Ulla Holst - Academia.edu (original) (raw)

Papers by Ulla Holst

Research paper thumbnail of Recursive estimators for stationary, strong mixing processes—a representation theorem and asymptotic distributions

Stochastic Processes and their Applications, 1989

Many generalizations of the Robbins-Monro process have been proposed for the purpose of recursive... more Many generalizations of the Robbins-Monro process have been proposed for the purpose of recursive estimation. In this paper it is shown that the recursive estimates can be represented as sums of possibly dependent random variables and can therefore be studied using limit theorems for sums. One application which is particularly studied is recursive M-estimators of location and scale for dependent strong mixing sequences.

Research paper thumbnail of Robust local polynomial regression and statistical evaluation of DOAS measurements

This paper deals with an absorption spectroscopic method for trace gas measurementscalled DOAS (D... more This paper deals with an absorption spectroscopic method for trace gas measurementscalled DOAS (Differential Optical Absorption Spectroscopy) froma statistical point of view. The DOAS technique is an absorption spectroscopictechnique to measure trace gas concentrations. It is capable of detectingand measuring a number of important trace gases at tropospheric concentrationlevels by observing their structured light absorption features. We studythe evaluation procedure

Research paper thumbnail of Convergence of a recursive robust algorithm with strongly regular observations

Stochastic Processes and their Applications, 1984

Robust estimation of parameters may be obtained via stochastic approximation algorithms. This pap... more Robust estimation of parameters may be obtained via stochastic approximation algorithms. This paper deals with the properties of a recursive estimator of a location parameter in a stationary strongly regular process. Adaptive estimators of particular interest are also studied. stochastic approximation strong regularity robust estimation L 0304-4~451/83/S3.00 @I 1983, Elsevier Science Publishers B.V. (North-Holland)

Research paper thumbnail of Correction to: Convergence of a recursive stochastic algorithm with m- dependent observations

Scandinavian Journal of Statistics

Research paper thumbnail of Recursive estimation of quantitles using recursive kernel density estimators

Sequential Analysis, 1987

Recursive estimation of quantiles may be obained via adaptive stochastic approximation approximat... more Recursive estimation of quantiles may be obained via adaptive stochastic approximation approximation theorms can be used to obtained the asympotic properties when the obervation are independent. for dependent sequences matingale theory cannot be applied straight forwardly as the tool for asympototic analysis.In this paper we consider both the case when the observation are i.i.d. and when they form a stationary

Research paper thumbnail of Validation of Grey Box Models

Research paper thumbnail of Improving Video Segmentation Algorithms by Detection of and Adaption to Altered Illumination

Changing illumination constitutes a serious challenge for video segmentation algorithms, especial... more Changing illumination constitutes a serious challenge for video segmentation algorithms, especially in outdoor scenes under cloudy conditions. Rapid illumination changes, e.g. caused by varying cloud cover, often cause existing segmentation algorithms to erroneously classify large parts of the image as foreground.

Research paper thumbnail of Background and foreground modelling using an online EM algorithm

novel approach to background/foreground segmentation using an online EM algorithm is presented. T... more novel approach to background/foreground segmentation using an online EM algorithm is presented. The method models each layer as a Gaussian mixture, with local, per pixel, parameters for the background layer and global parameters for the foreground layer, utilising information from the entire scene when estimating the foreground. Additionally, the online EM algorithm uses a progressive learning rate where the relative update speed of each Gaussian component depends on how often the component has been observed. It is shown that the progressive learning rate follows naturally from introduction of a forgetting factor in the log-likelihood. To reduce the number of mixture components similar fore- ground components are merged using a method based on the Kullback-Leibler distance. A bias is introduced in the variance estimates to avoid the known problem of singularities in the log- likelihood of Gaussian mixtures when the variance tends to zero. To allow a decoupling of the learning rate o...

Research paper thumbnail of Video Segmentation Using a Bayesian Online EM Algorithm

Research paper thumbnail of Statistical evaluation of cell kinetic data from DNA flow cytometry (FCM) by the EM algorithm

Cytometry, 1989

Flow cytometric DNA measurements yield the amount of DNA for each of a large number of cells. A D... more Flow cytometric DNA measurements yield the amount of DNA for each of a large number of cells. A DNA histogram normally consists of a mixture of one or more constellations of G0/G1-, S-, G2/M-phase cells, together with internal standards, debris, background noise, and one or more populations of clumped cells. We have modelled typical DNA histograms as a mixed distribution with Gaussian densities for the G0/G1 and G2/M phases, an S-phase density, assumed to be uniform between the G0/G1 and G2/M peaks, observed with a Gaussian error, and with Gaussian densities for standards of chicken and trout red blood cells. The debris is modelled as a truncated exponential distribution, and we also have included a uniform background noise distribution over the whole observation interval. We have explored a new approach for maximum-likelihood analyses of complex DNA histograms by the application of the EM algorithm. This algorithm was used for four observed DNA histograms of varying complexity. Our...

Research paper thumbnail of Local Polynomial Variance-Function Estimation

Technometrics, 1997

The conditional variance function in a heteroscedastic, nonparametric regression model is estimat... more The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focussed on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The e ect of preliminary estimation of the mean is studied, and a \degrees of freedom" is proposed. The corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known. A proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions. The proposal is illustrated with data from the LIDAR method of measuring atmospheric pollutants and from turbulence model computations.

Research paper thumbnail of Recursive estimators for stationary, strong mixing processes—a representation theorem and asymptotic distributions

Stochastic Processes and their Applications, 1989

Research paper thumbnail of Forecasting near-surface ocean winds with Kalman filter techniques

Ocean Engineering, 2005

In this paper a statistical forecasting model designed for bounded areas of near-surface ocean wi... more In this paper a statistical forecasting model designed for bounded areas of near-surface ocean wind speeds is implemented.

Research paper thumbnail of Estimating the variation in S phase duration from flow cytometric histograms

Mathematical Biosciences, 2008

A stochastic model for interpreting BrdUrd DNA FCM-derived data is proposed. The model is based o... more A stochastic model for interpreting BrdUrd DNA FCM-derived data is proposed. The model is based on branching processes and describes the progression of the DNA distribution of BrdUrd-labelled cells through the cell cycle. With the main focus on estimating the S phase duration and its variation, the DNA replication rate is modelled by a piecewise linear function, while assuming a gamma distribution for the S phase duration. Estimation of model parameters was carried out using maximum likelihood for data from two different cell lines. The results provided quite a good fit to the data, suggesting that stochastic models may be a valuable tool for analysing this kind of data.

Research paper thumbnail of Estimating the distribution of the G2 phase duration from flow cytometric histograms

Mathematical Biosciences, 2008

A mathematical model, based on branching processes, is proposed to interpret BrdUrd DNA FCMderive... more A mathematical model, based on branching processes, is proposed to interpret BrdUrd DNA FCMderived data. Our main interest is in determining the distribution of the G 2 phase duration. Two different model classes involving different assumptions on the distribution of the G 2 phase duration are considered. Different assumptions of the G 2 phase duration result in very similar distributions of the S phase duration and the estimated means and standard deviations of the G 2 phase duration are all in the same range.

Research paper thumbnail of Recursive Estimation in Switching Autoregressions with a Markov Regime

Journal of Time Series Analysis, 1994

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, a... more JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . Wiley and Board of the Foundation of the Scandinavian Journal of Statistics are collaborating with JSTOR to digitize, preserve and extend access to Scandinavian Journal of Statistics. ABSTRACT. This paper outlines the statistical theory of global and local extremes of stationary processes with applications to a number of engineering problems. First the asymptotic theory of extremes and exceedances of i.i.d. r.v.'s is outlined and applied to strength of brittle materials. Extremes of stationary sequences and continuous parameter processes are treated, with general theory as well as theory for special processes such as regenerative and Markov processes, ARMA processes, etc. For continuous parameter processes we treat level crossing problems, local extremes and wave characteristics such as wavelength and amplitude distributions. The concept of a Slepian model is discussed in some detail and used as a tool to describe the behaviour of the process after events defined by level crossings. Several examples are given from mechanical and electrical engineering including click noise in FM radio and the so-called Rain Flow Cycle counting procedure, frequently used in fatigue analysis.

Research paper thumbnail of Influence of solar zenith angles on observed trends in the NOAA/NASA 8‐km Pathfinder normalized difference vegetation index over the African Sahel

International Journal of Remote Sensing, 2006

The strong systematic change in solar zenith angles (SZA) due to annual orbital drift of the NOAA... more The strong systematic change in solar zenith angles (SZA) due to annual orbital drift of the NOAA satellites has raised the suspicion of the influence of residual illumination on the calibrated normalized difference vegetation index (NDVI) derived from the Pathfinder AVHRR Land (PAL) database. The aim of this work is to analyse if trends in AVHRR NDVI from 1982 to 2000 over the Sahel region in Africa depend on variations in SZA.The analysis uses both ordinary least squares regression and cointegration to analyse possible linear dependencies between NDVI and SZA on a per satellite basis. Tests for integration and cointegration fail to find any significant evidence for either. This, together with the ability of simple deterministic models to explain primarily SZA constitutes evidence against integration and cointegration, indicating that linear relationships can be examined using ordinary linear regression. Regression gives no consistent relationship between NDVI and SZA and the explanatory power (R ) of the regression is low (on average 0.08).However there is some evidence for downward bias in NDVI due to nonlinear interactions between NDVI and SZA when SZA is large (⩾80°) leading to the conclusion that PAL data from the year 2000 should not be used for analyses in these environments.

Research paper thumbnail of On-line density estimators with high efficiency

IEEE Transactions on Information Theory, 1995

Research paper thumbnail of A real-time assimilation algorithm applied to near-surface ocean wind fields

Environmetrics, 2008

Marine operations depend on the ability to forecast suddenly appearing storms, and failures often... more Marine operations depend on the ability to forecast suddenly appearing storms, and failures often cause great damage. As part of a sea-state alarm study, meteorological forecasts overlaid with satellite observations sent to ships have been found to be a useful tool. In this paper we present a real-time assimilation algorithm that extends this tool using statistical methods. The algorithm is applied to near-surface ocean wind fields. A Kalman filter based on a spatio-temporal state-space model provides a basis for emulation of the atmospheric model. The main contribution of this paper is the algorithm that makes it possible to use the information in the satellite observations over the full spatial domain of interest at a real-time basis.

Research paper thumbnail of Analysis of lidar fields using local polynomial regression

Environmetrics, 2005

Lidar (light detection and ranging) is a laser based tool for remote measurement of several atmos... more Lidar (light detection and ranging) is a laser based tool for remote measurement of several atmospheric species of importance. We consider the analysis of a field, consisting of several consecutive measurements, in which the concentrations are proportional to the derivatives in the directions of the light paths. Inference is based on local polynomial kernel regression, both for estimation of the derivatives of the mean-function and for estimation of the variance-function. Bivariate bandwidth matrices are selected using the empirical-bias bandwidth selector (EBBS) adapted to allow for dependent data and to support selection of bivariate bandwidths. The estimation procedure is demonstrated on measurements of atomic mercury from the Solvay industries mercury cell chlor-alkali plant in Rosignano Solvay, Italy.

Research paper thumbnail of Recursive estimators for stationary, strong mixing processes—a representation theorem and asymptotic distributions

Stochastic Processes and their Applications, 1989

Many generalizations of the Robbins-Monro process have been proposed for the purpose of recursive... more Many generalizations of the Robbins-Monro process have been proposed for the purpose of recursive estimation. In this paper it is shown that the recursive estimates can be represented as sums of possibly dependent random variables and can therefore be studied using limit theorems for sums. One application which is particularly studied is recursive M-estimators of location and scale for dependent strong mixing sequences.

Research paper thumbnail of Robust local polynomial regression and statistical evaluation of DOAS measurements

This paper deals with an absorption spectroscopic method for trace gas measurementscalled DOAS (D... more This paper deals with an absorption spectroscopic method for trace gas measurementscalled DOAS (Differential Optical Absorption Spectroscopy) froma statistical point of view. The DOAS technique is an absorption spectroscopictechnique to measure trace gas concentrations. It is capable of detectingand measuring a number of important trace gases at tropospheric concentrationlevels by observing their structured light absorption features. We studythe evaluation procedure

Research paper thumbnail of Convergence of a recursive robust algorithm with strongly regular observations

Stochastic Processes and their Applications, 1984

Robust estimation of parameters may be obtained via stochastic approximation algorithms. This pap... more Robust estimation of parameters may be obtained via stochastic approximation algorithms. This paper deals with the properties of a recursive estimator of a location parameter in a stationary strongly regular process. Adaptive estimators of particular interest are also studied. stochastic approximation strong regularity robust estimation L 0304-4~451/83/S3.00 @I 1983, Elsevier Science Publishers B.V. (North-Holland)

Research paper thumbnail of Correction to: Convergence of a recursive stochastic algorithm with m- dependent observations

Scandinavian Journal of Statistics

Research paper thumbnail of Recursive estimation of quantitles using recursive kernel density estimators

Sequential Analysis, 1987

Recursive estimation of quantiles may be obained via adaptive stochastic approximation approximat... more Recursive estimation of quantiles may be obained via adaptive stochastic approximation approximation theorms can be used to obtained the asympotic properties when the obervation are independent. for dependent sequences matingale theory cannot be applied straight forwardly as the tool for asympototic analysis.In this paper we consider both the case when the observation are i.i.d. and when they form a stationary

Research paper thumbnail of Validation of Grey Box Models

Research paper thumbnail of Improving Video Segmentation Algorithms by Detection of and Adaption to Altered Illumination

Changing illumination constitutes a serious challenge for video segmentation algorithms, especial... more Changing illumination constitutes a serious challenge for video segmentation algorithms, especially in outdoor scenes under cloudy conditions. Rapid illumination changes, e.g. caused by varying cloud cover, often cause existing segmentation algorithms to erroneously classify large parts of the image as foreground.

Research paper thumbnail of Background and foreground modelling using an online EM algorithm

novel approach to background/foreground segmentation using an online EM algorithm is presented. T... more novel approach to background/foreground segmentation using an online EM algorithm is presented. The method models each layer as a Gaussian mixture, with local, per pixel, parameters for the background layer and global parameters for the foreground layer, utilising information from the entire scene when estimating the foreground. Additionally, the online EM algorithm uses a progressive learning rate where the relative update speed of each Gaussian component depends on how often the component has been observed. It is shown that the progressive learning rate follows naturally from introduction of a forgetting factor in the log-likelihood. To reduce the number of mixture components similar fore- ground components are merged using a method based on the Kullback-Leibler distance. A bias is introduced in the variance estimates to avoid the known problem of singularities in the log- likelihood of Gaussian mixtures when the variance tends to zero. To allow a decoupling of the learning rate o...

Research paper thumbnail of Video Segmentation Using a Bayesian Online EM Algorithm

Research paper thumbnail of Statistical evaluation of cell kinetic data from DNA flow cytometry (FCM) by the EM algorithm

Cytometry, 1989

Flow cytometric DNA measurements yield the amount of DNA for each of a large number of cells. A D... more Flow cytometric DNA measurements yield the amount of DNA for each of a large number of cells. A DNA histogram normally consists of a mixture of one or more constellations of G0/G1-, S-, G2/M-phase cells, together with internal standards, debris, background noise, and one or more populations of clumped cells. We have modelled typical DNA histograms as a mixed distribution with Gaussian densities for the G0/G1 and G2/M phases, an S-phase density, assumed to be uniform between the G0/G1 and G2/M peaks, observed with a Gaussian error, and with Gaussian densities for standards of chicken and trout red blood cells. The debris is modelled as a truncated exponential distribution, and we also have included a uniform background noise distribution over the whole observation interval. We have explored a new approach for maximum-likelihood analyses of complex DNA histograms by the application of the EM algorithm. This algorithm was used for four observed DNA histograms of varying complexity. Our...

Research paper thumbnail of Local Polynomial Variance-Function Estimation

Technometrics, 1997

The conditional variance function in a heteroscedastic, nonparametric regression model is estimat... more The conditional variance function in a heteroscedastic, nonparametric regression model is estimated by linear smoothing of squared residuals. Attention is focussed on local polynomial smoothers. Both the mean and variance functions are assumed to be smooth, but neither is assumed to be in a parametric family. The e ect of preliminary estimation of the mean is studied, and a \degrees of freedom" is proposed. The corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known. A proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions. The proposal is illustrated with data from the LIDAR method of measuring atmospheric pollutants and from turbulence model computations.

Research paper thumbnail of Recursive estimators for stationary, strong mixing processes—a representation theorem and asymptotic distributions

Stochastic Processes and their Applications, 1989

Research paper thumbnail of Forecasting near-surface ocean winds with Kalman filter techniques

Ocean Engineering, 2005

In this paper a statistical forecasting model designed for bounded areas of near-surface ocean wi... more In this paper a statistical forecasting model designed for bounded areas of near-surface ocean wind speeds is implemented.

Research paper thumbnail of Estimating the variation in S phase duration from flow cytometric histograms

Mathematical Biosciences, 2008

A stochastic model for interpreting BrdUrd DNA FCM-derived data is proposed. The model is based o... more A stochastic model for interpreting BrdUrd DNA FCM-derived data is proposed. The model is based on branching processes and describes the progression of the DNA distribution of BrdUrd-labelled cells through the cell cycle. With the main focus on estimating the S phase duration and its variation, the DNA replication rate is modelled by a piecewise linear function, while assuming a gamma distribution for the S phase duration. Estimation of model parameters was carried out using maximum likelihood for data from two different cell lines. The results provided quite a good fit to the data, suggesting that stochastic models may be a valuable tool for analysing this kind of data.

Research paper thumbnail of Estimating the distribution of the G2 phase duration from flow cytometric histograms

Mathematical Biosciences, 2008

A mathematical model, based on branching processes, is proposed to interpret BrdUrd DNA FCMderive... more A mathematical model, based on branching processes, is proposed to interpret BrdUrd DNA FCMderived data. Our main interest is in determining the distribution of the G 2 phase duration. Two different model classes involving different assumptions on the distribution of the G 2 phase duration are considered. Different assumptions of the G 2 phase duration result in very similar distributions of the S phase duration and the estimated means and standard deviations of the G 2 phase duration are all in the same range.

Research paper thumbnail of Recursive Estimation in Switching Autoregressions with a Markov Regime

Journal of Time Series Analysis, 1994

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, a... more JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. . Wiley and Board of the Foundation of the Scandinavian Journal of Statistics are collaborating with JSTOR to digitize, preserve and extend access to Scandinavian Journal of Statistics. ABSTRACT. This paper outlines the statistical theory of global and local extremes of stationary processes with applications to a number of engineering problems. First the asymptotic theory of extremes and exceedances of i.i.d. r.v.'s is outlined and applied to strength of brittle materials. Extremes of stationary sequences and continuous parameter processes are treated, with general theory as well as theory for special processes such as regenerative and Markov processes, ARMA processes, etc. For continuous parameter processes we treat level crossing problems, local extremes and wave characteristics such as wavelength and amplitude distributions. The concept of a Slepian model is discussed in some detail and used as a tool to describe the behaviour of the process after events defined by level crossings. Several examples are given from mechanical and electrical engineering including click noise in FM radio and the so-called Rain Flow Cycle counting procedure, frequently used in fatigue analysis.

Research paper thumbnail of Influence of solar zenith angles on observed trends in the NOAA/NASA 8‐km Pathfinder normalized difference vegetation index over the African Sahel

International Journal of Remote Sensing, 2006

The strong systematic change in solar zenith angles (SZA) due to annual orbital drift of the NOAA... more The strong systematic change in solar zenith angles (SZA) due to annual orbital drift of the NOAA satellites has raised the suspicion of the influence of residual illumination on the calibrated normalized difference vegetation index (NDVI) derived from the Pathfinder AVHRR Land (PAL) database. The aim of this work is to analyse if trends in AVHRR NDVI from 1982 to 2000 over the Sahel region in Africa depend on variations in SZA.The analysis uses both ordinary least squares regression and cointegration to analyse possible linear dependencies between NDVI and SZA on a per satellite basis. Tests for integration and cointegration fail to find any significant evidence for either. This, together with the ability of simple deterministic models to explain primarily SZA constitutes evidence against integration and cointegration, indicating that linear relationships can be examined using ordinary linear regression. Regression gives no consistent relationship between NDVI and SZA and the explanatory power (R ) of the regression is low (on average 0.08).However there is some evidence for downward bias in NDVI due to nonlinear interactions between NDVI and SZA when SZA is large (⩾80°) leading to the conclusion that PAL data from the year 2000 should not be used for analyses in these environments.

Research paper thumbnail of On-line density estimators with high efficiency

IEEE Transactions on Information Theory, 1995

Research paper thumbnail of A real-time assimilation algorithm applied to near-surface ocean wind fields

Environmetrics, 2008

Marine operations depend on the ability to forecast suddenly appearing storms, and failures often... more Marine operations depend on the ability to forecast suddenly appearing storms, and failures often cause great damage. As part of a sea-state alarm study, meteorological forecasts overlaid with satellite observations sent to ships have been found to be a useful tool. In this paper we present a real-time assimilation algorithm that extends this tool using statistical methods. The algorithm is applied to near-surface ocean wind fields. A Kalman filter based on a spatio-temporal state-space model provides a basis for emulation of the atmospheric model. The main contribution of this paper is the algorithm that makes it possible to use the information in the satellite observations over the full spatial domain of interest at a real-time basis.

Research paper thumbnail of Analysis of lidar fields using local polynomial regression

Environmetrics, 2005

Lidar (light detection and ranging) is a laser based tool for remote measurement of several atmos... more Lidar (light detection and ranging) is a laser based tool for remote measurement of several atmospheric species of importance. We consider the analysis of a field, consisting of several consecutive measurements, in which the concentrations are proportional to the derivatives in the directions of the light paths. Inference is based on local polynomial kernel regression, both for estimation of the derivatives of the mean-function and for estimation of the variance-function. Bivariate bandwidth matrices are selected using the empirical-bias bandwidth selector (EBBS) adapted to allow for dependent data and to support selection of bivariate bandwidths. The estimation procedure is demonstrated on measurements of atomic mercury from the Solvay industries mercury cell chlor-alkali plant in Rosignano Solvay, Italy.