Accuracy in estimating motor commands using neuronal population coding

We consider the problem of estimating motor commands from an ensemble of neuronal activities. The population vector algorithm proposed by Georgopoulos provides largely biased estimations when preferred directions of neurons are non-uniformly distributed. To improve this, various decoding methods have been proposed. However, dependence of decoding accuracy on the motor command and other features of neural activities, such as baseline firing rates or amplitudes of tuning curves, have not been quantitatively discussed. In this study, we propose a new method to estimate the motor command in the maximum likelihood estimation framework, which is analytically tractable. We find that the estimation accuracy is independent of the motor command. Using our estimation method, we can estimate the motor command with equal accuracy in all directions.     

Semiparametric estimation exploiting covariate independence in two-phase randomized trials

Summary .  Recent results for case–control sampling suggest when the covariate distribution is constrained by gene-environment independence, semiparametric estimation exploiting such independence yields a great deal of efficiency gain. We consider the efficient estimation of the treatment–biomarker interaction in two-phase sampling nested within randomized clinical trials, incorporating the independence between a randomized treatment and the baseline markers. We develop a Newton–Raphson algorithm based on the profile likelihood to compute the semiparametric maximum likelihood estimate (SPMLE). Our algorithm accommodates both continuous phase-one outcomes and continuous phase-two biomarkers. The profile information matrix is computed explicitly via numerical differentiation. In certain situations where computing the SPMLE is slow, we propose a maximum estimated likelihood estimator (MELE), which is also capable of incorporating the covariate independence. This estimated likelihood approach uses a one-step empirical covariate distribution, thus is straightforward to maximize. It offers a closed-form variance estimate with limited increase in variance relative to the fully efficient SPMLE. Our results suggest exploiting the covariate independence in two-phase sampling increases the efficiency substantially, particularly for estimating treatment–biomarker interactions.     

A targeted maximum likelihood estimator for two-stage designs

We consider two-stage sampling designs, including so-called nested case control studies, where one takes a random sample from a target population and completes measurements on each subject in the first stage. The second stage involves drawing a subsample from the original sample, collecting additional data on the subsample. This data structure can be viewed as a missing data structure on the full-data structure collected in the second-stage of the study. Methods for analyzing two-stage designs include parametric maximum likelihood estimation and estimating equation methodology. We propose an inverse probability of censoring weighted targeted maximum likelihood estimator (IPCW-TMLE) in two-stage sampling designs and present simulation studies featuring this estimator.     

Inference from single occasion capture experiments using genetic markers

Accurate estimation of the size of animal populations is an important task in ecological science. Recent advances in the field of molecular genetics researches allow the use of genetic data to estimate the size of a population from a single capture occasion rather than repeated occasions as in the usual capture–recapture experiments. Estimating the population size using genetic data also has sometimes led to estimates that differ markedly from each other and also from classical capture–recapture estimates. Here, we develop a closed form estimator that uses genetic information to estimate the size of a population consisting of mothers and daughters, focusing on estimating the number of mothers, using data from a single sample. We demonstrate the estimator is consistent and propose a parametric bootstrap to estimate the standard errors. The estimator is evaluated in a simulation study and applied to real data. We also consider maximum likelihood in this setting and discover problems that preclude its general use.     

Estimation of evolutionary parameters with phylogenetic trees

An important issue in the phylogenetic analysis of nucleotide sequence data using the maximum likelihood (ML) method is the underlying evolutionary model employed. We consider the problem of simultaneously estimating the tree topology and the parameters in the underlying substitution model and of obtaining estimates of the standard errors of these parameter estimates. Given a fixed tree topology and corresponding set of branch lengths, the ML estimates of standard evolutionary model parameters are asymptotically efficient, in the sense that their joint distribution is asymptotically normal with the variance–covariance matrix given by the inverse of the Fisher information matrix. We propose a new estimate of this conditional variance based on estimation of the expected information using a Monte Carlo sampling (MCS) method. Simulations are used to compare this conditional variance estimate to the standard technique of using the observed information under a variety of experimental conditions. In the case in which one wishes to estimate simultaneously the tree and parameters, we provide a bootstrapping approach that can be used in conjunction with the MCS method to estimate the unconditional standard error. The methods developed are applied to a real data set consisting of 30 papillomavirus sequences. This overall method is easily incorporated into standard bootstrapping procedures to allow for proper variance estimation.     

Pooling designs for outcomes under a Gaussian random effects model

Due to the rising cost of laboratory assays, it has become increasingly common in epidemiological studies to pool biospecimens. This is particularly true in longitudinal studies, where the cost of performing multiple assays over time can be prohibitive. In this article, we consider the problem of estimating the parameters of a Gaussian random effects model when the repeated outcome is subject to pooling. We consider different pooling designs for the efficient maximum likelihood estimation of variance components, with particular attention to estimating the intraclass correlation coefficient. We evaluate the efficiencies of different pooling design strategies using analytic and simulation study results. We examine the robustness of the designs to skewed distributions and consider unbalanced designs. The design methodology is illustrated with a longitudinal study of premenopausal women focusing on assessing the reproducibility of F2-isoprostane, a biomarker of oxidative stress, over the menstrual cycle.     

MAP estimation algorithm for phase response curves based on analysis of the observation process

Many research groups have sought to measure phase response curves (PRCs) from real neurons. However, methods of estimating PRCs from noisy spike-response data have yet to be established. In this paper, we propose a Bayesian approach for estimating PRCs. First, we analytically obtain a likelihood function of the PRC from a detailed model of the observation process formulated as Langevin equations. Then we construct a maximum a posteriori (MAP) estimation algorithm based on the analytically obtained likelihood function. The MAP estimation algorithm derived here is equivalent to the spherical spin model. Moreover, we analytically calculate a marginal likelihood corresponding to the free energy of the spherical spin model, which enables us to estimate the hyper-parameters, i.e., the intensity of the Langevin force and the smoothness of the prior. Action Editor: John Rinzel     

Maximum Likelihood Estimation of Genetic Parameters in Cell Populations

In this paper we consider a cell population such as bacteria consisting of two types of cells, mutant and nonmutant. Under the mutation and homogeneous pure birth processes, this paper derives a maximum likelihood estimation procedure for estimating mutation rate and birth rate. The method is applied to Newcombe's data; further some Monte Carlo studies are generated. The numerical results indicate that the method is quite efficient for estimating genetic parameters in cell populations.     

二个区域的封闭种群的标记重捕模型

通过引入区域的初始比例因子,考虑了二个区域A与B的封闭种群标记重捕模型,再利用完整的极大似然函数和多项分布函数的性质,给出了当个体在不同区域的个体捕捉率相等时的二个区域之间的转移概率与各区域的初始比例的求法,推导出在不同区域的个体捕捉率不相等但个体低转移率条件下二个区域的封闭种群的标记重捕模型的参数表达式,并用实例说明。     

A weighted partial likelihood approach for zero‐truncated models

Zero‐truncated data arises in various disciplines where counts are observed but the zero count category cannot be observed during sampling. Maximum likelihood estimation can be used to model these data; however, due to its nonstandard form it cannot be easily implemented using well‐known software packages, and additional programming is often required. Motivated by the Rao–Blackwell theorem, we develop a weighted partial likelihood approach to estimate model parameters for zero‐truncated binomial and Poisson data. The resulting estimating function is equivalent to a weighted score function for standard count data models, and allows for applying readily available software. We evaluate the efficiency for this new approach and show that it performs almost as well as maximum likelihood estimation. The weighted partial likelihood approach is then extended to regression modelling and variable selection. We examine the performance of the proposed methods through simulation and present two case studies using real data.     

SNP calling, genotype calling, and sample allele frequency estimation from new-generation sequencing data

We present a statistical framework for estimation and application of sample allele frequency spectra from New-Generation Sequencing (NGS) data. In this method, we first estimate the allele frequency spectrum using maximum likelihood. In contrast to previous methods, the likelihood function is calculated using a dynamic programming algorithm and numerically optimized using analytical derivatives. We then use a Bayesian method for estimating the sample allele frequency in a single site, and show how the method can be used for genotype calling and SNP calling. We also show how the method can be extended to various other cases including cases with deviations from Hardy-Weinberg equilibrium. We evaluate the statistical properties of the methods using simulations and by application to a real data set.     

Parameter estimation in a Gompertzian stochastic model for tumor growth

The problem of estimating parameters in the drift coefficient when a diffusion process is observed continuously requires some specific assumptions. In this paper, we consider a stochastic version of the Gompertzian model that describes in vivo tumor growth and its sensitivity to treatment with antiangiogenic drugs. An explicit likelihood function is obtained, and we discuss some properties of the maximum likelihood estimator for the intrinsic growth rate of the stochastic Gompertzian model. Furthermore, we show some simulation results on the behavior of the corresponding discrete estimator. Finally, an application is given to illustrate the estimate of the model parameters using real data.     

A targeted maximum likelihood estimator of a causal effect on a bounded continuous outcome

Targeted maximum likelihood estimation of a parameter of a data generating distribution, known to be an element of a semi-parametric model, involves constructing a parametric model through an initial density estimator with parameter ? representing an amount of fluctuation of the initial density estimator, where the score of this fluctuation model at ? = 0 equals the efficient influence curve/canonical gradient. The latter constraint can be satisfied by many parametric fluctuation models since it represents only a local constraint of its behavior at zero fluctuation. However, it is very important that the fluctuations stay within the semi-parametric model for the observed data distribution, even if the parameter can be defined on fluctuations that fall outside the assumed observed data model. In particular, in the context of sparse data, by which we mean situations where the Fisher information is low, a violation of this property can heavily affect the performance of the estimator. This paper presents a fluctuation approach that guarantees the fluctuated density estimator remains inside the bounds of the data model. We demonstrate this in the context of estimation of a causal effect of a binary treatment on a continuous outcome that is bounded. It results in a targeted maximum likelihood estimator that inherently respects known bounds, and consequently is more robust in sparse data situations than the targeted MLE using a naive fluctuation model. When an estimation procedure incorporates weights, observations having large weights relative to the rest heavily influence the point estimate and inflate the variance. Truncating these weights is a common approach to reducing the variance, but it can also introduce bias into the estimate. We present an alternative targeted maximum likelihood estimation (TMLE) approach that dampens the effect of these heavily weighted observations. As a substitution estimator, TMLE respects the global constraints of the observed data model. For example, when outcomes are binary, a fluctuation of an initial density estimate on the logit scale constrains predicted probabilities to be between 0 and 1. This inherent enforcement of bounds has been extended to continuous outcomes. Simulation study results indicate that this approach is on a par with, and many times superior to, fluctuating on the linear scale, and in particular is more robust when there is sparsity in the data.     

Plant-capture estimation of the size of a homogeneous population

We consider maximum likelihood estimation of the size of a targetpopulation to which has been added a known number of plantedindividuals. The standard equal-catchability model used in mark-recaptureis assumed to be applicable to the augmented population. Afterproving the unimodality of the profile likelihood for the targetpopulation size, we obtain both the maximum likelihood estimatorof this size and interval estimators based on its asymptoticdistribution.     

Maximum likelihood estimation of marginal pairwise associations with multiple source predictors

Researchers interested in the association of a predictor with an outcome will often collect information about that predictor from more than one source. Standard multiple regression methods allow estimation of the effect of each predictor on the outcome while controlling for the remaining predictors. The resulting regression coefficient for each predictor has an interpretation that is conditional on all other predictors. In settings in which interest is in comparison of the marginal pairwise relationships between each predictor and the outcome separately (e.g., studies in psychiatry with multiple informants or comparison of the predictive values of diagnostic tests), standard regression methods are not appropriate. Instead, the generalized estimating equations (GEE) approach can be used to simultaneously estimate, and make comparisons among, the separate pairwise marginal associations. In this paper, we consider maximum likelihood (ML) estimation of these marginal relationships when the outcome is binary. ML enjoys benefits over GEE methods in that it is asymptotically efficient, can accommodate missing data that are ignorable, and allows likelihood-based inferences about the pairwise marginal relationships. We also explore the asymptotic relative efficiency of ML and GEE methods in this setting.     

Minimum Norm Invariant Quadratic Estimation of a Covariance Matrix in Linear Model

A general linear model with a known covariance structure is considered. The method of Minimum Norm Quadratic estimation extending RAO'S (1972) argument is outlined. This method is illustrated for a particular model where it is noted that MINQE used for estimating intraclass correlation coefficient yields the maximum likelihood estimate.     

Targeted maximum likelihood estimation for dynamic treatment regimes in sequentially randomized controlled trials

Sequential Randomized Controlled Trials (SRCTs) are rapidly becoming essential tools in the search for optimized treatment regimes in ongoing treatment settings. Analyzing data for multiple time-point treatments with a view toward optimal treatment regimes is of interest in many types of afflictions: HIV infection, Attention Deficit Hyperactivity Disorder in children, leukemia, prostate cancer, renal failure, and many others. Methods for analyzing data from SRCTs exist but they are either inefficient or suffer from the drawbacks of estimating equation methodology. We describe an estimation procedure, targeted maximum likelihood estimation (TMLE), which has been fully developed and implemented in point treatment settings, including time to event outcomes, binary outcomes and continuous outcomes. Here we develop and implement TMLE in the SRCT setting. As in the former settings, the TMLE procedure is targeted toward a pre-specified parameter of the distribution of the observed data, and thereby achieves important bias reduction in estimation of that parameter. As with the so-called Augmented Inverse Probability of Censoring Weight (A-IPCW) estimator, TMLE is double-robust and locally efficient. We report simulation results corresponding to two data-generating distributions from a longitudinal data structure.     

EM Algorithm for Segregation Analysis

We consider the problem of estimating segregation ratios in families based on ascertainment through affected children, formulate it as an incomplete problem and work out the EM algorithm for maximum likelihood estimation of segregation ratios. We treat both the cases of known and unknown ascertainment probability. We also derive expressions for the covariance matrix of the estimators suitable for computing along with the EM algorithm. We illustrate the method with an example, compare the computational effort with that required in using the scoring method and argue that the EM algorithm is simpler.     

Improved estimation of the proportion of triploids in populations with diploid and triploid individuals

We consider the estimation of the proportion of triploids in populations of plants or animals in which diploid and triploid individuals coexist, using data from electrophoretic analysis of isozyme or microsatellite markers. Individuals that have three distinct alleles at a locus are unambiguously triploid. However, other individuals cannot be classified with certainty as diploid or triploid, unless allelic dosage can be determined reliably. This is impossible for microsatellite markers, and for many isozyme markers. We therefore present a maximum likelihood method of estimating the proportion of triploids based only on the presence or absence of different alleles.     

Estimating a Logistic Discrimination Functions When One of the Training Samples Is Subject to Misclassification: A Maximum Likelihood Approach

The problem of discrimination and classification is central to much of epidemiology. Here we consider the estimation of a logistic regression/discrimination function from training samples, when one of the training samples is subject to misclassification or mislabeling, e.g. diseased individuals are incorrectly classified/labeled as healthy controls. We show that this leads to zero-inflated binomial model with a defective logistic regression or discrimination function, whose parameters can be estimated using standard statistical methods such as maximum likelihood. These parameters can be used to estimate the probability of true group membership among those, possibly erroneously, classified as controls. Two examples are analyzed and discussed. A simulation study explores properties of the maximum likelihood parameter estimates and the estimates of the number of mislabeled observations.