Statistical Analysis of Spectral Images

Tämä diplomityö liittyy Spektrikuvien tutkimiseen tilastollisen kuvamallin näkökulmasta. Diplomityön ensimmäisessä osassa tarkastellaan tilastollisten parametrien jakaumien vaikutusta väreihin ja korostumiin erilaisissa valaistusolosuhteissa. Havaittiin, että tilastollisten parametrien väliset suhteet eivät riipu valaistusolosuhteista, mutta riippuvat kuvan häiriöttömyydestä. Ilmeni myös, että korkea huipukkuus saattaa aiheutua värikylläisyydestä. Lisäksi työssä kehitettiin tilastolliseen spektrimalliin perustuvaa tekstuurinyhdistämisalgoritmia. Sillä saavutettiin hyviä tuloksia, kun tilastollisten parametrien väliset riippuvuussuhteet olivat voimassa. Työn toisessa osassa erilaisia spektrikuvia tutkittiin käyttäen itsenäistä komponenttien analyysia (ICA). Seuraavia itsenäiseen komponenttien analyysiin tarkoitettuja algoritmia tarkasteltiin: JADE, kiinteän pisteen ICA ja momenttikeskeinen ICA. Tutkimuksissa painotettiin erottelun laatua. Paras erottelu saavutettiin JADE- algoritmilla, joskin erot muiden algoritmien välillä eivät olleet merkittäviä. Algoritmi jakoi kuvan kahteen itsenäiseen, joko korostuneeseen ja korostumattomaan tai kromaattiseen ja akromaattiseen, komponenttiin. Lopuksi pohditaan huipukkuuden suhdetta kuvan ominaisuuksiin, kuten korostuneisuuteen ja värikylläisyyteen. Työn viimeisessä osassa ehdotetaan mahdollisia jatkotutkimuskohteita.

Hardness of FRHC-Cu determined by statistical analysis

A statistical indentation method has been employed to study the hardness value of fire-refined high conductivity copper, using nanoindentation technique. The Joslin and Oliver approach was used with the aim to separate the hardness (H) influence of copper matrix, from that of inclusions and grain boundaries. This approach relies on a large array of imprints (around 400 indentations), performed at 150 nm of indentation depth. A statistical study using a cumulative distribution function fit and Gaussian simulated distributions, exhibits that H for each phase can be extracted when the indentation depth is much lower than the size of the secondary phases. It is found that the thermal treatment produces a hardness increase, due to the partly re-dissolution of the inclusions (mainly Pb and Sn) in the matrix.

Regression-based techniques for statistical decision making in single-case designs

The present study evaluates the performance of four methods for estimating regression coefficients used to make statistical decisions regarding intervention effectiveness in single-case designs. Ordinary least squares estimation is compared to two correction techniques dealing with general trend and one eliminating autocorrelation whenever it is present. Type I error rates and statistical power are studied for experimental conditions defined by the presence or absence of treatment effect (change in level or in slope), general trend, and serial dependence. The results show that empirical Type I error rates do not approximate the nominal ones in presence of autocorrelation or general trend when ordinary and generalized least squares are applied. The techniques controlling trend show lower false alarm rates, but prove to be insufficiently sensitive to existing treatment effects. Consequently, the use of the statistical significance of the regression coefficients for detecting treatment effects is not recommended for short data series.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

A statistical shape model of the human second cervical vertebra.

PURPOSE: Statistical shape and appearance models play an important role in reducing the segmentation processing time of a vertebra and in improving results for 3D model development. Here, we describe the different steps in generating a statistical shape model (SSM) of the second cervical vertebra (C2) and provide the shape model for general use by the scientific community. The main difficulties in its construction are the morphological complexity of the C2 and its variability in the population. METHODS: The input dataset is composed of manually segmented anonymized patient computerized tomography (CT) scans. The alignment of the different datasets is done with the procrustes alignment on surface models, and then, the registration is cast as a model-fitting problem using a Gaussian process. A principal component analysis (PCA)-based model is generated which includes the variability of the C2. RESULTS: The SSM was generated using 92 CT scans. The resulting SSM was evaluated for specificity, compactness and generalization ability. The SSM of the C2 is freely available to the scientific community in Slicer (an open source software for image analysis and scientific visualization) with a module created to visualize the SSM using Statismo, a framework for statistical shape modeling. CONCLUSION: The SSM of the vertebra allows the shape variability of the C2 to be represented. Moreover, the SSM will enable semi-automatic segmentation and 3D model generation of the vertebra, which would greatly benefit surgery planning.

Use of Statistical Methods in Demand Planning

In a very volatile industry of high technology it is of utmost importance to accurately forecast customers’ demand. However, statistical forecasting of sales, especially in heavily competitive electronics product business, has always been a challenging task due to very high variation in demand and very short product life cycles of products. The purpose of this thesis is to validate if statistical methods can be applied to forecasting sales of short life cycle electronics products and provide a feasible framework for implementing statistical forecasting in the environment of the case company. Two different approaches have been developed for forecasting on short and medium term and long term horizons. Both models are based on decomposition models, but differ in interpretation of the model residuals. For long term horizons residuals are assumed to represent white noise, whereas for short and medium term forecasting horizon residuals are modeled using statistical forecasting methods. Implementation of both approaches is performed in Matlab. Modeling results have shown that different markets exhibit different demand patterns and therefore different analytical approaches are appropriate for modeling demand in these markets. Moreover, the outcomes of modeling imply that statistical forecasting can not be handled separately from judgmental forecasting, but should be perceived only as a basis for judgmental forecasting activities. Based on modeling results recommendations for further deployment of statistical methods in sales forecasting of the case company are developed.

Dynamics of integrable birational maps preserving genus 0 foliations

Pòster presentat al congrés NPDDS2014

Statistical hypothesis testing and common misinterpretations: should we abandon p-value in forensic science applications?

Many people regard the concept of hypothesis testing as fundamental to inferential statistics. Various schools of thought, in particular frequentist and Bayesian, have promoted radically different solutions for taking a decision about the plausibility of competing hypotheses. Comprehensive philosophical comparisons about their advantages and drawbacks are widely available and continue to span over large debates in the literature. More recently, controversial discussion was initiated by an editorial decision of a scientific journal [1] to refuse any paper submitted for publication containing null hypothesis testing procedures. Since the large majority of papers published in forensic journals propose the evaluation of statistical evidence based on the so called p-values, it is of interest to expose the discussion of this journal's decision within the forensic science community. This paper aims to provide forensic science researchers with a primer on the main concepts and their implications for making informed methodological choices.

Statistics in Public Understanding of Science review: How to achieve high statistical standards?

This article proposes a checklist to improve statistical reporting in the manuscripts submitted to Public Understanding of Science. Generally, these guidelines will allow the reviewers (and readers) to judge whether the evidence provided in the manuscript is relevant. The article ends with other suggestions for a better statistical quality of the journal.

High-density linkage maps fail to detect any genetic component to sex determination in a Rana temporaria family.

Sex chromosome differentiation in Rana temporaria varies strikingly among populations or families: whereas some males display well-differentiated Y haplotypes at microsatellite markers on linkage group 2 (LG2 ), others are genetically undistinguishable from females. We analysed with RADseq markers one family from a Swiss lowland population with no differentiated sex chromosomes, and where sibship analyses had failed to detect any association between the phenotypic sex of progeny and parental haplotypes. Offspring were reared in a common tank in outdoor conditions and sexed at the froglet stage. We could map a total of 2177 SNPs (1123 in the mother, 1054 in the father), recovering in both adults 13 linkage groups (= chromosome pairs) that were strongly syntenic to Xenopus tropicalis despite > 200 My divergence. Sexes differed strikingly in the localization of crossovers, which were uniformly distributed in the female but limited to chromosome ends in the male. None of the 2177 markers showed significant association with offspring sex. Considering the very high power of our analysis, we conclude that sex determination was not genetic in this family; which factors determined sex remain to be investigated.