Browsing by Author "Frisén, Marianne"

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Characterization of methods for surveillance by optimality
(University of Gothenburg, 1999-12-02) Frisén, Marianne
Different criteria of optimality are discussed. The shortcomings of some criteria of optimality are demonstrated by their implications. The correspondences between some criteria of optimality and some methods are examined. The situations and parameter values for which some commonly used methods have certain optimality properties are thus illuminated. A linear approximation of the full likelihood ratio method, which satisfies several criteria of optimality, is presented. This linear approximation is used for comparisons with the exponentially weighted moving average method. Via these comparisons it is possible to illuminate the influence of different criteria of optimality on the "optimal" parameter of a method. A uniform presentation of methods, by expressions oflikelihood ratios, facilitates the comparisons between methods.
CHARACTERIZATION OF METHODS FOR SURVEILLANCE BY OPTIMALITY
(University of Gothenburg, 1994-02-01) Frisén, Marianne
Different criteria of optimality are discussed. The shortcomings of some earlier criteria of optimality are demonstrated by their implications. The correspondences between some criteria of optimality and some methods are examined. The situations under which some commonly used methods have a certain optimality are thus illuminated. Linear approximations of the LR (likelihood ratio) method, which satisfies several criteria of optimality, are presented. These linear approximations are used for comparisons with other linear methods, especially the EWMA (exponentially weighted moving average) method. These comparisons specify the situations for which the linear methods can be regarded as approximations of the LR method.
COMPARISON BETWEEN TWO METHODS OF SURVEILLANCE: EXPONENTIALLY WEIGHTED MOVING AVERAGE VS CUSUM
(University of Gothenburg, 1993-01-01) Frisén, Marianne; Åkermo, Göran
When control charts are used in practice it is necessary to know the characteristics of the charts in order to know which action is appropriate at an alarm. The probability of a false alarm, the probability of successful detection and the predictive value are three measures (besides the usual ARL) used for comparing the performance of two methods often used in surveillance systems. One is the "Exponentially weighted moving average" method, EWMA, (with several variants) and the other one is the CUSUM method (Vmask). Illustrations are presented to explain the observed differences. It is demonstrated that a high probability of alarm in the beginning (although it gives good ARL properties) might cause difficulties since a low predicted value makes action redundant at early alarms.
Detection of turning points in business cycles
(University of Gothenburg, 2002-06-01) Andersson, Eva; Bock, David; Frisén, Marianne
Methods for on-line monitoring of business cycles are compared with respect to the ability of early prediction of the next turn by an alarm for a turn in a leading index. Three likelihood based methods for turning point detection are compared in detail by using the theory of statistical surveillance and by simulations. One of the methods is based on a Hidden Markov Model. Another includes a non-parametric estimation procedure. Evaluations are made of several features such as knowledge of shape and parameters of the curve, types and probabilities of transitions and smoothing. Results on the expected delay time to a correct alarm and the predictive value of an alarm are discussed. The three methods are also used to analyze an actual data set of a period of the Swedish industrial production. The relative merits of evaluation of methods by one real data set or by simulations are discussed.
Evaluation of multivariate surveillance
(2009-05-15T14:20:56Z) Frisén, Marianne; Andersson, Eva; Schiöler, Linus
Multivariate surveillance is of interest in many areas such as industrial production, bioterrorism detection, spatial surveillance, and financial transaction strategies. Some of the suggested approaches to multivariate surveillance have been multivariate counterparts to the univariate Shewhart, EWMA, and CUSUM methods. Our emphasis is on the special challenges of evaluating multivariate surveillance methods. Some new measures are suggested and the properties of several measures are demonstrated by applications to various situations. It is demonstrated that zero-state and steady-state ARL, which are widely used in univariate surveillance, should be used with care in multivariate surveillance.
Evaluations of likelihood ratio methods for surveillance
(University of Gothenburg, 1996-03-01) Frisén, Marianne; Wessman, Peter
Methods based on likelihood ratios are known to have several optimality properties. When control charts are used in practice, knowledge about several characteristics of the method is important for the judgement of which action is appropriate at an alarm. The probability of a false alarm, the delay of an alarm and the predictive value of an alarm are qualities (besides the usual ARL) which are described by a simulation study for the evaluations. Since the methods also have interesting optimality properties, the results also enlighten different criteria of optimality. Evaluations are made of the "The Likelihood Ratio Method" which utilizes an assumption on the intensity and has the Shiryaevoptimality. Also, the Roberts and the CUSUM method are evaluated. These two methods combine the likelihood ratios in other ways. A comparison is also made with the Shewhart method, which is a commonly used method.
Evaluations of likelihood ratio methods for surveillance. Differences and robustness.
(University of Gothenburg, 1998-02-01) Frisén, Marianne; Wessman, Peter
In many areas there is a need for continual observation of a time series, with the goal of detecting an important change in the underlying process as soon as possible after it has occurred. In recent years there have been a growing number of papers in economics, medicine, environmental control and other areas dealing with the need of methods for surveillance. Examples are given in Frisen (1992) and Frisen (1994a). The timeliness of decisions is taken into account in the vast literature on quality control charts where simplicity is often a major concern. Also, the literature on stopping rules is relevant. For an overview, see the textbook by Wetherill and Brown (1990) the surveys by Zacks (1983) or Lai (1995) and the bibliography by Frisen (1994b). Methods based on likelihood ratios are known to have several optimality properties. Evaluations are made of the full likelihood ratio (LR) method, which will be expressed as a certain combination of conditional likelihood ratios. In the cases studied here, the LR method has the Shiryaev optimality. Also, the Shiryaev-Roberts and the CUSUM methods are evaluated. These two methods combine conditional likelihood ratios in other ways. A comparison is also made with the Shewhart method that is a commonly used method. When control charts are used in practice, it is necessary to know several characteristics of the method. Asymptotic properties have been studied by Srivastava and Wu (1993) and Siegmund and Venkatraman (1995) and others. Here, properties for fInite time of change are studied. The usual ARLo and ARLl (which are the average nm lengths until an alarm under the hypothesis of no change and the hypothesis of immediate change, respectively) are used. Besides that, the probability of a false alarm, the expected delay, the probability of successful detection and the predictive value are used for evaluations. Since the methods have interesting optimality properties, the results also enlighten different criteria of optimality .
Graphical evaluation of statistical surveillance
(2003-10-01) Frisén, Marianne; Gottlow, Mattias
A computer program which simultaneously gives graphical information on important characteristics of statistical surveillance methods is presented. Surveillance, that is continual observation of a time series with the goal of timely detection of possible important changes in the underlying process, is used in quality control, economics, medicine and other fields. When surveillance is used in practice it is necessary to evaluate the method in order to know which action is appropriate at an alarm. The probability of a false alarm, the probability of successful detection and the predictive value are three measures (besides the usual ARL), which are illustrated by the program.
INFERENCE PRINCIPLES FOR MULTIVARIATE SURVEILLANCE
(2011-03-29) Frisén, Marianne; Statistical Research Unit, Department of Economics, GU
Multivariate surveillance is of interest in industrial production as it enables the monitoring of several components. Recently there has been an increased interest also in other areas such as detection of bioterrorism, spatial surveillance and transaction strategies in finance. Multivariate counterparts to the univariate Shewhart, EWMA and CUSUM methods have earlier been proposed. A review of general approaches to multivariate surveillance is given with respect to how suggested methods relate to general statistical inference principles. Multivariate on-line surveillance problems can be complex. The sufficiency principle can be of great use to find simplifications without loss of information. We will use this to clarify the structure of some problems. This will be of help to find relevant metrics for evaluations of multivariate surveillance and to find optimal methods. The sufficiency principle will be used to determine efficient methods to combine data from sources with different time lag. Surveillance of spatial data is one example. Illustrations will be given of surveillance of outbreaks of influenza.
Introduction to financial surveillance
(2008-02-08T13:13:49Z) Frisén, Marianne
Likelihood based methods for detection of turning points in business cycles - A comparative study
(University of Gothenburg, 2001-05-01) Andersson, Eva; Bock, David; Frisén, Marianne
Methods for on-line monitoring of business cycles are compared with respect to the ability of early prediction of the next tum by an alarm for a tum in a leading index. Three likelihood-based methods for turning point detection are compared in detail by using the theory of statistical surveillance and by simulations. One of the methods is based on a Hidden Markov Model. Another includes a non-parametric estimation procedure. Evaluations are made of several features such as knowledge of shape and parameters of the curve, types and probabilities of transitions and smoothing. The methods are made comparable by alarm limits, which give the same median time to the first false alarm, but also other approaches for comparability are discussed. Results are given on the expected delay time to a correct alarm, the probability of detection of a turning point within a specified time and the predictive value of an alarm. The three methods are also used to analyze an actual data set of a period of the Swedish industrial production. The relative merits of evaluation of methods by one real data set or by simulations are discussed.
Longitudinal methods for analysis of the influence of breastfeeding on early child health in Pakistan
(University of Gothenburg, 1999-11-01) Carlquist, Anders; Erling, Valdemar; Frisén, Marianne
Statistical methods for analysing aspects of early child health in Lahore, Pakistan are discussed. We construct generalised linear mixed models with a binomial response variable and both fixed and random explaining effects. In order to elucidate the causal effects of breastfeeding on early child health we use the two-step approach recently advocated in the statistical literature, but we modify the procedure to be practicable for the present longitudinal study. The selection effects of breastfeeding are examined, and variables with major effect on the breastfeeding pattern are included in the final model. For some, but not all, social groups the analysis gives enough motivation for the conclusion that breastfeeding prevents the occurrence of diarrhoea
Methods and evaluations for surveillance in industry, business, finance, and public health
(University of Gothenburg, 2011-02-10) Frisén, Marianne
n overview on surveillance in different areas is given. Even though methods have been developed under different scientific cultures, the statistical concepts can be the same. When the statistical problems are the same, progress in one area can be used also in other areas. The aim of surveillance is to detect an important change in an underlying process as soon as possible after the change has occurred. In practice, we have complexities such as gradual changes and multivariate settings. Approaches to handling some of these complexities are discussed. The correspondence between the measures for evaluation and the aims of the ap-plication is important. Thus, the choice of evaluation measure deserves attention. The com-monly used ARL criterion should be used with care.
Minimax Optimality of CUSUM for an Autoregressive Model
(University of Gothenburg, 2011-02-11) Knoth, Sven; Frisén, Marianne
Different change point models for AR(1) processes are reviewed. For some models, the change is in the distribution conditional on earlier observations. For others the change is in the unconditional distribution. Some models include an observation before the first possible change time — others not. Earlier and new CUSUM type methods are given and minimax optimality is examined. For the conditional model with an observation before the possible change there are sharp results of optimality in the literature. The unconditional model with possible change at (or before) the first observation is of interest for applications. We examined this case and derived new variants of four earlier suggestions. By numerical methods and Monte Carlo simulations it was demonstrated that the new variants dominate the original ones. However, none of the methods is uniformly minimax optimal.
Modeling influenza incidence for the purpose of on-line monitoring
(2007-11-27T12:08:00Z) Andersson, Eva; Bock, David; Frisén, Marianne
We describe and discuss statistical models of Swedish influenza data, with special focus on aspects which are important in on-line monitoring. Earlier suggested statistical models are reviewed and the possibility of using them to describe the variation in influenza-like illness (ILI) and laboratory diagnoses (LDI) is discussed. Exponential functions were found to work better than earlier suggested models for describing the influenza incidence. However, the parameters of the estimated functions varied considerably between years. For monitoring purposes we need models which focus on stable indicators of the change at the outbreak and at the peak. For outbreak detection we focus on ILI data. Instead of a parametric estimate of the baseline (which could be very uncertain,), we suggest a model utilizing the monotonicity property of a rise in the incidence. For ILI data at the outbreak, Poisson distributions can be used as a first approximation. To confirm that the peak has occurred and the decline has started, we focus on LDI data. A Gaussian distribution is a reasonable approximation near the peak. In view of the variability of the shape of the peak, we suggest that a detection system use the monotonicity properties of a peak.
Multivariate outbreak detection
(University of Gothenburg, 2010) Schiöler, Linus; Frisén, Marianne; Statistical Research Unit
On-line monitoring is needed to detect outbreaks of diseases like influenza. Surveillance is also needed for other kinds of outbreaks, in the sense of an increasing expected value after a constant period. Information on spatial location or other variables might be available and may be utilized. We adapted a robust method for outbreak detection to a multivariate case. The relation between the times of the onsets of the outbreaks at different locations (or some other variable) was used to determine the sufficient statistic for surveillance. The derived maximum likelihood estimator of the outbreak regression was semi-parametric in the sense that the baseline and the slope were non-parametric while the distribution belonged to the exponential family. The estimator was used in a generalized likelihood ratio surveillance method. The method was evaluated with respect to robustness and efficiency in a simulation study and applied to spatial data for detection of influenza outbreaks in Sweden.
On multivariate control charts
(University of Gothenburg, 2011-02-10) Frisén, Marianne
Industrial production requires multivariate control charts to enable monitoring of several components. Recently there has been an increased interest also in other areas such as detection of bioterrorism, spatial surveillance and transaction strategies in finance. In the literature, several types of multivariate counterparts to the univariate Shewhart, EWMA and CUSUM methods have been proposed. We review general approaches to multivariate control chart. Suggestions are made on the special challenges of evaluating multivariate surveillance methods.
On statistical surveillance of the performance of fund managers
(2009-02-17T11:56:22Z) Schiöler, Linus; Frisén, Marianne
The aim of this report is to describe if and how statistical surveillance methods for monitoring of the performance of fund managers has been used. Statistical surveillance is a methodology for on-line monitoring, in which a warning signal is given if the performance declines. Since these methods are advanced you can expect the methods to be described in scientific literature. Problems in this area which will not be treated in this report are: 1. Estimation of the performance. 2. Hypothesis testing of if this manager always have a poor performance. 3. Examination of how managers are influenced by being evaluated.
Optimal surveillance Based on exponentially weighted moving averages
(University of Gothenburg, 2002-01-01) Frisén, Marianne; Sonesson, Christian
Statistical surveillance is used to detect an important change in a process as soon as possible after it has occurred, with control of false alarms. The EWMA, exponentially weighted moving average, method for surveillance is used in different areas, such as industry, economy and medicine. Three optimality criteria of surveillance are studied and the implications are described for the EWMA method and for suggested modifications. The first criterion concerns the average run length to alarm, ARL. This is the most commonly used criterion. Results on ARL optimality for EWMA are demonstrated. Equal weight for old and recent observations give good ARL-properties but bad properties otherwise. Thus, uncritical use of this criterion should be avoided. The second criterion is the ED criterion based on the minimal expected delay from change to detection. The full likelihood ratio method is optimal according to this criterion. Various approximations of this method tum out to be modifications of the EWMA method. Two of these modifications keep the EWMA statistic unchanged and just alter the alarm limits slightly. The approximations lead to a formula for the value of the weight parameter of the EWMA statistic. The usefulness of this formula is demonstrated. The conventional EWMA and the modifications are compared to the optimal full likelihood ratio method. No modification of EWMA is necessary for detection of large changes (where also the Shewhart 2 method is useful) but all the modifications give considerable improvement for small changes. The third criterion is based on the minimax of the expected delay after a change with respect to the time of the change. It is demonstrated that the value of the smoothing parameter, which is optimal according to this criterion, agrees well with that of the ED criterion but not with that of the ARL criterion. A restriction on the false alarm property is necessary. For the ARL criterion it is the ARL without any change. For the other two criteria we here use the false alarm probability. It is demonstrated that these two restrictions favor different methods.
Optimal Surveillance Based on Exponentially Weighted Moving Averages
(Taylor & Francis, 2006) Frisén, Marianne; Sonesson, Christian
Statistical surveillance is used to detect an important change in a process as soon as possible after it has occurred. The EWMA method is used in industry, economics and medicine. Three optimality criteria of surveillance are studied. The ARL criterion violates commonly accepted inference principles and the drawbacks are demonstrated. The ED criterion is based on the minimal expected delay from change to detection. The full likelihood ratio method is optimal according to this criterion. Approximations of this method turn out to be modifications of the EWMA method. The approximations lead to a formula for the optimal value of the smoothing parameter of the EWMA statistic. The usefulness of this formula is shown. It is demonstrated that, for EWMA, the minimax criterion agrees well with that of the ED criterion but not with that of the ARL criterion.