Multiple comparisons and selection procedures are commonly studied in research and employed in application. Clinical trial is one of popular fields to which the subject of multiple comparisons is extensively applied. Based on the Federal Food, Drug, and Cosmetic Act, drug manufacturers need to not only demonstrate safety of their drug products but also establish effectiveness by substantial evidence in order to obtain marketing approval. However, the problem of error inflation occurs when there are more than two groups to compare with at the same time. How to design a test procedure with high power while controlling type I error becomes an important issue. The treatment with the largest population mean is considered to be the best one in the study. Potentially the best treatments can receive increased resources and further investigation by excluding clearly inferior treatments. Hence, a small number of possibly the best treatments is preferred. This thesis focuses on the problem of eliminating the less effective treatments among three in clinical trials. The goal is to increase the ability to identify any inferior treatment providing that the probability of excluding any best treatment is guaranteed to be less than or equal to alpha. A step-down procedure is applied to solve the problem. The general step-down procedure with fixed thresholds is conservative in our problem. The test is not efficient in rejecting the less effective treatments. We propose two methods with sharper thresholds to improve current procedures and construct a subset containing strictly inferior treatments. The first method, the restricted parameter space approach, is designed for the scenario when prior information about range of treatment means is known. The second method, the step-down procedure with feedback, utilizes observations to modify the threshold and controls error rate for the whole parameter space. The new procedures have greater ability to detect more inferior treatments than the standard procedure. In addition, type I error is also controlled under mild violation of the assumptions demonstrated by simulation.

I consider statistical inference for clustering, that is the arrangement of experimental units in homogeneous groups. In particular, I discuss clustering for multivariate binary outcomes. Binary data is not very informative, making it less meaningful to proceed with traditional (deterministic) clustering methods. Meaningful inference needs to account for and report the considerable uncertainty related with any reported cluster arrangement. I review and implement an approach that was proposed in the recent literature. / text

Symmetrical multilevel diversity coding (SMDC) is a classical model for coding over distributed storage. In this setting, a simple separate encoding strategy known as superposition coding was shown to be optimal in terms of achieving the minimum sum rate and the entire admissible rate region of the problem in the literature. The proofs utilized carefully constructed induction arguments, for which the classical subset entropy inequality of Han played a key role. This thesis includes two parts. In the first part the existing optimality proofs for classical SMDC are revisited, with a focus on their connections to subset entropy inequalities. First, a new sliding-window subset entropy inequality is introduced and then used to establish the optimality of superposition coding for achieving the minimum sum rate under a weaker source-reconstruction requirement. Second, a subset entropy inequality recently proved by Madiman and Tetali is used to develop a new structural understanding to the proof of Yeung and Zhang on the optimality of superposition coding for achieving the entire admissible rate region. Building on the connections between classical SMDC and the subset entropy inequalities developed in the first part, in the second part the optimality of superposition coding is further extended to the cases where there is an additional all-access encoder, an additional secrecy constraint or an encoder hierarchy.

Cette thèse est une contribution à la problématique de la simulation d'événements rares. A partir de l'étude des méthodes de Splitting, un nouveau cadre théorique est développé, indépendant de tout algorithme. Ce cadre, basé sur la définition d'un processus ponctuel associé à toute variable aléatoire réelle, permet de définir des estimateurs de probabilités, quantiles et moments sans aucune hypothèse sur la variable aléatoire. Le caractère artificiel du Splitting (sélection de seuils) disparaît et l'estimateur de la probabilité de dépasser un seuil est en fait un estimateur de la fonction de répartition jusqu'au seuil considéré. De plus, les estimateurs sont basés sur des processus ponctuels indépendants et identiquement distribués et permettent donc l'utilisation de machine de calcul massivement parallèle. Des algorithmes pratiques sont ainsi également proposés.Enfin l'utilisation de métamodèles est parfois nécessaire à cause d'un temps de calcul toujours trop important. Le cas de la modélisation par processus aléatoire est abordé. L'approche par processus ponctuel permet une estimation simplifiée de l'espérance et de la variance conditionnelles de la variable aléaoire résultante et définit un nouveau critère d'enrichissement SUR adapté aux événements rares / This thesis address the issue of extreme event simulation. From a original understanding of the Splitting methods, a new theoretical framework is proposed, regardless of any algorithm. This framework is based on a point process associated with any real-valued random variable and lets defined probability, quantile and moment estimators without any hypothesis on this random variable. The artificial selection of threshold in Splitting vanishes and the estimator of the probability of exceeding a threshold is indeed an estimator of the whole cumulative distribution function until the given threshold. These estimators are based on the simulation of independent and identically distributed replicas of the point process. So they allow for the use of massively parallel computer cluster. Suitable practical algorithms are thus proposed.Finally it can happen that these advanced statistics still require too much samples. In this context the computer code is considered as a random process with known distribution. The point process framework lets handle this additional source of uncertainty and estimate easily the conditional expectation and variance of the resulting random variable. It also defines new SUR enrichment criteria designed for extreme event probability estimation.

BACKGROUND: Some of the current software tools for comparative metagenomics provide ecologists with the ability to investigate and explore bacterial communities using α- & β-diversity. Feature subset selection - a sub-field of machine learning - can also provide a unique insight into the differences between metagenomic or 16S phenotypes. In particular, feature subset selection methods can obtain the operational taxonomic units (OTUs), or functional features, that have a high-level of influence on the condition being studied. For example, in a previous study we have used information-theoretic feature selection to understand the differences between protein family abundances that best discriminate between age groups in the human gut microbiome. RESULTS: We have developed a new Python command line tool, which is compatible with the widely adopted BIOM format, for microbial ecologists that implements information-theoretic subset selection methods for biological data formats. We demonstrate the software tools capabilities on publicly available datasets. CONCLUSIONS: We have made the software implementation of Fizzy available to the public under the GNU GPL license. The standalone implementation can be found at http://github.com/EESI/Fizzy.

With the transistor density on an integrated circuit doubling every 18 months, Moore’s law seems likely to hold for another decade at least. This exponential growth in digital circuits has led to its increased complexity, better performance and is quickly getting less manageable for design engineers. To combat this complexity, CAD tools have been introduced and are still being continuously developed, which prove to be of great help in the digital industry. One of the technologies, that is rapidly evolving as an industry standard, is the Very High Speed Integrated Circuit Hardware Description Language, (VHDL), language. The VHDL standard language along with logic synthesis tools are used to implement complex digital systems in a timely manner. The increase in the number of specialist design consultants, with specific tools accompanied by their own libraries written in VHDL, makes it important for a designer to have an in-depth knowledge about the available synthesis tools and technologies in order to design a system in the most efficient and reliable manner. This research dealt with writing VHDL code in terms of hardware modeling, based on coding styles, in order to get optimum results. Furthermore, it dealt with the interpretation of VHDL code into equivalent optimized hardware implementations, which satisfy the constraints of a set of specifications. In order to obtain a better understanding of the different VHDL tools and their usefulness in different situations, a comparative analysis between Altera’s QuartusII and Xilinx’s ISE Webpack tools, was performed. The analysis compared their Graphics User Interface, VHDL Code Portability and VHDL Synthesis constraints. The analysis was performed by designing and implementing a screensaver circuit on an FPGA and displaying it on the VGA Monitor.

<p>The need for broadcast encryption arises when a sender wishes to securely distribute messages to varying subsets of receivers, using a broadcast channel, for instance in a pay-TV scenario. This is done by selecting subsets of users and giving all users in the same subset a common decryption key. The subsets will in general be overlapping so that each user belongs to many subsets and has several different decryption keys. When the sender wants to send a message to some users, the message is encrypted using keys that those users have. In this thesis we describe some broadcast encryption schemes that have been proposed in the literature. We focus on stateless schemes which do not require receivers to update their decryption keys after the initial keys have been received; particularly we concentrate on the Subset Difference (SD) scheme.</p><p>We consider the effects that the logical placement of the receivers in the tree structure used by the SD scheme has on the number of required transmissions for each message. Bounds for the number of required transmissions are derived based on the adjacency of receivers in the tree structure. The tree structure itself is also studied, also resulting in bounds on the number of required transmissions based on the placement of the users in the tree structure.</p><p>By allowing a slight discrepancy between the set of receivers that the sender intends to send to and the set of receivers that actually can decrypt the message, we can reduce the cost in number of transmissions per message. We use the concept of distortion to quantify the discrepancy and develop three simple algorithms to illustrate how the cost and distortion are related.</p> / Report code: LIU-Tek-Lic-2005:70.

Let π1,  π2, ... π be k (&gt;_2) populations. Let  πi (i = 1, 2, ..., k) be characterized by the uniform distributionon (ai, bi), where exactly one of ai and bi is unknown. With unequal sample sizes, suppose that we wish to select arandom-size subset of the populations containing the one withthe smallest value of 0i = bi - ai. Rule Ri selects πi iff a likelihood-based k-dimensional confidence region for the unknown (01,..., 0k) contains at least one point having 0i as its smallest component. A second rule, R, is derived through a likelihood ratio and is equivalent to that of Barr and Rizvi (1966) when the sample sizes are equal. Numerical comparisons are made. The results apply to the larger class of densities g(z; 0i) = M(z)Q(0i) iff a(0i) &lt; z &lt; b(0i). Extensions to the cases when both ai and bi are unknown and when 0max is of interest are i i indicated. / digitalisering@umu

Let π1, ..., πk be k(&gt;_2) populations such that πi, i = 1, 2, ..., k, is characterized by the normal distribution with unknown mean and ui variance aio2 , where ai is known and o2 may be unknown. Suppose that on the basis of independent samples of size ni from π (i=1,2,...,k), we are interested in selecting a random-size subset of the given populations which hopefully contains the population with the largest mean.Based on likelihood ratios, several new procedures for this problem are derived in this report. Some of these procedures are compared with the classical procedure of Gupta (1956,1965) and are shown to be better in certain respects. / <p>Ny rev. utg.</p><p>This is a slightly revised version of Statistical Research Report No. 1978-6.</p> / digitalisering@umu

In general, subset sum problem is strongly believed to be computationally difficult to solve. But in 1983, Lagarias and Odlyzko proposed a probabilistic algorithm for solving subset sum problems of sufficiently low density in polynomial time. In 1991, Coster et. al. improved the Lagarias-Odlyzko algorithm and solved subset sum problems with higher density. Both algorithms reduce subset sum problem to finding shortest non-zero vectors in special lattices. In this thesis, we first proposed a new viewpoint to define the problems which can be solved by this two algorithms and shows the improved algorithm isn't always better than the Lagarias-Odlyzko algorithm. Then we verify this notion by experimentation. Finally, we find that the Lagrias-Odlyzko algorithm can solve the high-density subset sum problems if the weight of solution is higher than 0.7733n or lower than 0.2267n, even the density is close to 1.