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<p>This thesis is centered around three infinite dimensional diffusion processes:</p> <p>(i). the infinitely-many-neutral-alleles diffusion model [Ethier and Kurtz, 1981],</p> <p>(ii). the two-parameter infinite dimensional diffusion model [Petrov, 2009] and [Feng and Sun, 2010],</p> <p>(iii). the infinitely-many-alleles diffusion with symmetric dominance [Ethier and Kurtz, 1998].</p> <p>The partition structures, the ergodic inequalities and the asymptotic theory of these three models are discussed. In particular, the asymptotic theory turns out to be the major contribution of this thesis.</p> <p>In Chapter 2, a slightly altered version of Kingman's one-to-one correspondence theorem on partition structures is provided, which in turn becomes a handy tool for obtaining the asymptotic result on the partition structures associated with models (i) and (ii).</p> <p>In Chapter 3, the three diffusion models are briefly introduced. New representations of the transition densities of models (i) and (ii) are obtained simply by rearranging the previous representations obtained in [Ethier, 1992] and [Feng et al., 2011] respectively. These two new representations have their own advantages, by making use of which the corresponding ergodic inequalities easily follow. Furthermore, thanks to the functional inequalities in [Feng et al., 2011], the ergodic inequality for model (iii) becomes available as well.</p> <p>In Chapter 4, the asymptotic properties of models (i) and (ii) are thoroughly studied. Various asymptotic results are obtained, such as the weak limits of models (i) and (ii) at different time scales when the mutation rate approaches infinity, and the large deviation principle for models (i) and (ii) at a fixed time, and that of the transient partition structures of models (i) and (ii). Of all these results, the weak limit and the large deviation principle of the transient partition structures are of particular interest.</p> <p>In Chapter 5, the asymptotic results on the stationary distribution and the transient distribution of model (iii) are both obtained. The weak limit of the infinitely-many- alleles diffusion with symmetric overdominance at fixed time t serves as an alternative answer to Gillespie's conjecture [Gillespie, 1999]. The weak limit of the stationary distribution of the infinitely-many-alleles diffusion with symmetric overdominance provides a complete solution to the remaining problem in [Feng, 2009].</p> / Doctor of Philosophy (PhD)

The Expanded Program on Immunization Sampling Method (known simply as EPI sampling) is a two-stage sampling procedure originally intended for quick estimation of disease prevalence in large geographical regions. The method was developed in the 1970s and all the subsequent assessments of its performance have been conducted by simulation. In her master's thesis, Reyes (2016) studied in detail the second-stage sampling of the method by developing formulas for the exact calculation of the household inclusion probabilities when sectors are used to identify the initial household to generate the EPI samples. The inclusion probabilities were used in turn to obtain exact mean, bias, variance and mean square error of any estimator of disease prevalence in the population. Thus, no extensive simulations are required and the results are exact rather than just estimates. This thesis is an extension of Reyes' (2016) work. The extension is two-fold; (a) employing strips rather than sectors because they narrow the geographic area for field workers and to use strips to select the first household for the EPI sample at the secondary stage, and (b) carrying out an analysis on simulated population and sampling plans, using both stages of the EPI method. Analyzing the simulated populations showed that equal weight estimator that samples primary units with replacement with probability proportional to size (EW1) should be used when the target characteristic is thought to be spread randomly throughout the population, and the Horvitz-Thompson estimator that samples primary units systematically with replacement (HTSYS) should be used when the disease is believed to spread from a central location or through pocketing. Comparing the strip and sector sampling methods at the secondary stage using their effective areas leads to a comparative basis in which the inclusion probabilities are identical for both methods. / Thesis / Master of Science (MSc)

A gravel-bed stream's grain size distribution plays an important role in determining a river's depth, sediment transport rates, and stream bed stability as well as the survival rates of mussels and salmonids. Unfortunately, the material found in gravel-bed rivers exhibits vertical stratification as well as spatial variation in the horizontal direction and is difficult to sample. Previous research has largely dealt with the ability of grid, areal, and bulk sampling techniques to sample a single spot within a river. Little has been done in characterizing an entire river reach. Of the methods suggested, none is adequate because they are either inherently biased or are incapable of describing the spatial variations within a sampled region. The present research proposes a method that overcomes these problems. It shows that a single large grid sample, or composite grid sample, can be used to obtain an unbiased estimate of an area's overall grain size distribution at a known accuracy level. It then suggests that the arithmetic mean is a suitable parameter to characterize the coarseness of individual sediment deposits within a sampled area. Thus, by recording the size and location of each stone taken in the composite grid sample one can use statistical hypothesis testing to systematically analyze local means throughout the sampled area and locate sediment boundaries. Once the boundaries are located, stones from the composite grid sample falling within the boundaries of a particular deposit can be analyzed as separate grid samples representative of the individual deposits present and describe the local variability. / Master of Science

No / Sampling in the international environment needs to satisfy the same requirements as sampling in the domestic environment, but there are additional issues to consider, such as the need to balance within-country representativeness with cross-national comparability. However, most international marketing research studies fail to provide theoretical justification for their choice of sampling approach. This is because research design theory and sampling theory have not been well integrated in the context of international research. This paper seeks to fill the gap by developing a framework for determining a sampling approach in international studies. The framework is based on an assessment of the way in which sampling affects the validity of research results, and shows how different research objectives impact upon (a) the desired sampling method and (b) the desired sample characteristics. The aim is to provide researchers with operational guidance in choosing a sampling approach that is theoretically appropriate to their particular research aims.

<p>This master thesis describes a design exploration of a circuit capable of measuring high speed signals without adding significant capacitive load to the measuring node. </p><p>It is designed in a 0.13 CMOS process with a supply voltage of 1.2 Volt. The circuit is a master and slave, track-and-hold architecture incorporated with a capacitive voltage divider and a NMOS source follower as input buffer to protect the measuring node and increase the input voltage range. </p><p>This thesis presents the implementation process and the theory needed to understand the design decisions and consideration throughout the design. The results are based on transistor level simulations performed in Cadence Spectre. </p><p>The results show that it is possible to observe the analog behaviour of a high speed signal by down converting it to a lower frequency that can be brought off-chip. The trade off between capacitive load added to the measuring node and input bandwidth of the measurment circuit is also presented.</p>