency distribution of the true covariable, e.g., exposure. This is not widely recognized, and many existing methods focus only on the variability of the true covariable, rather than on the shape of its distribution. Confusion about this issue is exacerbated by the existence of two classical models, one in which the covariable is a sample from a distribution and the other in which it is a collection of fixed values. A unified approach is taken here, in which for the latter of these models more attention than usual is given to the frequency distribution of the fixed values. In epidemiology the distribution of exposures is often very skewed, making these issues particularly important. In addition, the data sets can be very large, and another premise is that differences in the performance of methods are much greater when the samples are very large. Traditionally, methods have largely been evaluated by their ability to remove bias from the regression estimates. A third premise is that in large samples there may be various methods that will adequately remove the bias, but they may differ widely in how nearly they approximate the estimates that would be obtained using the unobserved true values. A collection of old and new methods is considered, representing a variety of basic rationales and approaches. Some comparisons among them are made on theoretical grounds provided by the unified model. Simulation results are given which tend to confirm the major premises of this thesis. In particular, it is shown that the performance of one of the most standard approaches, the "correction for attenuation" method, is poor relative to other methods when the sample size is large and the distribution of covariables is skewed. / Graduation date: 1993

Using the error correction model, we link the long-run behavior of the Canada-US real exchange rate to its short-run dynamics. The equilibrium real exchange rate is determined by the energy and non-energy commodity prices over the period 1973Q1-1992Q1. However such a single long-run relationship does not hold when the sample period is extended to 2004Q4. This breakdown can be explained by the break point which we find at 1993Q3. At the break point, the effect of the energy price shocks on Canadas real exchange rate turns from negative to positive while the effect of the non-energy commodity price shocks is constantly positive. We find that after one year 40.03% of the gap between the actual and equilibrium real exchange rate is closed. The Canada-US interest rate differential affects the real exchange rate temporarily. The Canadas real exchange rate depreciates immediately after a decrease in Canadas interest rate and appreciates next quarter but not by as much as it has depreciated.

Behavioural symptoms, cognitive deficits, and findings from electrophysiological, neuroimaging and genetic studies all suggest atypical performance monitoring in ADHD. Performance monitoring involves error detection and post-error behavioural adjustment and is crucial to behavioural self-regulation and reinforcement learning, both of which are dysfunctional in ADHD. Therefore, post-error slowing was examined in children with ADHD and controls using a modified flanker task both with, and without, error detection provided. There was a significant main effect of group on post-error slowing across conditions and when error-detection was provided, significant post-error slowing deficits were found in children with ADHD. These findings suggest that the performance monitoring deficit in ADHD is specific to post-error behavioural adjustment and supports the inclusion of this deficit in the neurocognitive profile of ADHD. Findings are discussed in terms of current neurocognitive reinforcement learning models of ADHD.

When evaluating integration schemes used in molecular dynamics (MD) simulations, energy conservation is often cited as the primary criterion by which the integrators should be com- pared. As a result variable stepsize Runge-Kutta methods are often ruled out of consideration due to their characteristic energy drift. We have shown that by appropriately modifying the stepsize selection strategy in a variable stepsize RK method it is possible for the MD practitioner to obtain substantial control over the energy drift during the course of a simulation. This ability has been previously unreported in the literature, and we present numerical examples to illustrate that it can be achieved without sacrificing computational efficiency under currently obtainable timescales.