Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completelyabsent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and byMartín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involvedparts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method isintroduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that thetheoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approachhas reasonable properties from a compositional point of view. In particular, it is “natural” in the sense thatit recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in thesame paper a substitution method for missing values on compositional data sets is introduced

Bayesian Markov chain Monte Carlo inversion of geophysical data for the purpose of estimating the hydraulic properties of the unsaturated zone

Ground-penetrating radar (GPR) has the potential to provide valuable information on hydrological properties of the vadose zone because of their strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR data within a coupled geophysical-hydrological framework may allow for effective estimation of subsurface van-Genuchten-Mualem (VGM) parameters and their corresponding uncertainties. An important and still unresolved issue, however, is how to best integrate GPR data into a stochastic inversion in order to estimate the VGM parameters and their uncertainties, thus improving hydrological predictions. Recognizing the importance of this issue, the aim of the research presented in this thesis was to first introduce a fully Bayesian inversion called Markov-chain-Monte-carlo (MCMC) strategy to perform the stochastic inversion of steady-state GPR data to estimate the VGM parameters and their uncertainties. Within this study, the choice of the prior parameter probability distributions from which potential model configurations are drawn and tested against observed data was also investigated. Analysis of both synthetic and field data collected at the Eggborough (UK) site indicates that the geophysical data alone contain valuable information regarding the VGM parameters. However, significantly better results are obtained when these data are combined with a realistic, informative prior. A subsequent study explore in detail the dynamic infiltration case, specifically to what extent time-lapse ZOP GPR data, collected during a forced infiltration experiment at the Arrenaes field site (Denmark), can help to quantify VGM parameters and their uncertainties using the MCMC inversion strategy. The findings indicate that the stochastic inversion of time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions. In turn, this significantly improves knowledge of the hydraulic properties, which are required to predict hydraulic behaviour. Finally, another aspect that needed to be addressed involved the comparison of time-lapse GPR data collected under different infiltration conditions (i.e., natural loading and forced infiltration conditions) to estimate the VGM parameters using the MCMC inversion strategy. The results show that for the synthetic example, considering data collected during a forced infiltration test helps to better refine soil hydraulic properties compared to data collected under natural infiltration conditions. When investigating data collected at the Arrenaes field site, further complications arised due to model error and showed the importance of also including a rigorous analysis of the propagation of model error with time and depth when considering time-lapse data. Although the efforts in this thesis were focused on GPR data, the corresponding findings are likely to have general applicability to other types of geophysical data and field environments. Moreover, the obtained results allow to have confidence for future developments in integration of geophysical data with stochastic inversions to improve the characterization of the unsaturated zone but also reveal important issues linked with stochastic inversions, namely model errors, that should definitely be addressed in future research.

Intuitiosta esitykseen : Lear-prosessi itsereflektion ja katsojapalautteen valossa

My final project presents the directing process of my experimental production based on King Lear by William Shakespeare. I describe the process from the first visions of the beginning to the completed performance and finally the feedback from the audience. I concentrate on the special qualities of the production, such as interaction, small and moveable audience, cinematic qualities, polyphonic dramaturgy, and use of the video. The Project is divided into six parts. The first part introduces the project as a whole. The second part concentrates on the process before the beginning of the rehearsals. The third part focuses on the rehearsals and co-operation with the actors, whereas the fourth part deals with the performance and its special qualities. Following this, in the fifth part I study the interaction of the performance with the help of the audience feedback. In the final part conclusions are drawn. The focus of this work is the use of intuition even as a starting point of the theatre directing process. My conclusions drawn from the description of the process suggest that the starting point of the theatre production may be an intuitive vision as well as some conscious subject or message.

Uhkaava ennenaikainen synnytys: hoitotyön prosessi Naistenklinikan osastolla 42 kätilöiden kokemana

Opinnäytetyön tarkoituksena oli selvittää ja kuvata miten hoitotyön prosessi etenee uhkaavassa ennenaikaisessa synnytyksessä Naistenklinikan osastolla 42 kätilöiden näkökulmasta. Lisäksi selvitettiin, minkälaisia haasteita uhkaavan ennenaikaisen synnytyksen hoitotyön prosessissa ilmenee. Opinnäytetyön tutkimusaineisto koottiin haastattelemalla viittä Naistenklinikan osastolla 42 työskentelevää kätilönä. Haastattelut toteutettiin teemahaastatteluina. Teemahaastatteluiden avulla pyrittiin saamaan vastauksia tutkimusongelmiin, jotka oli laadittu perehtymällä aihetta käsitteleviin tutkimuksiin ja kirjallisuuteen. Saatu tutkimusaineisto analysoitiin induktiivisen sisällönanalyysin avulla. Tulosten mukaan uhkaavan ennenaikaisen synnytyksen hoidossa kätilön rooli korostuu potilaan kokonaistilanteen kartoittamisessa sekä äidin fyysisen, psyykkisen ja sosiaalisen hyvinvoinnin tukemisessa. Osastolla toteutettavaa hoitoa ohjaavat lääkärin antamat yksilölliset hoito-ohjeet ja määräykset, mutta kätilöillä on myös oma hoitotyön näkökulma työskentelyssään äitien kanssa. Kätilötyön näkökulmasta uhkaavan ennenaikaisen synnytyksen hoito koostuu äidin ja sikiön fyysisen hyvinvoinnin sekä äidin psyykkisen ja sosiaalisen hyvinvoinnin tukemisesta. Fyysisen hyvinvoinnin tukemiseen kuuluvat lepohoidosta ja lääkehoidosta huolehtiminen, supistusten, vuotojen ja infektio-oireiden seuranta sekä sikiön voinnin tarkkailu. Psyykkisestä ja sosiaalisesta hyvinvoinnista huolehditaan pyrkimällä antamaan äideille riittävästi tukea, tietoa ja ohjausta sekä huomioimalla myös potilaan muun perheen jaksaminen. Uhkaavan ennenaikaisen synnytyksen hoito on moniammatillista yhteistyötä, jossa kätilö toimii hoitotiimin koordinaattorina. Haasteellisimmaksi asiaksi hoitotyössä haastatteluihin osallistuneet kätilöt nimesivät äitien psyykkisen hyvinvoinnin tukemisen. Tämän opinnäytetyön tutkimustuloksia voidaan hyödyntää uhkaavan ennenaikaisen synnytyksen hoitotyön prosessin arvioinnissa ja kehittämisessä Naistenklinikan osastolla 42. Lisäksi tätä opinnäytetyötä tullaan käyttämään lähteenä, kun osastolla 42 tehdään prosessikuvaus uhkaavan ennenaikaisen synnytyksen hoidosta ja hoitopolusta.

Mass conservative three-dimensional water tracer distribution from Markov chain Monte Carlo inversion of time-lapse ground-penetrating radar data

Time-lapse geophysical measurements are widely used to monitor the movement of water and solutes through the subsurface. Yet commonly used deterministic least squares inversions typically suffer from relatively poor mass recovery, spread overestimation, and limited ability to appropriately estimate nonlinear model uncertainty. We describe herein a novel inversion methodology designed to reconstruct the three-dimensional distribution of a tracer anomaly from geophysical data and provide consistent uncertainty estimates using Markov chain Monte Carlo simulation. Posterior sampling is made tractable by using a lower-dimensional model space related both to the Legendre moments of the plume and to predefined morphological constraints. Benchmark results using cross-hole ground-penetrating radar travel times measurements during two synthetic water tracer application experiments involving increasingly complex plume geometries show that the proposed method not only conserves mass but also provides better estimates of plume morphology and posterior model uncertainty than deterministic inversion results.

Stochastic processes induced by dichotomous markov noise: Some exact dynamical results

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-FokkerPlanck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.

Análise da transição entre dias secos e chuvosos por meio da cadeia de Markov de terceira ordem

O objetivo deste trabalho foi verificar se as ocorrências de dias secos e chuvosos são condicionalmente dependentes da seqüência dos três dias secos e chuvosos anteriores, numa zona pluviometricamente homogênea, por meio da cadeia não-homogênea de Markov de terceira ordem. Os resultados mostraram que as probabilidades diárias de transição podem ser adequadamente estimadas, com base em dados agregados bimestralmente, seguidas de interpolação por meio de funções sinusoidais. Além disso, evidenciou-se que, naquela zona, as ocorrências diárias de chuva são condicionalmente dependentes da seqüência de dias secos e chuvosos nos três dias anteriores. A cadeia não-homogênea de Markov de terceira ordem é um importante instrumento para a análise da dependência entre as seqüências de dias secos e chuvosos em determinadas regiões.

Liiketalousinnovaatioiden keksiminen on myös kognitiivinen prosessi

Summary: Cognitive processes are essential parts of economic innovation

Bayesian Markov-chain-Monte-Carlo inversion of time-lapse cross hole ground-penetrating radar data to characterize the vadose zone at the Arrenaes field site, Denmark

The ground-penetrating radar (GPR) geophysical method has the potential to provide valuable information on the hydraulic properties of the vadose zone because of its strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR traveltime data can allow for a significant reduction in uncertainty regarding subsurface van Genuchten-Mualem (VGM) parameters. Much of the previous work on the stochastic estimation of VGM parameters from crosshole GPR data has considered the case of steady-state infiltration conditions, which represent only a small fraction of practically relevant scenarios. We explored in detail the dynamic infiltration case, specifically examining to what extent time-lapse crosshole GPR traveltimes, measured during a forced infiltration experiment at the Arreneas field site in Denmark, could help to quantify VGM parameters and their uncertainties in a layered medium, as well as the corresponding soil hydraulic properties. We used a Bayesian Markov-chain-Monte-Carlo inversion approach. We first explored the advantages and limitations of this approach with regard to a realistic synthetic example before applying it to field measurements. In our analysis, we also considered different degrees of prior information. Our findings indicate that the stochastic inversion of the time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions compared with the corresponding priors, which in turn significantly improves knowledge of soil hydraulic properties. Overall, the results obtained clearly demonstrate the value of the information contained in time-lapse GPR data for characterizing vadose zone dynamics.