A nonlinear approach for the on-line estimation of the kinetic rates in bioreactors

The objective of this paper is to propose simple nonlinear observer-based estimators which allow the on-line estimation of kinetic rates inside a bioreactor from the measurements of components' concentrations. The design of these estimators does not require any model for the kinetic rates and the corresponding gains do not necessitate the resolution of any dynamical system. One of the main characteristics of these estimators lies in the easiness of their implementation and in particular their calibration. Their performances are firstly illustrated in simulation through a typical example. Then, estimation results corresponding to a real-life experiment are given in order to confirm the theoretical results and to demonstrate the usefulness of the proposed estimators in practical situations.     

Design of delay-dependent state estimator for discrete-time recurrent neural networks with interval discrete and infinite-distributed time-varying delays

The state estimation problem for discrete-time recurrent neural networks with both interval discrete and infinite-distributed time-varying delays is studied in this paper, where interval discrete time-varying delay is in a given range. The activation functions are assumed to be globally Lipschitz continuous. A delay-dependent condition for the existence of state estimators is proposed based on new bounding techniques. Via solutions to certain linear matrix inequalities, general full-order state estimators are designed that ensure globally asymptotic stability. The significant feature is that no inequality is needed for seeking upper bounds for the inner product between two vectors, which can reduce the conservatism of the criterion by employing the new bounding techniques. Two illustrative examples are given to demonstrate the effectiveness and applicability of the proposed approach.     

Neural networks for self-adjusting mutation rate estimation when the recombination rate is unknown

Estimating the mutation rate, or equivalently effective population size, is a common task in population genetics. If recombination is low or high, optimal linear estimation methods are known and well understood. For intermediate recombination rates, the calculation of optimal estimators is more challenging. As an alternative to model-based estimation, neural networks and other machine learning tools could help to develop good estimators in these involved scenarios. However, if no benchmark is available it is difficult to assess how well suited these tools are for different applications in population genetics.Here we investigate feedforward neural networks for the estimation of the mutation rate based on the site frequency spectrum and compare their performance with model-based estimators. For this we use the model-based estimators introduced by Fu, Futschik et al., and Watterson that minimize the variance or mean squared error for no and free recombination. We find that neural networks reproduce these estimators if provided with the appropriate features and training sets. Remarkably, using the model-based estimators to adjust the weights of the training data, only one hidden layer is necessary to obtain a single estimator that performs almost as well as model-based estimators for low and high recombination rates, and at the same time provides a superior estimation method for intermediate recombination rates. We apply the method to simulated data based on the human chromosome 2 recombination map, highlighting its robustness in a realistic setting where local recombination rates vary and/or are unknown.     

Estimation of multiple biomass growth rates and biomass concentration in a class of bioprocesses

In this paper, an approach to the estimation of multiple biomass growth rates and biomass concentration is proposed for a class of aerobic bioprocesses characterized by on-line measurements of dissolved oxygen and carbon dioxide concentrations, as well as off-line measurements of biomass concentration. The approach is based on adaptive observer theory and includes two steps. In the first step, an adaptive estimator of two out of three biomass growth rates is designed. In the second step, the third biomass growth rate and the biomass concentration are estimated, using two different adaptive estimators. One of them is based on on-line measurements of dissolved oxygen concentration and off-line measurement of biomass concentrations, while the other needs only on-line measurements of the carbon dioxide concentration. Simulations demonstrated good performance of the proposed estimators under continuous and batch-fed conditions.     

Structural inference in transition measurement error models for longitudinal data

We propose a new class of models, transition measurement error models, to study the effects of covariates and the past responses on the current response in longitudinal studies when one of the covariates is measured with error. We show that the response variable conditional on the error-prone covariate follows a complex transition mixed effects model. The naive model obtained by ignoring the measurement error correctly specifies the transition part of the model, but misspecifies the covariate effect structure and ignores the random effects. We next study the asymptotic bias in naive estimator obtained by ignoring the measurement error for both continuous and discrete outcomes. We show that the naive estimator of the regression coefficient of the error-prone covariate is attenuated, while the naive estimators of the regression coefficients of the past responses are generally inflated. We then develop a structural modeling approach for parameter estimation using the maximum likelihood estimation method. In view of the multidimensional integration required by full maximum likelihood estimation, an EM algorithm is developed to calculate maximum likelihood estimators, in which Monte Carlo simulations are used to evaluate the conditional expectations in the E-step. We evaluate the performance of the proposed method through a simulation study and apply it to a longitudinal social support study for elderly women with heart disease. An additional simulation study shows that the Bayesian information criterion (BIC) performs well in choosing the correct transition orders of the models.     

Sensitivity Analysis of Variable-Size Group Testing and its Related Continuous Models

Parallels between the discrete group-testing model and some closely-related continuous models are elucidated. It is shown that in both the discrete and continuous cases, the maximum likelihood estimators may suffer from similar lack of robustness. Isotonic regression and maximum likelihood estimation were therefore compared for a modified group testing model.     

Bias-corrected variance estimation and hypothesis testing for spatial point and marked point processes using subsampling

Summary We introduce novel regression extrapolation based methods to correct the often large bias in subsampling variance estimation as well as hypothesis testing for spatial point and marked point processes. For variance estimation, our proposed estimators are linear combinations of the usual subsampling variance estimator based on subblock sizes in a continuous interval. We show that they can achieve better rates in mean squared error than the usual subsampling variance estimator. In particular, for n×n observation windows, the optimal rate of n^?2 can be achieved if the data have a finite dependence range. For hypothesis testing, we apply the proposed regression extrapolation directly to the test statistics based on different subblock sizes, and therefore avoid the need to conduct bias correction for each element in the covariance matrix used to set up the test statistics. We assess the numerical performance of the proposed methods through simulation, and apply them to analyze a tropical forest data set.     

Estimation in the progressive illness‐death model: A nonexhaustive review

Multistate models can be successfully used for describing complex event history data, for example, describing stages in the disease progression of a patient. The so‐called “illness‐death” model plays a central role in the theory and practice of these models. Many time‐to‐event datasets from medical studies with multiple end points can be reduced to this generic structure. In these models one important goal is the modeling of transition rates but biomedical researchers are also interested in reporting interpretable results in a simple and summarized manner. These include estimates of predictive probabilities, such as the transition probabilities, occupation probabilities, cumulative incidence functions, and the sojourn time distributions. We will give a review of some of the available methods for estimating such quantities in the progressive illness‐death model conditionally (or not) on covariate measures. For some of these quantities estimators based on subsampling are employed. Subsampling, also referred to as landmarking, leads to small sample sizes and usually to heavily censored data leading to estimators with higher variability. To overcome this issue estimators based on a preliminary estimation (presmoothing) of the probability of censoring may be used. Among these, the presmoothed estimators for the cumulative incidences are new. We also introduce feasible estimation methods for the cumulative incidence function conditionally on covariate measures. The proposed methods are illustrated using real data. A comparative simulation study of several estimation approaches is performed and existing software in the form of R packages is discussed.     

Estimation of Parameters in the Two-Compartment Model for Exhaled Nitric Oxide

The fractional concentration of exhaled nitric oxide (FeNO) is a biomarker of airway inflammation that is being increasingly considered in clinical, occupational, and epidemiological applications ranging from asthma management to the detection of air pollution health effects. FeNO depends strongly on exhalation flow rate. This dependency has allowed for the development of mathematical models whose parameters quantify airway and alveolar compartment contributions to FeNO. Numerous methods have been proposed to estimate these parameters using FeNO measured at multiple flow rates. These methods—which allow for non-invasive assessment of localized airway inflammation—have the potential to provide important insights on inflammatory mechanisms. However, different estimation methods produce different results and a serious barrier to progress in this field is the lack of a single recommended method. With the goal of resolving this methodological problem, we have developed a unifying framework in which to present a comprehensive set of existing and novel statistical methods for estimating parameters in the simple two-compartment model. We compared statistical properties of the estimators in simulation studies and investigated model fit and parameter estimate sensitivity across methods using data from 1507 schoolchildren from the Southern California Children''s Health Study, one of the largest multiple flow FeNO studies to date. We recommend a novel nonlinear least squares model with natural log transformation on both sides that produced estimators with good properties, satisfied model assumptions, and fit the Children''s Health Study data well.     

Confidence Intervals of the Simple Difference between the Proportions of a Primary Infection and a Secondary Infection,Given the Primary Infection

This paper discusses interval estimation of the simple difference (SD) between the proportions of the primary infection and the secondary infection, given the primary infection, by developing three asymptotic interval estimators using Wald's test statistic, the likelihood‐ratio test, and the basic principle of Fieller's theorem. This paper further evaluates and compares the performance of these interval estimators with respect to the coverage probability and the expected length of the resulting confidence intervals. This paper finds that the asymptotic confidence interval using the likelihood ratio test consistently performs well in all situations considered here. When the underlying SD is within 0.10 and the total number of subjects is not large (say, 50), this paper further finds that the interval estimators using Fieller's theorem would be preferable to the estimator using the Wald's test statistic if the primary infection probability were moderate (say, 0.30), but the latter is preferable to the former if this probability were large (say, 0.80). When the total number of subjects is large (say, ≥200), all the three interval estimators perform well in almost all situations considered in this paper. In these cases, for simplicity, we may apply either of the two interval estimators using Wald's test statistic or Fieller's theorem without losing much accuracy and efficiency as compared with the interval estimator using the asymptotic likelihood ratio test.     

Asymptotic behavior of the scaled mutation rate estimators

Important aspects of population evolution have been investigated using nucleotide sequences. Under the neutral Wright–Fisher model, the scaled mutation rate represents twice the average number of new mutations per generations and it is one of the key parameters in population genetics. In this study, we present various methods of estimation of this parameter, analytical studies of their asymptotic behavior as well as comparisons of the distribution's behavior of these estimators through simulations. As knowledge of the genealogy is needed to estimate the maximum likelihood estimator (MLE), an application with real data is also presented, using jackknife to correct the bias of the MLE, which can be generated by the estimation of the tree. We proved analytically that the Waterson's estimator and the MLE are asymptotically equivalent with the same rate of convergence to normality. Furthermore, we showed that the MLE has a better rate of convergence than Waterson's estimator for values of the parameter greater than one and this relationship is reversed when the parameter is less than one.     

On the estimation of average treatment effects with right-censored time to event outcome and competing risks

We are interested in the estimation of average treatment effects based on right-censored data of an observational study. We focus on causal inference of differences between t-year absolute event risks in a situation with competing risks. We derive doubly robust estimation equations and implement estimators for the nuisance parameters based on working regression models for the outcome, censoring, and treatment distribution conditional on auxiliary baseline covariates. We use the functional delta method to show that these estimators are regular asymptotically linear estimators and estimate their variances based on estimates of their influence functions. In empirical studies, we assess the robustness of the estimators and the coverage of confidence intervals. The methods are further illustrated using data from a Danish registry study.     

A Class of Ratio-Cum-Product-Type Estimator

The problem of estimating the population mean using an auxiliary information has been dealt with in literature quite extensively. Ratio, product, linear regression and ratio-type estimators are well known. A class of ratio-cum-product-type estimator is proposed in this paper. Its bias and variance to the first order of approximation are obtained. For an appropriate weight ‘a’ and good range of α-values, it is found that the proposed estimator is superior than a set of estimators (i.e., sample mean, usual ratio and product estimators, SRIVASTAVA's (1967) estimator, CHAKRABARTY's (1979) estimator and a product-type estimator) which are, in fact, the particular cases of it. At optimum value of α, the proposed estimator is as efficient as linear regression estimator.     

Estimating Transfer Entropy in Continuous Time Between Neural Spike Trains or Other Event-Based Data

Transfer entropy (TE) is a widely used measure of directed information flows in a number of domains including neuroscience. Many real-world time series for which we are interested in information flows come in the form of (near) instantaneous events occurring over time. Examples include the spiking of biological neurons, trades on stock markets and posts to social media, amongst myriad other systems involving events in continuous time throughout the natural and social sciences. However, there exist severe limitations to the current approach to TE estimation on such event-based data via discretising the time series into time bins: it is not consistent, has high bias, converges slowly and cannot simultaneously capture relationships that occur with very fine time precision as well as those that occur over long time intervals. Building on recent work which derived a theoretical framework for TE in continuous time, we present an estimation framework for TE on event-based data and develop a k-nearest-neighbours estimator within this framework. This estimator is provably consistent, has favourable bias properties and converges orders of magnitude more quickly than the current state-of-the-art in discrete-time estimation on synthetic examples. We demonstrate failures of the traditionally-used source-time-shift method for null surrogate generation. In order to overcome these failures, we develop a local permutation scheme for generating surrogate time series conforming to the appropriate null hypothesis in order to test for the statistical significance of the TE and, as such, test for the conditional independence between the history of one point process and the updates of another. Our approach is shown to be capable of correctly rejecting or accepting the null hypothesis of conditional independence even in the presence of strong pairwise time-directed correlations. This capacity to accurately test for conditional independence is further demonstrated on models of a spiking neural circuit inspired by the pyloric circuit of the crustacean stomatogastric ganglion, succeeding where previous related estimators have failed.     

A continuous time version and a generalization of a Markov-recapture model for trapping experiments

Wileyto et al. [E.P. Wileyto, W.J. Ewens, M.A. Mullen, Markov-recapture population estimates: a tool for improving interpretation of trapping experiments, Ecology 75 (1994) 1109] propose a four-state discrete time Markov process, which describes the structure of a marking-capture experiment as a method of population estimation. They propose this method primarily for estimation of closed insect populations. Their method provides a mark-recapture estimate from a single trap observation by allowing subjects to mark themselves. The estimate of the unknown population size is based on the assumption of a closed population and a simple Markov model in which the rates of marking, capture, and recapture are assumed to be equal. Using the one step transition probability matrix of their model, we illustrate how to go from an embedded discrete time Markov process to a continuous time Markov process assuming exponentially distributed holding times. We also compute the transition probabilities after time t for the continuous time case and compare the limiting behavior of the continuous and discrete time processes. Finally, we generalize their model by relaxing the assumption of equal per capita rates for marking, capture, and recapture. Other questions about how their results change when using a continuous time Markov process are examined.     

A classification of bioinformatics algorithms from the viewpoint of maximizing expected accuracy (MEA)

Many estimation problems in bioinformatics are formulated as point estimation problems in a high-dimensional discrete space. In general, it is difficult to design reliable estimators for this type of problem, because the number of possible solutions is immense, which leads to an extremely low probability for every solution-even for the one with the highest probability. Therefore, maximum score and maximum likelihood estimators do not work well in this situation although they are widely employed in a number of applications. Maximizing expected accuracy (MEA) estimation, in which accuracy measures of the target problem and the entire distribution of solutions are considered, is a more successful approach. In this review, we provide an extensive discussion of algorithms and software based on MEA. We describe how a number of algorithms used in previous studies can be classified from the viewpoint of MEA. We believe that this review will be useful not only for users wishing to utilize software to solve the estimation problems appearing in this article, but also for developers wishing to design algorithms on the basis of MEA.     

On the Properties of GEE Estimators in the Presence of Invariant Covariates

Since Liang and Zeger (1986) proposed the ‘generalized estimating equations’ approach for the estimation of regression parameters in models with correlated discrete responses, a lot of work has been devoted to the investigation of the properties of the corresponding GEE estimators. However, the effects of different kinds of covariates have often been overlooked. In this paper it is shown that the use of non-singular block invariant matrices of covariates, as e.g. a design matrix in an analysis of variance model, leads to GEE estimators which are identical regardless of the ‘working’ correlation matrix used. Moreover, they are efficient (McCullagh, 1983). If on the other hand only covariates are used which are invariant within blocks, the efficiency gain in choosing the ‘correct’ vs. an ‘incorrect’ correlation structure is shown to be negligible. The results of a simple simulation study suggest that although different GEE estimators are not identical and are not as efficient as a ML estimator, the differences are still negligible if both types of invariant covariates are present.     

Bayesian Procedures for the Estimation of Mutation Rates from Fluctuation Experiments

Bayesian procedures are developed for estimating mutation rates from fluctuation experiments. Three Bayesian point estimators are compared with four traditional ones using the results of 10,000 simulated experiments. The Bayesian estimators were found to be at least as efficient as the best of the previously known estimators. The best Bayesian estimator is one that uses (1/m(2)) as the prior probability density function and a quadratic loss function. The advantage of using these estimators is most pronounced when the number of fluctuation test tubes is small. Bayesian estimation allows the incorporation of prior knowledge about the estimated parameter, in which case the resulting estimators are the most efficient. It enables the straightforward construction of confidence intervals for the estimated parameter. The increase of efficiency with prior information and the narrowing of the confidence intervals with additional experimental results are investigated. The results of the simulations show that any potential inaccuracy of estimation arising from lumping together all cultures with more than n mutants (the jackpots) almost disappears at n = 70 (provided that the number of mutations in a culture is low). These methods are applied to a set of experimental data to illustrate their use.     

A unified likelihood-based approach for estimating population size in continuous-time capture-recapture experiments with frailty

A unified likelihood-based approach is proposed to estimate population size for a continuous-time closed capture-recapture experiment with frailty. The frailty model allows the capture intensity to vary with individual heterogeneity, time, and behavioral response. The individual heterogeneity effect is modeled as being gamma distributed. The first-capture and recapture intensities are assumed to be in constant proportion but may otherwise vary arbitrarily through time. The approach is also extended to capture-recapture experiments with possible random removals. Simulation studies are conducted to examine the performance of the proposed estimators. By asymptotic efficiency comparison and simulation studies, the proposed estimators have been shown to be superior to their discrete-time model counterparts in genuine continuous-time capture-recapture experiments.