18 resultados para inverse probability weighted

em Helda - Digital Repository of University of Helsinki


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Modern sample surveys started to spread after statistician at the U.S. Bureau of the Census in the 1940s had developed a sampling design for the Current Population Survey (CPS). A significant factor was also that digital computers became available for statisticians. In the beginning of 1950s, the theory was documented in textbooks on survey sampling. This thesis is about the development of the statistical inference for sample surveys. For the first time the idea of statistical inference was enunciated by a French scientist, P. S. Laplace. In 1781, he published a plan for a partial investigation in which he determined the sample size needed to reach the desired accuracy in estimation. The plan was based on Laplace s Principle of Inverse Probability and on his derivation of the Central Limit Theorem. They were published in a memoir in 1774 which is one of the origins of statistical inference. Laplace s inference model was based on Bernoulli trials and binominal probabilities. He assumed that populations were changing constantly. It was depicted by assuming a priori distributions for parameters. Laplace s inference model dominated statistical thinking for a century. Sample selection in Laplace s investigations was purposive. In 1894 in the International Statistical Institute meeting, Norwegian Anders Kiaer presented the idea of the Representative Method to draw samples. Its idea was that the sample would be a miniature of the population. It is still prevailing. The virtues of random sampling were known but practical problems of sample selection and data collection hindered its use. Arhtur Bowley realized the potentials of Kiaer s method and in the beginning of the 20th century carried out several surveys in the UK. He also developed the theory of statistical inference for finite populations. It was based on Laplace s inference model. R. A. Fisher contributions in the 1920 s constitute a watershed in the statistical science He revolutionized the theory of statistics. In addition, he introduced a new statistical inference model which is still the prevailing paradigm. The essential idea is to draw repeatedly samples from the same population and the assumption that population parameters are constants. Fisher s theory did not include a priori probabilities. Jerzy Neyman adopted Fisher s inference model and applied it to finite populations with the difference that Neyman s inference model does not include any assumptions of the distributions of the study variables. Applying Fisher s fiducial argument he developed the theory for confidence intervals. Neyman s last contribution to survey sampling presented a theory for double sampling. This gave the central idea for statisticians at the U.S. Census Bureau to develop the complex survey design for the CPS. Important criterion was to have a method in which the costs of data collection were acceptable, and which provided approximately equal interviewer workloads, besides sufficient accuracy in estimation.

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Whether a statistician wants to complement a probability model for observed data with a prior distribution and carry out fully probabilistic inference, or base the inference only on the likelihood function, may be a fundamental question in theory, but in practice it may well be of less importance if the likelihood contains much more information than the prior. Maximum likelihood inference can be justified as a Gaussian approximation at the posterior mode, using flat priors. However, in situations where parametric assumptions in standard statistical models would be too rigid, more flexible model formulation, combined with fully probabilistic inference, can be achieved using hierarchical Bayesian parametrization. This work includes five articles, all of which apply probability modeling under various problems involving incomplete observation. Three of the papers apply maximum likelihood estimation and two of them hierarchical Bayesian modeling. Because maximum likelihood may be presented as a special case of Bayesian inference, but not the other way round, in the introductory part of this work we present a framework for probability-based inference using only Bayesian concepts. We also re-derive some results presented in the original articles using the toolbox equipped herein, to show that they are also justifiable under this more general framework. Here the assumption of exchangeability and de Finetti's representation theorem are applied repeatedly for justifying the use of standard parametric probability models with conditionally independent likelihood contributions. It is argued that this same reasoning can be applied also under sampling from a finite population. The main emphasis here is in probability-based inference under incomplete observation due to study design. This is illustrated using a generic two-phase cohort sampling design as an example. The alternative approaches presented for analysis of such a design are full likelihood, which utilizes all observed information, and conditional likelihood, which is restricted to a completely observed set, conditioning on the rule that generated that set. Conditional likelihood inference is also applied for a joint analysis of prevalence and incidence data, a situation subject to both left censoring and left truncation. Other topics covered are model uncertainty and causal inference using posterior predictive distributions. We formulate a non-parametric monotonic regression model for one or more covariates and a Bayesian estimation procedure, and apply the model in the context of optimal sequential treatment regimes, demonstrating that inference based on posterior predictive distributions is feasible also in this case.

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The problem of recovering information from measurement data has already been studied for a long time. In the beginning, the methods were mostly empirical, but already towards the end of the sixties Backus and Gilbert started the development of mathematical methods for the interpretation of geophysical data. The problem of recovering information about a physical phenomenon from measurement data is an inverse problem. Throughout this work, the statistical inversion method is used to obtain a solution. Assuming that the measurement vector is a realization of fractional Brownian motion, the goal is to retrieve the amplitude and the Hurst parameter. We prove that under some conditions, the solution of the discretized problem coincides with the solution of the corresponding continuous problem as the number of observations tends to infinity. The measurement data is usually noisy, and we assume the data to be the sum of two vectors: the trend and the noise. Both vectors are supposed to be realizations of fractional Brownian motions, and the goal is to retrieve their parameters using the statistical inversion method. We prove a partial uniqueness of the solution. Moreover, with the support of numerical simulations, we show that in certain cases the solution is reliable and the reconstruction of the trend vector is quite accurate.

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We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

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Plasma membrane adopts myriad of different shapes to carry out essential cellular processes such as nutrient uptake, immunological defence mechanisms and cell migration. Therefore, the details how different plasma membrane structures are made and remodelled are of the upmost importance. Bending of plasma membrane into different shapes requires substantial amount of force, which can be provided by the actin cytoskeleton, however, the molecules that regulate the interplay between the actin cytoskeleton and plasma membrane have remained elusive. Recent findings have placed new types of effectors at sites of plasma membrane remodelling, including BAR proteins, which can directly bind and deform plasma membrane into different shapes. In addition to their membrane-bending abilities, BAR proteins also harbor protein domains that intimately link them to the actin cytoskeleton. The ancient BAR domain fold has evolved into at least three structurally and functionally different sub-groups: the BAR, F-BAR and I-BAR domains. This thesis work describes the discovery and functional characterization of the Inverse-BAR domains (I-BARs). Using synthetic model membranes, we have shown that I-BAR domains bind and deform membranes into tubular structures through a binding-surface composed of positively charged amino acids. Importantly, the membrane-binding surface of I-BAR domains displays an inverse geometry to that of the BAR and F-BAR domains, and these structural differences explain why I-BAR domains induce cell protrusions whereas BAR and most F-BAR domains induce cell invaginations. In addition, our results indicate that the binding of I-BAR domains to membranes can alter the spatial organization of phosphoinositides within membranes. Intriguingly, we also found that some I-BAR domains can insert helical motifs into the membrane bilayer, which has important consequences for their membrane binding/bending functions. In mammals there are five I-BAR domain containing proteins. Cell biological studies on ABBA revealed that it is highly expressed in radial glial cells during the development of the central nervous system and plays an important role in the extension process of radial glia-like C6R cells by regulating lamellipodial dynamics through its I-BAR domain. To reveal the role of these proteins in the context of animals, we analyzed MIM knockout mice and found that MIM is required for proper renal functions in adult mice. MIM deficient mice displayed a severe urine concentration defect due to defective intercellular junctions of the kidney epithelia. Consistently, MIM localized to adherens junctions in cultured kidney epithelial cells, where it promoted actin assembly through its I-BAR andWH2 domains. In summary, this thesis describes the mechanism how I-BAR proteins deform membranes and provides information about the biological role of these proteins, which to our knowledge are the first proteins that have been shown to directly deform plasma membrane to make cell protrusions.

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We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

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We present a measurement of the top quark mass with t-tbar dilepton events produced in p-pbar collisions at the Fermilab Tevatron $\sqrt{s}$=1.96 TeV and collected by the CDF II detector. A sample of 328 events with a charged electron or muon and an isolated track, corresponding to an integrated luminosity of 2.9 fb$^{-1}$, are selected as t-tbar candidates. To account for the unconstrained event kinematics, we scan over the phase space of the azimuthal angles ($\phi_{\nu_1},\phi_{\nu_2}$) of neutrinos and reconstruct the top quark mass for each $\phi_{\nu_1},\phi_{\nu_2}$ pair by minimizing a $\chi^2$ function in the t-tbar dilepton hypothesis. We assign $\chi^2$-dependent weights to the solutions in order to build a preferred mass for each event. Preferred mass distributions (templates) are built from simulated t-tbar and background events, and parameterized in order to provide continuous probability density functions. A likelihood fit to the mass distribution in data as a weighted sum of signal and background probability density functions gives a top quark mass of $165.5^{+{3.4}}_{-{3.3}}$(stat.)$\pm 3.1$(syst.) GeV/$c^2$.

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We present a search for standard model Higgs boson production in association with a W boson in proton-antiproton collisions at a center of mass energy of 1.96 TeV. The search employs data collected with the CDF II detector that correspond to an integrated luminosity of approximately 1.9 inverse fb. We select events consistent with a signature of a single charged lepton, missing transverse energy, and two jets. Jets corresponding to bottom quarks are identified with a secondary vertex tagging method, a jet probability tagging method, and a neural network filter. We use kinematic information in an artificial neural network to improve discrimination between signal and background compared to previous analyses. The observed number of events and the neural network output distributions are consistent with the standard model background expectations, and we set 95% confidence level upper limits on the production cross section times branching fraction ranging from 1.2 to 1.1 pb or 7.5 to 102 times the standard model expectation for Higgs boson masses from 110 to $150 GeV/c^2, respectively.

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Biological membranes are tightly linked to the evolution of life, because they provide a way to concentrate molecules into partially closed compartments. The dynamic shaping of cellular membranes is essential for many physiological processes, including cell morphogenesis, motility, cytokinesis, endocytosis, and secretion. It is therefore essential to understand the structure of the membrane and recognize the players that directly sculpt the membrane and enable it to adopt different shapes. The actin cytoskeleton provides the force to push eukaryotic plasma membrane in order to form different protrusions or/and invaginations. It has now became evident that actin directly co-operates with many membrane sculptors, including BAR domain proteins, in these important events. However, the molecular mechanisms behind BAR domain function and the differences between the members of this large protein family remain largely unresolved. In this thesis, the structure and functions of the I-BAR domain family members IRSp53 and MIM were thoroughly analyzed. By using several methods such as electron microscopy and systematic mutagenesis, we showed that these I-BAR domain proteins bind to PI(4,5)P2-rich membranes, generate negative membrane curvature and are involved in the formation of plasma membrane protrusions in cells e.g. filopodia. Importantly, we characterized a novel member of the BAR-domain superfamily which we named Pinkbar. We revealed that Pinkbar is specifically expressed in kidney and epithelial cells, and it localizes to Rab13-positive vesicles in intestinal epithelial cells. Remarkably, we learned that the I-BAR domain of Pinkbar does not generate membrane curvature but instead stabilizes planar membranes. Based on structural, mutagenesis and biochemical work we present a model for the mechanism of the novel membrane deforming activity of Pinkbar. Collectively, this work describes the mechanism by which I-BAR domain proteins deform membranes and provides new information about the biological roles of these proteins. Intriguingly, this work also gives evidence that significant functional plasticity exists within the I-BAR domain family. I-BAR proteins can either generate negative membrane curvature or stabilize planar membrane sheets, depending on the specific structural properties of their I-BAR domains. The results presented in this thesis expand our knowledge on membrane sculpting mechanisms and shows for the first time how flat membranes can be generated in cells.

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An inverse problem for the wave equation is a mathematical formulation of the problem to convert measurements of sound waves to information about the wave speed governing the propagation of the waves. This doctoral thesis extends the theory on the inverse problems for the wave equation in cases with partial measurement data and also considers detection of discontinuous interfaces in the wave speed. A possible application of the theory is obstetric sonography in which ultrasound measurements are transformed into an image of the fetus in its mother's uterus. The wave speed inside the body can not be directly observed but sound waves can be produced outside the body and their echoes from the body can be recorded. The present work contains five research articles. In the first and the fifth articles we show that it is possible to determine the wave speed uniquely by using far apart sound sources and receivers. This extends a previously known result which requires the sound waves to be produced and recorded in the same place. Our result is motivated by a possible application to reflection seismology which seeks to create an image of the Earth s crust from recording of echoes stimulated for example by explosions. For this purpose, the receivers can not typically lie near the powerful sound sources. In the second article we present a sound source that allows us to recover many essential features of the wave speed from the echo produced by the source. Moreover, these features are known to determine the wave speed under certain geometric assumptions. Previously known results permitted the same features to be recovered only by sequential measurement of echoes produced by multiple different sources. The reduced number of measurements could increase the number possible applications of acoustic probing. In the third and fourth articles we develop an acoustic probing method to locate discontinuous interfaces in the wave speed. These interfaces typically correspond to interfaces between different materials and their locations are of interest in many applications. There are many previous approaches to this problem but none of them exploits sound sources varying freely in time. Our use of more variable sources could allow more robust implementation of the probing.

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We propose to compress weighted graphs (networks), motivated by the observation that large networks of social, biological, or other relations can be complex to handle and visualize. In the process also known as graph simplication, nodes and (unweighted) edges are grouped to supernodes and superedges, respectively, to obtain a smaller graph. We propose models and algorithms for weighted graphs. The interpretation (i.e. decompression) of a compressed, weighted graph is that a pair of original nodes is connected by an edge if their supernodes are connected by one, and that the weight of an edge is approximated to be the weight of the superedge. The compression problem now consists of choosing supernodes, superedges, and superedge weights so that the approximation error is minimized while the amount of compression is maximized. In this paper, we formulate this task as the 'simple weighted graph compression problem'. We then propose a much wider class of tasks under the name of 'generalized weighted graph compression problem'. The generalized task extends the optimization to preserve longer-range connectivities between nodes, not just individual edge weights. We study the properties of these problems and propose a range of algorithms to solve them, with dierent balances between complexity and quality of the result. We evaluate the problems and algorithms experimentally on real networks. The results indicate that weighted graphs can be compressed efficiently with relatively little compression error.

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We use parallel weighted finite-state transducers to implement a part-of-speech tagger, which obtains state-of-the-art accuracy when used to tag the Europarl corpora for Finnish, Swedish and English. Our system consists of a weighted lexicon and a guesser combined with a bigram model factored into two weighted transducers. We use both lemmas and tag sequences in the bigram model, which guarantees reliable bigram estimates.