Master of Science / Department of Statistics / Christopher Vahl / Among the most used statistical concepts and techniques, seen even in the most cursory of introductory courses, are the confidence interval, binomial distribution, and sample size estimation. This paper investigates a particular case of generating a confidence interval from a binomial experiment in the case where zero successes are expected. Several current methods of generating a binomial proportion confidence interval are examined by means of large-scale simulations and compared in order to determine an ad-hoc method for generating a confidence interval with coverage as close as possible to nominal while minimizing width. This is then used to construct a formula which allows for the estimation of a sample size necessary to obtain a sufficiently narrow confidence interval (with some predetermined probability of success) using the ad-hoc method given a prior estimate of the probability of success for a single trial. With this formula, binomial experiments could potentially be planned more efficiently, allowing researchers to plan only for the amount of precision they deem necessary, rather than trying to work with methods of producing confidence intervals that result in inefficient or, at worst, meaningless bounds.

abstract: In many biological research studies, including speech analysis, clinical research, and prediction studies, the validity of the study is dependent on the effectiveness of the training data set to represent the target population. For example, in speech analysis, if one is performing emotion classification based on speech, the performance of the classifier is mainly dependent on the number and quality of the training data set. For small sample sizes and unbalanced data, classifiers developed in this context may be focusing on the differences in the training data set rather than emotion (e.g., focusing on gender, age, and dialect). This thesis evaluates several sampling methods and a non-parametric approach to sample sizes required to minimize the effect of these nuisance variables on classification performance. This work specifically focused on speech analysis applications, and hence the work was done with speech features like Mel-Frequency Cepstral Coefficients (MFCC) and Filter Bank Cepstral Coefficients (FBCC). The non-parametric divergence (D_p divergence) measure was used to study the difference between different sampling schemes (Stratified and Multistage sampling) and the changes due to the sentence types in the sampling set for the process. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2020

The Finkelstein and Schoenfeld (FS) test is a popular generalized pairwise comparison approach to analyze prioritized composite endpoints (e.g., components are assessed in order of clinical importance). Power and sample size estimation for the FS test, however, are generally done via simulation studies. This simulation approach can be extremely computationally burdensome, compounded by an increasing number of composite endpoints and with increasing sample size. We propose an analytic solution to calculate power and sample size for commonly encountered two-component hierarchical composite endpoints. The power formulas are derived assuming underlying distributions in each of the component outcomes on the population level, which provide a computationally efficient and practical alternative to the standard simulation approach. The proposed analytic approach is extended to derive conditional power formulas, which are used in combination with the promising zone methodology to perform sample size re-estimation in the setting of adaptive clinical trials. Prioritized composite endpoints with more than two components are also investigated. Extensive Monte Carlo simulation studies were conducted to demonstrate that the performance of the proposed analytic approach is consistent with that of the standard simulation approach. We also demonstrate through simulations that the proposed methodology possesses generally desirable objective properties including robustness to mis-specified underlying distributional assumptions. We illustrate our proposed methods through application of the proposed formulas by calculating power and sample size for the Transthyretin Amyloidosis Cardiomyopathy Clinical Trial (ATTR-ACT) and the EMPULSE trial for empagliozin treatment of acute heart failure.

One of the most important factors that influences a stream's hydraulic and ecological health is the streambed's sediment size distribution. This distribution affects streambed stability, sediment transport rates, and flood levels by defining the roughness of the stream channel. Adverse effects on water quality and wildlife can be expected when excessive fine sediments enter a stream. Many chemicals and toxic materials are transported through streams by binding to fine sediments. Increases in fine sediments also seriously impact the survival of fish species present in the stream. Fine sediments fill tiny spaces between larger particles thereby denying fish embryos the necessary fresh water to survive. Reforestation, constructed wetlands, and slope stabilization are a few management practices typically utilized to reduce the amount of sediment entering a stream. To effectively gauge the success of these techniques, the sediment size distribution of the stream must be monitored. Gravel bed streams are typically stratified vertically, in terms of particle size, in three layers, with each layer having its own distinct grain size distribution. The top two layers of the stream bed, the pavement and subpavement, are the most significant in determining the characteristics of the stream. These top two layers are only as thick as the largest particle size contained within each layer. This vertical stratification by particle size makes it difficult to characterize the grain size distribution of the surface layer. The traditional bulk or volume sampling procedure removes a specified volume of material from the stream bed. However, if the bed exhibits vertical stratification, the volume sample will mix different populations, resulting in inaccurate sample results. To obtain accurate results for the pavement size distribution, a surface oriented sampling technique must be employed. The most common types of surface oriented sampling are grid and areal sampling. Due to limitations in the sampling techniques, grid samples typically truncate the sample at the finer grain sizes, while areal samples typically truncate the sample at the coarser grain sizes. When combined with an analysis technique, either frequency-by-number or frequency-by-weight, the sample results can be represented in terms of a cumulative grain size distribution. However, the results of different sampling and analysis procedures can lead to biased results, which are not equivalent to traditional volume sampling results. Different conversions, dependent on both the sampling and analysis technique, are employed to remove the bias from surface sample results. The topic of the present study is to determine the accuracy of sediment samples obtained by the different sampling techniques. Knowing the accuracy of a sample is imperative if the sample results are to be meaningful. Different methods are discussed for placing confidence intervals on grid sample results based on statistical distributions. The binomial distribution and its approximation with the normal distribution have been suggested for these confidence intervals in previous studies. In this study, the use of the multinomial distribution for these confidence intervals is also explored. The multinomial distribution seems to best represent the grid sampling process. Based on analyses of the different distributions, recommendations are made. Additionally, figures are given to estimate the grid sample size necessary to achieve a required accuracy for each distribution. This type of sample size determination figure is extremely useful when preparing for grid sampling in the field. Accuracy and sample size determination for areal and volume samples present difficulties not encountered with grid sampling. The variability in number of particles contained in the sample coupled with the wide range of particle sizes present make direct statistical analysis impossible. Limited studies have been reported on the necessary volume to sample for gravel deposits. The majority of these studies make recommendations based on empirical results that may not be applicable to different size distributions. Even fewer studies have been published that address the issue of areal sample size. However, using grid sample results as a basis, a technique is presented to estimate the necessary sizes for areal and volume samples. These areal and volume sample sizes are designed to match the accuracy of the original grid sample for a specified grain size percentile of interest. Obtaining grid and areal results with the same accuracy can be useful when considering hybrid samples. A hybrid sample represents a combination of grid and areal sample results that give a final grain size distribution curve that is not truncated. Laboratory experiments were performed on synthetic stream beds to test these theories. The synthetic stream beds were created using both glass beads and natural sediments. Reducing sampling errors and obtaining accurate samples in the field are also briefly discussed. Additionally, recommendations are also made for using the most efficient sampling technique to achieve the required accuracy. / Master of Science

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