Ego-motion sensors are commonly used for pose estimation in Simultaneous Localization And Mapping (SLAM) algorithms. Inertial Measurement Units (IMUs) are popular sensors but suffer from integration drift over longer time scales. To remedy the drift they are often used in combination with additional sensors, such as a LiDAR. Pose estimation is used when scans, produced by these additional sensors, are being matched. The matching of scans can be computationally heavy as one scan can contain millions of data points. Methods exist to simplify the problem of finding the relative pose between sensor data, such as the Normal Distribution Transform SLAM algorithm. The algorithm separates the point cloud data into a voxelgrid and represent each voxel as a normal distribution, effectively decreasing the amount of data points. Registration is based on a function which converges to a minimum. Sub-optimal conditions can cause the function to converge at a local minimum. To remedy this problem this thesis explores the benefits of combining IMU sensor data to estimate the pose to be used in the NDT SLAM algorithm.

本文主要目的在檢定臺灣股票報酬率是否為序列隨機；臺灣股票報酬率分 配是否符合常態分配、穩定分配。其中實證結果發現：拒絕臺灣股票報酬 率為序列隨機；拒絕臺灣股票報酬率分配呈常態分配、穩定分配。由於拒 絕臺灣股票報酬率為序列隨機，故將原資料隨機化後再次進行常態、穩定 分配之檢定、結果發現拒絕隨機化後之臺灣股票報酬率分配呈常態分配， 但不能拒絕隨機化後之臺灣股票報酬率分配呈穩定分配。

<p>We investigate the use of noise degraded facial images in the application of facial expression recognition. In particular, we trained Gabor+SVMclassifiers to recognize facial expressions images with various types of noise. We applied Gaussian noise, Poisson noise, varying levels of salt and pepper noise, and speckle noise to noiseless facial images. Classifiers were trained with images without noise and then tested on the images with noise. Next, the classifiers were trained using images with noise, and then on tested both images that had noise, and images that were noiseless. Finally, classifiers were tested on images while increasing the levels of salt and pepper in the test set. Our results reflected distinct degradation of recognition accuracy. We also discovered that certain types of noise, particularly Gaussian and Poisson noise, boost recognition rates to levels greater than would be achieved by normal, noiseless images. We attribute this effect to the Gaussian envelope component of Gabor filters being sympathetic to Gaussian-like noise, which is similar in variance to that of the Gabor filters. Finally, using linear regression, we mapped a mathematical model to this degradation and used it to suggest how recognition rates would degrade further should more noise be added to the images.</p>

The use of positron emission tomography (PET) for imaging in oncology has grown rapidly in recent years. 2-[18F]-fluorodeoxyglucose (FDG) is the most common tracer of PET, although drawbacks exist. Radiolabeled 1-[11C]-acetate (C-AC) is a simple probe for evaluation of perfusion, anabolism (lipogenesis) and catabolism (oxidative metabolism) in all living tissues. This study explored the potential of AC PET in head and neck cancer, benign and malignant lymph nodes in prostate cancer and normal distribution.  In head and neck cancer, C-AC PET detected more primaries and lymph node metastases than FDG PET. The mean primary tumor volumes delineated by C-AC was 51% larger than that of FDG before radiotherapy (RT). Both FDG and C-AC PET tumor volumes must be carefully validated before used in clinical routine. Baseline tumor clearance rate (kmono) was higher in complete responders (CR) than that in partial responders (PR). kmono tended to correlate inversely with FDG SUV at baseline. Radiosensitive tumors might rely predominantly on oxidative metabolism for their biogenetic needs. kmono increased in PR during RT. The potential reversibility of impaired kmono in radioresistant tumors imply that treatment targeting the intermediary metabolism might improve the outcome. Tumor relative perfusion index (rF) and kmono were coupled in CR throughout the RT, but not in PR. Dynamic C-AC PET provides a new non-invasive method to simultaneously evaluate the tumor oxidative metabolism and perfusion which link the RT response in patients by a single tracer injection. In prostate cancer, elevated C-AC accumulation is common in benign inguinal lymph nodes, probably due to increased lipogenesis rather than lymphatic drainage. CT Hounsfield unit of benign nodes was lower than that of metastases, suggesting that density measurement using CT might improve the specificity of nodal staging of prostate cancer. A novel tracer 2-[18F]-fluoroacetate (F-AC) was synthesized and used for dynamic PET-CT imaging in animals. Compared with C-AC PET-CT, F-AC showed prolonged blood retention, no detectable trapping in myocardium and salivary glands, rapid excretion from liver to bile and urine and de-fluorination resulting in intensive skeletal activity. F-AC does not mimic the normal physiologic path of C-AC and appears to be of little use for assessment of perfusion, intermediary metabolism or lipogenesis.

The role of risk management has gained momentum in recent years most notably after the recent financial crisis. This thesis uses a quantitative approach to evaluate the theory of value at risk which is considered a benchmark to measure financial risk. The thesis makes use of both parametric and non parametric approaches to evaluate the effectiveness of VAR as a standard tool in measuring risk of stock portfolio. This study uses the normal distribution, student t-distribution, historical simulation and the exponential weighted moving average at 95% and 99% confidence levels on the stock returns of Sonny Ericsson, Three Months Swedish Treasury bill (STB3M) and Nordea Bank. The evaluations of the VAR models are based on the Kupiec (1995) Test. From a general perspective, the results of the study indicate that VAR as a proxy of risk measurement has some imprecision in its estimates. However, this imprecision is not all the same for all the approaches. The results indicate that models which assume normality of return distribution display poor performance at both confidence levels than models which assume fatter tails or have leptokurtic characteristics. Another finding from the study which may be interesting is the fact that during the period of high volatility such as the financial crisis of 2008, the imprecision of VAR estimates increases. For the parametric approaches, the t-distribution VAR estimates were accurate at 95% confidence level, while normal distribution approach produced inaccurate estimates at 95% confidence level. However both approaches were unable to provide accurate estimates at 99% confidence level. For the non parametric approaches the exponentially weighted moving average outperformed the historical simulation approach at 95% confidence level, while at the 99% confidence level both approaches tend to perform equally. The results of this study thus question the reliability on VAR as a standard tool in measuring risk on stock portfolio. It also suggest that more research should be done to improve on the accuracy of VAR approaches, given that the role of risk management in today’s business environment is increasing ever than before. The study suggest VAR should be complemented with other risk measures such as Extreme value theory and stress testing, and that more than one back testing techniques should be used to test the accuracy of VAR.

In this discusses four different approaches used during a statistics tutorial of a group of first year undergraduates studying computer science related degrees at the University of Westminster UK. The four approaches were each implemented in an attempt to keep the students interested in the statistics topics delivered. It was found that “Chalk and Talk” (i.e. board work) was not the best form of imparting knowledge to the students of the group as determined by student analysing feedback forms and generally observing student behaviour and listening to student comments over a number of years delivering statistics topics. The duration of each tutorial was two hours. The teaching strategies adopted were: a) A class quiz. b) Group explanation of material to members of the individual’s group. c) Group explanation of material to members of the entire class. d) Students teaching at the front of the class. Each of the methods will now be discussed with the relative merits and defects included for a comparison. It was found that each method worked better at the end of each module when the students were more familiar with the topics introduced on the module.

The study of properties of probability distributions has always been a persistent theme of statistics and of applied probability. This thesis deals with an investigation of distribution functions under the following two topics: (i) characterization of distributions based on record values and order statistics, (ii) properties of the skew-t distribution. Within the extensive characterization literature there are several results involving properties of record values and order statistics. Although there have been many well known results already developed, it is still of great interest to find new characterization of distributions based on record values and order statistics. In the first part, we provide the conditional distribution of any record value given the maximum order statistics and study characterizations of distributions based on record values and the maximum order statistics. We also give some characterizations of the mean value function within the class of order statistics point processes, by using certain relations between the conditional moments of the jump times or current lives. These results can be applied to characterize the uniform distribution using the sequence of order statistics, and the exponential distribution using the sequence of record values, respectively. Azzalini (1985, 1986) introduced the skew-normal distribution which includes the normal distribution and has some properties like the normal and yet is skew. This class of distributions is useful in studying robustness and for modeling skewness. Since then, skew-symmetric distributions have been proposed by many authors. In the second part, the so-called generalized skew-t distribution is defined and studied. Examples of distributions in this class, generated by the ratio of two independent skew-symmetric distributions, are given. We also investigate properties of the skew-symmetric distribution.

Progressive Type-II censoring was introduced by Cohen (1963) and has since been the topic of much research. The question stands whether it is sensible to use this sampling plan by design, instead of regular Type-II right censoring. We introduce an asymptotic progressive censoring model, and find optimal censoring schemes for location-scale families. Our optimality criterion is the determinant of the 2x2 covariance matrix of the asymptotic best linear unbiased estimators. We present an explicit expression for this criterion, and conditions for its boundedness. By means of numerical optimization, we determine optimal censoring schemes for the extreme value, the Weibull and the normal distributions. In many situations, it is shown that these progressive schemes significantly improve upon regular Type-II right censoring.

Mελετάται η μίξη δύο συνεχών κατανομών με αύξοντα ρυθμό αποτυχίας και δίνονται συνθήκες για να έχει η μίξη φθίνοντα ρυθμό αποτυχίας. Όταν η μία από τις δύο κατανομές της μίξης είναι η εκθετική γίνεται αντιστροφή του ρυθμού αποτυχίας. Στην περίπτωση της μίξης δύο κανονικών κατανομών παρουσιάζεται ο τρόπος που συνδέεται το πλήθος των κορυφών της πυκνότητας με τον ρυθμό αποτυχίας της μίξης. Mελετάται επίσης, η μονοτονία του ρυθμού αποτυχίας διακριτών κατανομών χρησιμοποιώντας τον λόγο δύο διαδοχικών πιθανοτήτων και δίδεται μία συνθήκη για να έχει η μίξη δύο διακριτών κατανομών φθίνοντα ρυθμό αποτυχίας όταν η μία από τις δύο κατανομές της μίξης είναι η γεωμετρική. Τέλος, χρησιμοποιώντας τον λόγο διαδοχικών πιθανοτήτων, μελετούμε την μονοτονία του ρυθμού αποτυχίας για διδιάστατες διακριτές κατανομές. / The mixture of two continuous distributions, with increasing failure rates, is considered and the necessary conditions to have decreasing failure rate (DFR) are given. When one of these distributions is the Exponential, reversal of the failure rate is observed. In the case of two normal distributions the failure rate is associated with the number of modes. It is also considered the failure rate for discrete distributions in regard with the ratio of two consecutive probabilities. A condition to have DFR is given when one of the distributions of the mixture is the geometric. Finally, we make use of the ratio of two consecutive probabilities to study the failure rate for bivariate discrete distributions.

Οι δείκτες αποτελεσματικότητας μιας διαδικασίας μετρούν τον βαθμό στον οποίο μια διαδικασία, που βρίσκεται σε στατιστική ισορροπία, παράγει προϊόντα τα οποία ικανοποιούν τις προδιαγραφές του πελάτη. Στη διπλωματική αυτή εργασία δίνονται οι ορισμοί διαφόρων τέτοιων δεικτών που έχουν προταθεί από τη βιβλιογραφία, για μονοδιάστατες και διδιάστατες μεταβλητές, οι οποίες ακολουθούν κανονική κατανομή. Παρουσιάζονται οι ιδιότητες καθώς και οι σχέσεις μεταξύ των δεικτών αυτών και αναλύονται τα μειονεκτήματα και τα πλεονεκτήματα της χρήσης τους. Δίνονται εκτιμητές κάποιων δεικτών και ιδιότητες αυτών όπως αναμενόμενη τιμή, διασπορά, συνάρτηση πυκνότητας. Κατασκευάζονται επίσης διαστήματα εμπιστοσύνης και έλεγχοι υποθέσεων για τους εκτιμητές των δεικτών. Τέλος, παρουσιάζονται αριθμητικά παραδείγματα και εφαρμογές των δεικτών αποτελεσματικότητας στη βιομηχανία. / Process capability indices are intended to provide single-number assessment of the capability, of a process in statistical control, to produce items that meet the customer΄s specifications. We present the definitions of various such indices that have been proposed for univariate and bivariate normal distributions. We refer to their properties, the relations among them and the weaknesses or benefits from their use. Estimators of the indices are considered and their properties such as expected value, variance and probability density function are derived. Confidence intervals and tests of hypothesis are constructed for their estimators. Finally, numerical examples and applications of process capability indices in industry are presented.