Em Estimation of the Offspring Distribution in Mutitype Branching Processes - a Model in Cell Kinetics

2000 Mathematics Subject Classification: 60J80, 60J85, 62P10, 92D25.

Robust Mixture Modelling Using the t Distribution

Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consider a more robust approach by modelling the data by a mixture of t distributions. The use of the ECM algorithm to fit this t mixture model is described and examples of its use are given in the context of clustering multivariate data in the presence of atypical observations in the form of background noise.

A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

ML approaches to channel estimation for pilot-aided multi-rate DS/CDMA systems

This paper analyzes the asymptotic performance of maximum likelihood (ML) channel estimation algorithms in wideband code division multiple access (WCDMA) scenarios. We concentrate on systems with periodic spreading sequences (period larger than or equal to the symbol span) where the transmitted signal contains a code division multiplexed pilot for channel estimation purposes. First, the asymptotic covariances of the training-only, semi-blind conditional maximum likelihood (CML) and semi-blind Gaussian maximum likelihood (GML) channelestimators are derived. Then, these formulas are further simplified assuming randomized spreading and training sequences under the approximation of high spreading factors and high number of codes. The results provide a useful tool to describe the performance of the channel estimators as a function of basicsystem parameters such as number of codes, spreading factors, or traffic to training power ratio.

Error in body weight estimation leads to inadequate parenteral anticoagulation

Parenteral anticoagulation is a cornerstone in the management of venous and arterial thrombosis. Unfractionated heparin has a wide dose/response relationship, requiring frequent and troublesome laboratorial follow-up. Because of all these factors, low-molecular-weight heparin use has been increasing. Inadequate dosage has been pointed out as a potential problem because the use of subjectively estimated weight instead of real measured weight is common practice in the emergency department (ED). To evaluate the impact of inadequate weight estimation on enoxaparin dosage, we investigated the adequacy of anticoagulation of patients in a tertiary ED where subjective weight estimation is common practice. We obtained the estimated, informed, and measured weight of 28 patients in need of parenteral anticoagulation. Basal and steady-state (after the second subcutaneous shot of enoxaparin) anti-Xa activity was obtained as a measure of adequate anticoagulation. The patients were divided into 2 groups according the anticoagulation adequacy. From the 28 patients enrolled, 75% (group 1, n = 21) received at least 0.9 mg/kg per dose BID and 25% (group 2, n = 7) received less than 0.9 mg/kg per dose BID of enoxaparin. Only 4 (14.3%) of all patients had anti-Xa activity less than the inferior limit of the therapeutic range (<0.5 UI/mL), all of them from group 2. In conclusion, when weight estimation was used to determine the enoxaparin dosage, 25% of the patients were inadequately anticoagulated (anti-Xa activity <0.5 UI/mL) during the initial crucial phase of treatment. (C) 2011 Elsevier Inc. All rights reserved.

Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Estimation of glomerular filtration rate in hospitalised patients: are we overestimating renal function?

QUESTIONS UNDER STUDY AND PRINCIPLES: Estimating glomerular filtration rate (GFR) in hospitalised patients with chronic kidney disease (CKD) is important for drug prescription but it remains a difficult task. The purpose of this study was to investigate the reliability of selected algorithms based on serum creatinine, cystatin C and beta-trace protein to estimate GFR and the potential added advantage of measuring muscle mass by bioimpedance. In a prospective unselected group of patients hospitalised in a general internal medicine ward with CKD, GFR was evaluated using inulin clearance as the gold standard and the algorithms of Cockcroft, MDRD, Larsson (cystatin C), White (beta-trace) and MacDonald (creatinine and muscle mass by bioimpedance). 69 patients were included in the study. Median age (interquartile range) was 80 years (73-83); weight 74.7 kg (67.0-85.6), appendicular lean mass 19.1 kg (14.9-22.3), serum creatinine 126 μmol/l (100-149), cystatin C 1.45 mg/l (1.19-1.90), beta-trace protein 1.17 mg/l (0.99-1.53) and GFR measured by inulin 30.9 ml/min (22.0-43.3). The errors in the estimation of GFR and the area under the ROC curves (95% confidence interval) relative to inulin were respectively: Cockcroft 14.3 ml/min (5.55-23.2) and 0.68 (0.55-0.81), MDRD 16.3 ml/min (6.4-27.5) and 0.76 (0.64-0.87), Larsson 12.8 ml/min (4.50-25.3) and 0.82 (0.72-0.92), White 17.6 ml/min (11.5-31.5) and 0.75 (0.63-0.87), MacDonald 32.2 ml/min (13.9-45.4) and 0.65 (0.52-0.78). Currently used algorithms overestimate GFR in hospitalised patients with CKD. As a consequence eGFR targeted prescriptions of renal-cleared drugs, might expose patients to overdosing. The best results were obtained with the Larsson algorithm. The determination of muscle mass by bioimpedance did not provide significant contributions.

Assessment of adult formulas for glomerular filtration rate estimation in children.

BACKGROUND: Estimated glomerular filtration rate (eGFR) is an important diagnostic instrument in clinical practice. The National Kidney Foundation-Kidney Disease Quality Initiative (NKF-KDOQI) guidelines do not recommend using formulas developed for adults to estimate GFR in children; however, studies confirming these recommendations are scarce. The aim of our study was to evaluate the accuracy of the new Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) formula, the Modification of Diet in Renal Disease (MDRD) formula, and the Cockcroft-Gault formula in children with various stages of chronic kidney disease (CKD). METHODS: A total of 550 inulin clearance (iGFR) measurements for 391 children were analyzed. The cohort was divided into three groups: group 1, with iGFR >90 ml/min/1.73 m(2); group 2, with iGFR between 60 and 90 ml/min/1.73 m(2); group 3, with iGFR of <60 ml/min/1.73 m(2). RESULTS: All formulas overestimate iGFR with a significant bias (p < 0.001), present poor accuracies, and have poor Spearman correlations. For an accuracy of 10 %, only 11, 6, and 27 % of the eGFRs are accurate when using the MDRD, CKD-EPI, and Cockcroft-Gault formulas, respectively. For an accuracy of 30 %, these formulas do not reach the NKF-KDOQI guidelines for validation, with only 25, 20, and 70 % of the eGFRs, respectively, being accurate. CONCLUSIONS: Based on our results, the performances of all of these formulas are unreliable for eGFR in children across all CKD stages and cannot therefore be applied in the pediatric population group.

Estimation de la fonction rénale par l'equation MDRD: intérêt et limites pour l'adaptation des doses de médicaments [Renal function estimation by MDRD equation: interest and limitations for drug dosing].

The MDRD (Modification of diet in renal disease) equation enables glomerular filtration rate (GFR) estimation from serum creatinine only. Thus, the laboratory can report an estimated GFR (eGFR) with each serum creatinine assessment, increasing therefore the recognition of renal failure. Predictive performance of MDRD equation is better for GFR < 60 ml/min/1,73 m2. A normal or near-normal renal function is often underestimated by this equation. Overall, MDRD provides more reliable estimations of renal function than the Cockcroft-Gault (C-G) formula, but both lack precision. MDRD is not superior to C-G for drug dosing. Being adjusted to 1,73 m2, MDRD eGFR has to be back adjusted to the patient's body surface area for drug dosing. Besides, C-G has the advantage of a greater simplicity and a longer use.

Estimation du débit de filtration glomérulaire par la formule DFG = K x T/Pcr [Estimation of glomerular filtration rate by the formula GFR = K x T/Pc].

BACKGROUND: Creatinine clearance is the most common method used to assess glomerular filtration rate (GFR). In children, GFR can also be estimated without urine collection, using the formula GFR (mL/min x 1.73 m2) = K x height [cm]/Pcr [mumol/L]), where Pcr represents the plasma creatinine concentration. K is usually calculated using creatinine clearance (Ccr) as an index of GFR. The aim of the present study was to evaluate the reliability of the formula, using the standard UV/P inulin clearance to calculate K. METHODS: Clearance data obtained in 200 patients (1 month to 23 years) during the years 1988-1994 were used to calculate the factor K as a function of age. Forty-four additional patients were studied prospectively in conditions of either hydropenia or water diuresis in order to evaluate the possible variation of K as a function of urine flow rate. RESULTS: When GFR was estimated by the standard inulin clearance, the calculated values of K was 39 (infants less than 6 months), 44 (1-2 years) and 47 (2-12 years). The correlation between the values of GFR, as estimated by the formula, and the values measured by the standard clearance of inulin was highly significant; the scatter of individual values was however substantial. When K was calculated using Ccr, the formula overestimated Cin at all urine flow rates. When calculated from Ccr, K varied as a function of urine flow rate (K = 50 at urine flow rates of 3.5 and K = 64 at urine flow rates of 8.5 mL/min x 1.73 m2). When calculated from Cin, in the same conditions, K remained constant with a value of 50. CONCLUSIONS: The formula GFR = K x H/Pcr can be used to estimate GFR. The scatter of values precludes however the use of the formula to estimate GFR in pathophysiological studies. The formula should only be used when K is calculated from Cin, and the plasma creatinine concentration is measured in well defined conditions of hydration.

Maximum-likelihood estimation of specific differential phase and attenuation in rain

Precise estimation of propagation parameters inprecipitation media is of interest to improve the performanceof communications systems and in remote sensing applications.In this paper, we present maximum-likelihood estimators ofspecific attenuation and specific differential phase in rain. Themodel used for obtaining the cited estimators assumes coherentpropagation, reflection symmetry of the medium, and Gaussianstatistics of the scattering matrix measurements. No assumptionsabout the microphysical properties of the medium are needed.The performance of the estimators is evaluated through simulateddata. Results show negligible estimators bias and variances closeto Cramer–Rao bounds.

Automated DNA extraction using the QIAsymphony platform: Estimation of DNA recovery from simulated forensic stains

The aim of this study was to evaluate the forensic protocol recently developed by Qiagen for the QIAsymphony automated DNA extraction platform. Samples containing low amounts of DNA were specifically considered, since they represent the majority of samples processed in our laboratory. The analysis of simulated blood and saliva traces showed that the highest DNA yields were obtained with the maximal elution volume available for the forensic protocol, that is 200 ml. Resulting DNA extracts were too diluted for successful DNA profiling and required a concentration. This additional step is time consuming and potentially increases inversion and contamination risks. The 200 ml DNA extracts were concentrated to 25 ml, and the DNA recovery estimated with real-time PCR as well as with the percentage of SGM Plus alleles detected. Results using our manual protocol, based on the QIAamp DNA mini kit, and the automated protocol were comparable. Further tests will be conducted to determine more precisely DNA recovery, contamination risk and PCR inhibitors removal, once a definitive procedure, allowing the concentration of DNA extracts from low yield samples, will be available for the QIAsymphony.

On the inclusion of channel's time dependence in a hidden Markov model for blind channel estimation

In this paper, the theory of hidden Markov models (HMM) isapplied to the problem of blind (without training sequences) channel estimationand data detection. Within a HMM framework, the Baum–Welch(BW) identification algorithm is frequently used to find out maximum-likelihood (ML) estimates of the corresponding model. However, such a procedureassumes the model (i.e., the channel response) to be static throughoutthe observation sequence. By means of introducing a parametric model fortime-varying channel responses, a version of the algorithm, which is moreappropriate for mobile channels [time-dependent Baum-Welch (TDBW)] isderived. Aiming to compare algorithm behavior, a set of computer simulationsfor a GSM scenario is provided. Results indicate that, in comparisonto other Baum–Welch (BW) versions of the algorithm, the TDBW approachattains a remarkable enhancement in performance. For that purpose, onlya moderate increase in computational complexity is needed.

Second-order parameter estimation

This work provides a general framework for the design of second-order blind estimators without adopting anyapproximation about the observation statistics or the a prioridistribution of the parameters. The proposed solution is obtainedminimizing the estimator variance subject to some constraints onthe estimator bias. The resulting optimal estimator is found todepend on the observation fourth-order moments that can be calculatedanalytically from the known signal model. Unfortunately,in most cases, the performance of this estimator is severely limitedby the residual bias inherent to nonlinear estimation problems.To overcome this limitation, the second-order minimum varianceunbiased estimator is deduced from the general solution by assumingaccurate prior information on the vector of parameters.This small-error approximation is adopted to design iterativeestimators or trackers. It is shown that the associated varianceconstitutes the lower bound for the variance of any unbiasedestimator based on the sample covariance matrix.The paper formulation is then applied to track the angle-of-arrival(AoA) of multiple digitally-modulated sources by means ofa uniform linear array. The optimal second-order tracker is comparedwith the classical maximum likelihood (ML) blind methodsthat are shown to be quadratic in the observed data as well. Simulationshave confirmed that the discrete nature of the transmittedsymbols can be exploited to improve considerably the discriminationof near sources in medium-to-high SNR scenarios.

ML estimator and hybrid beamformer for multipath and interference mitigation in GNSS receivers

This paper addresses the estimation of the code-phase(pseudorange) and the carrier-phase of the direct signal received from a direct-sequence spread-spectrum satellite transmitter. Thesignal is received by an antenna array in a scenario with interferenceand multipath propagation. These two effects are generallythe limiting error sources in most high-precision positioning applications.A new estimator of the code- and carrier-phases is derivedby using a simplified signal model and the maximum likelihood(ML) principle. The simplified model consists essentially ofgathering all signals, except for the direct one, in a component withunknown spatial correlation. The estimator exploits the knowledgeof the direction-of-arrival of the direct signal and is much simplerthan other estimators derived under more detailed signal models.Moreover, we present an iterative algorithm, that is adequate for apractical implementation and explores an interesting link betweenthe ML estimator and a hybrid beamformer. The mean squarederror and bias of the new estimator are computed for a numberof scenarios and compared with those of other methods. The presentedestimator and the hybrid beamforming outperform the existingtechniques of comparable complexity and attains, in manysituations, the Cramér–Rao lower bound of the problem at hand.