Statistical Parameter Estimation Research Articles

Hidden Markov random field model based brain MR image segmentation using clonal selection algorithm and Markov chain Monte Carlo method

The hidden Markov random field (HMRF) model has been widely used in image segmentation, as it provides a spatially constrained clustering scheme on two sets of random variables. However, in many HMRF-based segmentation approaches, both the latent class labels and statistical parameters have been estimated by deterministic techniques, which usually lead to local convergence and less accurate segmentation. In this paper, we incorporate the immune inspired clonal selection algorithm (CSA) and Markov chain Monte Carlo (MCMC) method into HMRF model estimation, and thus propose the HMRF–CSA algorithm for brain MR image segmentation. Our algorithm employs a three-step iterative process that consists of MCMC-based class labels estimation, bias field correction and CSA-based statistical parameter estimation. Since both the MCMC and CSA are global optimization techniques, the proposed algorithm has the potential to overcome the drawback of traditional HMRF-based segmentation approaches. We compared our algorithm to the state-of-the-art GA–EM algorithm, deformable cosegmentation algorithm, the segmentation routines in the widely-used statistical parametric mapping (SPM) software package and the FMRIB software library (FSL) on both simulated and clinical brain MR images. Our results show that the proposed HMRF–CSA algorithm is robust to image artifacts and can differentiate major brain structures more accurately than other three algorithms.

An efficient approach to large-scale genotype–phenotype association analyses

Modern molecular biotechnology generates a great deal of intermediate information, such as transcriptional and metabolic products in bridging DNA and complex traits. In genome-wide linkage analysis and genome-wide association study, regression analysis for large-scale correlated phenotypes is applied to map genes for those by-products that are regarded as quantitative traits. For a single trait, least absolute shrinkage and selection operator with coordinate descent step can be employed to efficiently shrink sparse non-zero genetic effects of quantitative trait loci (QTLs). However, regression analyses in a trait-by-trait basis do not take account of the correlations among the analyzed traits. In this study, conditional phenotype of each trait is defined, given other traits. Large-scale genotype-phenotype association analyses are therefore transformed to separate genotype-conditional phenotype ones. Meanwhile, the correlation architecture between each trait and other traits can also be provided by shrinkage estimation for each conditional phenotype. Simulation demonstrates that the proposed conditional mapping method is generally identical to joint mapping method based on multivariate analysis in terms of statistical detection power and parameter estimation. Application of the method is provided to locate eQTL in yeast.

Three-Dimensional Elemental Mapping at the Atomic Scale in Bimetallic Nanocrystals

A thorough understanding of the three-dimensional (3D) atomic structure and composition of core-shell nanostructures is indispensable to obtain a deeper insight on their physical behavior. Such 3D information can be reconstructed from two-dimensional (2D) projection images using electron tomography. Recently, different electron tomography techniques have enabled the 3D characterization of a variety of nanostructures down to the atomic level. However, these methods have all focused on the investigation of nanomaterials containing only one type of chemical element. Here, we combine statistical parameter estimation theory with compressive sensing based tomography to determine the positions and atom type of each atom in heteronanostructures. The approach is applied here to investigate the interface in core-shell Au@Ag nanorods but it is of great interest in the investigation of a broad range of nanostructures.

Dynamic bidding strategies in search-based advertising

Search-based advertising allows the advertisers to run special campaigns targeted to different groups of potential consumers at low costs. Google, Yahoo and Microsoft advertising programs allow the advertisers to bid for an ad position on the result page of a user’s query when the user searches for a keyword that the advertiser relates to its products or services. The expected revenue generated by the ad depends on the ad position, and the ad positions of the advertisers are concurrently determined after an instantaneous auction based on the bids of the advertisers. The advertisers are charged only when their ads are clicked by the users. To avoid excessive ad expenditures due to sudden surges in the keyword-search activities, each advertiser reserves a fixed finite daily budget, and the ads are not shown in the remainder of the day when the budget is depleted. Arrival times of keyword-search instances, ad positions, ad selections, and sales generated by the ads are random. Therefore, an advertiser faces a dynamic stochastic total net revenue optimization problem subject to a strict budget constraint. Here we formulate and solve this problem using dynamic programming. We show that there is always an optimal dynamic bidding policy. We describe an iterative numerical approximation algorithm that uniformly converges to the optimal solution at an exponential rate of the number of iterations. We illustrate the algorithm on numerical examples. Because dynamic programing calculations of the optimal bidding policies are computationally demanding, we also propose both static and dynamic alternative bidding policies. We numerically compare the performances of optimal and alternative bidding policies by systematically changing each input parameter. The relative percentage total net revenue losses of the alternative bidding policies increases with the budget loading, but were never more than 3.5 % of maximum expected total net revenue. The best alternative to the optimal bidding policy turned out to be a static greedy bidding policy. Finally, statistical estimation of the model parameters is visited.

Statistically-based approach for monitoring of micro-seismic events

We consider the problem of optimal statistical estimation of micro-seismic source parameters using multichannel data from surface arrays of seismometers affected by a strong seismic noise. The problem is treated as a statistical task of parameter estimation for a general type multidimensional linear model with random or completely unknown input time functions. The maximum-likelihood generic estimators are derived and their relationship with the well-known seismic emission tomography (SET) algorithm is established. The proposed estimation algorithms perform processing of multichannel discrete observations in the frequency domain and can be implemented in on-line mode. Using the method of successive independent trials (Monte-Carlo), we demonstrate that a proposed statistical estimation algorithm provides much higher accuracy of the micro-seismic event source location in real noise conditions than the widely used SET algorithm and, as a consequence, is more reliable in practical applications.

A Shape‐Aware Model for Discrete Texture Synthesis

AbstractWe present a novel shape‐aware method for synthesizing 2D and 3D discrete element textures consisting of collections of distinct vector graphics objects. Extending the long‐proven point process framework, we propose a shape process, a novel stochastic model based on spatial measurements that fully take into account the geometry of the elements. We demonstrate that our approach is well‐suited for discrete texture synthesis by example. Our model enables for both robust statistical parameter estimation and reliable output generation by Monte Carlo sampling. Our numerous experiments show that contrary to current state‐of‐the‐art techniques, our algorithm manages to capture anisotropic element distributions and systematically prevents undesirable collisions between objects.

A Nonparametric Approach to Cognitive Diagnosis by Proximity to Ideal Response Patterns

A trend in educational testing is to go beyond unidimensional scoring and provide a more complete profile of skills that have been mastered and those that have not. To achieve this, cognitive diagnosis models have been developed that can be viewed as restricted latent class models. Diagnosis of class membership is the statistical objective of these models. As an alternative to latent class modeling, a nonparametric procedure is introduced that only requires specification of an item-by-attribute association matrix, and classifies according to minimizing a distance measure between observed responses, and the ideal response for a given attribute profile that would be implied by the item-by-attribute association matrix. This procedure requires no statistical parameter estimation, and can be used on a sample size as small as 1. Heuristic arguments are given for why the nonparametric procedure should be effective under various possible cognitive diagnosis models for data generation. Simulation studies compare classification rates with parametric models, and consider a variety of distance measures, data generation models, and the effects of model misspecification. A real data example is provided with an analysis of agreement between the nonparametric method and parametric approaches.

Both species sorting and neutral processes drive assembly of bacterial communities in aquatic microcosms

A focus of ecology is to determine drivers of community assembly. Here, we investigate effects of immigration and species sorting (environmental selection) on structuring aquatic bacterial communities in both colonised and previously uncolonised environments. We used nonsterilised and presterilised water from three chemically distinct ponds to establish microcosms, which were opened for 12, 24, 48, 96 or 167 h and then closed again to allow airborne bacterial immigration and subsequent succession. Community similarity, richness, evenness and the parameters of a neutral model were investigated after 167 h. Immigration appeared to govern the assembly of communities in the presterilised water as there were no significant differences in evenness among microcosm communities containing water from each pond. Statistical estimation of neutral model parameters confirmed these findings, because the estimated immigration rate changed significantly with time of exposure to immigration. Species sorting also occurred because significant differences in community similarity (for presterilised and nonsterilised communities) and evenness (only for nonsterilised communities) were detected among microcosms containing different pond water; the magnitude of these differences was greater for communities in nonsterilised microcosms. Our study provides evidence for both processes being important during the colonisation of aquatic environments and presents a novel way to apply the neutral model.

Foreword: inverse problems in biology

Advances in the understanding of biology are often based on successful interpretation of indirect measurements. Those measurements may take the form of microscopic images, electrical neurophysiology data, X-ray microtomography reconstructions, observations of the end products of chemical reactions, or spatial distribution of species. Sometimes the quantity of interest causes only a small and noise-sensitive effect to the measured data, which makes the interpretation task an ill-posed inverse problem. Generally, inverse problems are defined as the problem of recovering information from indirect, incomplete or noisy observationswith amathematicalmodel. Both theoretical and computational inversion methods have developed tremendously in recent years. The purpose of the present Special Issue is to promote the application of the newest inversion methods to studies in mathematical biology, hopefully giving a boost to both fields. The collection of articles in this special issue covers a wide spectrum of topics connecting the mathematics of biology and of inverse problems. Included are results related to population dynamics, therapeutic strategies for diseases, tumor growth, and analysis of models for heart and neural cables. Furthermore, there are studies of inverse problems appearing in the information recovery in molecular biology, protein polymerization, and chemical dynamics in neurons. Methodologically, the present articles combine severalmathematical tools used in inverse problems, such as statistical methods, control theory, and parameter estimation, and apply them to both classical and novel models used in mathematical biology.

Estimation of unknown structure parameters from high-resolution (S)TEM images: What are the limits?

Statistical parameter estimation theory is proposed as a quantitative method to measure unknown structure parameters from electron microscopy images. Images are then purely considered as data planes from which structure parameters have to be determined as accurately and precisely as possible using a parametric statistical model of the observations. For this purpose, an efficient algorithm is proposed for the estimation of atomic column positions and intensities from high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images. Furthermore, the so-called Cramér-Rao lower bound (CRLB) is reviewed to determine the limits to the precision with which continuous parameters such as atomic column positions and intensities can be estimated. Since this lower bound can only be derived for continuous parameters, alternative measures using the principles of detection theory are introduced for problems concerning the estimation of discrete parameters such as atomic numbers. An experimental case study is presented to show the practical use of these measures for the optimization of the experiment design if the purpose is to decide between the presence of specific atom types using STEM images.

Atom counting in HAADF STEM using a statistical model-based approach: Methodology, possibilities, and inherent limitations

In the present paper, a statistical model-based method to count the number of atoms of monotype crystalline nanostructures from high resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images is discussed in detail together with a thorough study on the possibilities and inherent limitations. In order to count the number of atoms, it is assumed that the total scattered intensity scales with the number of atoms per atom column. These intensities are quantitatively determined using model-based statistical parameter estimation theory. The distribution describing the probability that intensity values are generated by atomic columns containing a specific number of atoms is inferred on the basis of the experimental scattered intensities. Finally, the number of atoms per atom column is quantified using this estimated probability distribution. The number of atom columns available in the observed STEM image, the number of components in the estimated probability distribution, the width of the components of the probability distribution, and the typical shape of a criterion to assess the number of components in the probability distribution directly affect the accuracy and precision with which the number of atoms in a particular atom column can be estimated. It is shown that single atom sensitivity is feasible taking the latter aspects into consideration.

An efficient method for the estimation of parameters of stochastic gamma process from noisy degradation measurements

The stochastic gamma process model is widely used in modeling a variety of degradation phenomena in engineering structures and components. If degradation in a component population can be accurately measured over time, the statistical estimation of gamma process parameters is a relatively straight-forward task. However, in most practical situations, degradation data are collected through in-service and non-destructive inspection methods, which invariably contaminate the data by adding random noises (or sizing errors) to the data. Therefore, a proper estimation method is needed to filter out the effect of sizing errors from the measured degradation data. This article presents an efficient method for estimating the parameters of the gamma process model based on a novel use of the Genz transform and quasi-Monte Carlo method in the maximum likelihood estimation. Examples presented show that the proposed method is very efficient compared with the Monte Carlo method currently used for this purpose in the literature.

Estimation of G-renewal process parameters as an ill-posed inverse problem

Statistical estimation of G-renewal process parameters is an important estimation problem, which has been considered by many authors. We view this problem from the standpoint of a mathematically ill-posed, inverse problem (the solution is not unique and/or is sensitive to statistical error) and propose a regularization approach specifically suited to the G-renewal process. Regardless of the estimation method, the respective objective function usually involves parameters of the underlying life-time distribution and simultaneously the restoration parameter. In this paper, we propose to regularize the problem by decoupling the estimation of the aforementioned parameters. Using a simulation study, we show that the resulting estimation/extrapolation accuracy of the proposed method is considerably higher than that of the existing methods.

Statistical analysis of CPT tip resistances

Selecting proper values for soil parameters is a crucial aspect in geotechnical engineering. Geomaterials exhibit an inherent, natural variability, which can be assessed by statistical methods. CPT data lend themselves well for statistical analysis, given the large amount of data retrieved in a single test. The aim of this study was to examine the guidelines for statistical parameter estimation set out in Eurocode 7, as applied to CPT tip resistances. First, the guidelines and methods for estimation of fractiles and mean value with a given confidence level were reviewed. Second, a number of 125 CPT datasets were analyzed: the goodness-of-fit tests have shown that the common assumption of a normal distribution does not hold. Third, different estimation methods for the 5% fractile, the mean and the median were evaluated with regard to robustness and efficiency.

Implicit Interaction: Mathematics on Local Description of Systems

Researches on co-creation systems and that on internal measurement share some basic views on complex systems. These are the researches on features of complex systems which include some duality such as explicit/implicit information or global/local interaction, etc. For experiments and analyses based on the views, we need a theoretical framework describing the duality. In this study, two types of interaction are introduced. One is “explicit interaction” which is defined by conventional usage of functions, and the other is “implicit interaction” which is defined by a generalized determination process of function parameters. These interactions are formalized via duality on vector spaces and generalized inverse matrices. Implicit interaction is defined by the form which is similar to statistical parameter estimation but is not the same. It derives a Cauchy distribution on parameter fluctuation and structural branch on parameters.

Optimal resource allocation in fetmocell networks based on Markov modeling of interferers’ activity

Femtocell networks offer a series of advantages with respect to conventional cellular networks. However, a potential massive deployment of femto-access points (FAPs) poses a big challenge in terms of interference management, which requires proper radio resource allocation techniques. In this article, we propose alternative optimal power/bit allocation strategies over a time-frequency frame based on a statistical modeling of the interference activity. Given the lack of knowledge of the interference activity, we assume a Bayesian approach that provides the optimal allocation, conditioned to periodic spectrum sensing, and estimation of the interference activity statistical parameters. We consider first a single FAP accessing the radio channel in the presence of a dynamical interference environment. Then, we extend the formulation to a multi-FAP scenario, where nearby FAP’s react to the strategies of the other FAP’s, still within a dynamical interference scenario. The multi-user case is first approached using a strategic non-cooperative game formulation. Then, we propose a coordination game based on the introduction of a pricing mechanism that exploits the backhaul link to enable the exchange of parameters (prices) among FAP’s.

Impact of coal output concentration on methane emission to longwall faces / Wpływ koncentracji wydobycia na wydzielanie metanu do wyrobisk ścianowych

An increase in concentration of coal output in Polish hard coal mines contributes to a significant increase in absolute methane-bearing capacity in mining areas. Measurements of methane concentration were taken in selected longwall faces in order to estimate the influence of coal output on methane hazard. The measurements were taken from 2006 to 2008 in 8 longwalls in mines with high methane hazard. The parameters for longwalls where measurements were taken are presented in table 1. Average daily output ranged from 1380 to 2320 Mg: however the maximum daily output amounted to 5335 Mg. Absolute methane-bearing capacity ranged from 4.44 to 56.41 m3/min. Longwalls were ventilated with a U and Y system and their ventilation schemes are presented in figure 1. The period of measurements ranged from 29 to 384 days. The results obtained were used to determine the influence of changes in output on methane hazard. For each longwall under research statistical estimation of parameters, such as: ventilation air methane (VAM) emission, amount of methane captured by a drainage system, absolute methane-bearing capacity and an advance of longwall face was conducted. In order to determine the influence of a longwall face advance on methane-bearing capacity the probabilistic model of the distribution of those parameters on the basis of the measurement results was used. In order to determine the dependence between ventilation air methane emission, methane drainage, absolute methane-bearing capacity and longwall advance, the distribution of analysed variables was checked by means of Kolmogorow-Smirnov normality test. The results of this test are presented in table 2. Table 3 presents values for correlation co-efficient r(x,y). When analyzing the results presented in table 3 it must be observed that in case of most longwalls there is a high correlation between ventilation air methane emission, absolute methane-bearing capacity and longwall advance. However, in longwalls N-10 i W-5 the correlation between methane drainage capture and longwall advance is equally strong. In all other longwalls the correlation is average. In all cases the correlations were positive, which means that together with an increase in advance, there is also an increase in ventilation air methane emission, methane drainage capture and absolute methane-bearing capacity On the basis of determination co-efficient it can be concluded that in cases under consideration at least half (about 50%) of results, ventilation air methane emission, methane drainage capture and absolute methane-bearing capacity can be explained linearly by an influence of longwall advance, while this statement can be assumed with the probability close to 100%. It should also be added that the lack of very high or full correlations means that examined parameters do not fully show linear dependence; however there might be other functional correlations. Because of a complex character of phenomena happening during mining it is not possible to determine full correlations. However, the interpretation of results allows us to claim that an influence of wall advance on methane emission amounts to 30 to 70% depending on a given case. Therefore, other factors, for example geological ones, which were not taken into consideration, will contribute to the level of methane hazard. Table 4 presents determined co-efficients of linear regression. On the basis of the data in table 4, an equation describing the dependence of absolute methane-bearing capacity in a longwall on a longwall advance in the form (11) can be formed. Table 5 presents determined co-efficients of non-linear regression. On the basis of the data in table 5, an equation describing the dependence of absolute methane-bearing capacity in a longwall on a longwall advance in the form (13) can be formed. When comparing co-efficient R2 of the contribution of the explained variance in tables 4 and 5 it can be obcserved that non-linear dependence explains better the results of mining measurements. The similar dependence presenting methane emission as dependent on output is suggested by Myszor (1985). The conditions for safe mining can be given for a determined methane emission.

A predictive modelling tool for assessing climate, land use and hydrological change on reservoir physicochemical and biological properties

Reservoirs are fundamental for water and energy supply but vulnerable to impacts including climate change. This paper outlines the steps in the development of a model to predict how climate, land use and hydrological change could affect the physiochemical and ecological quality of reservoirs in Portugal's Douro region. Climatic data will be downscaled for subsequent finer spatial scale models to develop scenarios and outputs. Field observations and satellite imagery analysis will create dynamic maps providing data on change in land use and vegetation cover, while Artificial Neural Networks will determine how climate, land use and vegetation cover change may influence catchment hydrology. Data from field surveys of biological indicators, greenhouse gas emissions plus additional research will be applied in the Stochastic Dynamic Methodology, a sequential modelling process based on statistical parameter estimation, developed to predict and model physiochemical and ecological changes in reservoirs. This interdisciplinary approach will provide vital modelling tools for end users essential for water resource management in Portugal and to comply with the EU Water Framework Directive.

Sequential Cross-Validated Bandwidth Selection Under Dependence and Anscombe-Type Extensions to Random Time Horizons

To detect changes in the mean of a time series, one may use previsible detection procedures based on nonparametric kernel prediction smoothers that cover various classic detection statistics as special cases. Bandwidth selection, particularly in a data-adaptive way, is a serious issue and not well studied for detection problems. To ensure data adaptation, we select the bandwidth by cross-validation but in a sequential way leading to a functional estimation approach. This article provides the asymptotic theory for the method under fairly weak assumptions on the dependence structure of the error terms, which cover, for example, GARCH(p, q) processes, by establishing (sequential) functional central limit theorems for the cross-validation objective function and the associated bandwidth selector. It turns out that the proof can be based in a neat way on Kurtz and Protter's (1996) results on the weak convergence of Itô integrals and a diagonal argument. Our gradual change-point model covers multiple change-points in that it allows for a nonlinear regression function after the first change-point possibly with further jumps and Lipschitz continuity between those discontinuities. In applications, the time horizon where monitoring stops latest is often determined by a random experiment; for example, a first-exit stopping time applied to a cumulated cost process or a risk measure, possibly stochastically dependent on the monitored time series. Thus, we also study that case and establish related limit theorems in the spirit of Anscombe's (1952) result. This is achieved by embedding the stopped processes into a sequence of processes, which allows us to handle the randomly determined time horizon as a random change of time problem. The result has various applications including statistical parameter estimation and monitoring financial investment strategies with risk-controlled early termination, which are briefly discussed.

Degrees of freedom estimation in Principal Component Analysis and Consensus Principal Component Analysis

The concept of degree of freedom (DF) is an important issue in statistical model assessment and parameter estimation. In this paper, we investigate this concept within the context of data modeling by Principal Component Analysis (PCA) and its multi-block extension, the Consensus Principal Component Analysis (CPCA). We run simulation studies and assess the degrees of freedom by comparing cross-validated error estimates with error estimates from uncorrected model fits. These simulation studies reveal that the DF consumption in PCA and CPCA depends on the eigenvalue structure of the data at hand. We also show that the obtained DF estimates can be used to obtain realistic error estimations without performing cross-validation. Furthermore, it is shown how different strategies of cross-validation and the use of an independent test set affect the estimate of the degrees of freedom and the estimate of the model error.