Generalized Walker-Duncan Procedure for Obtaining Maximum Likelihood Estimates of Parameters of Logistic Discriminant Function

A recursive method of obtaining the maximum likelihood estimates of the parameters of the quadratic logistic discriminant function is presented. This method is an extension of the Walker and Duncan procedure (1967) proposed for the linear logistic discriminant function in a dichotomous case. A generalization of the method to the problem of discrimination between several populations is also given in the paper. It works for both linear and quadratic logistic discriminant function. After an estimation of the parameters of the logistic function a classification can be performed. An example of application of the method to automatic diagnosis of some respiratory diseases is presented. Comparison with the standard procedures used for the estimation is done by a short simulation study.     

稻纵卷叶螟卷叶有虫率与化蛹率关系的研究

探索利用稻纵卷叶螟 Cnaphalocrocis medinalis（Guenée）卷叶有虫率估测化蛹率的方法和途径。本文基于稻纵卷叶螟化蛹进度的田间调查数据,用化蛹率（y）和卷叶有虫率（x）分别拟合直线函数、一元二次函数、一元三次函数、对数函数、指数函数和幂函数6种不同模型。结果表明,以一元三次函数方法估计精度最高,误差最小,应用效果最好,并根据最优数学模型建立化蛹率（y）与卷叶有虫率（x）的关系速查表。生产中可以应用拟合的 最优数学模型对田间稻纵卷叶螟化蛹进度进行监测。     

Accuracy of rate estimation using relaxed-clock models with a critical focus on the early metazoan radiation

In recent years, a number of phylogenetic methods have been developed for estimating molecular rates and divergence dates under models that relax the molecular clock constraint by allowing rate change throughout the tree. These methods are being used with increasing frequency, but there have been few studies into their accuracy. We tested the accuracy of several relaxed-clock methods (penalized likelihood and Bayesian inference using various models of rate change) using nucleotide sequences simulated on a nine-taxon tree. When the sequences evolved with a constant rate, the methods were able to infer rates accurately, but estimates were more precise when a molecular clock was assumed. When the sequences evolved under a model of auto-correlated rate change, rates were accurately estimated using penalized likelihood and by Bayesian inference using lognormal and exponential models of rate change, while other models did not perform as well. When the sequences evolved under a model of uncorrelated rate change, only Bayesian inference using an exponential rate model performed well. Collectively, the results provide a strong recommendation for using the exponential model of rate change if a conservative approach to divergence time estimation is required. A case study is presented in which we use a simulation-based approach to examine the hypothesis of elevated rates in the Cambrian period, and it is found that these high rate estimates might be an artifact of the rate estimation method. If this bias is present, then the ages of metazoan divergences would be systematically underestimated. The results of this study have implications for studies of molecular rates and divergence dates.     

Mechanisms of pollen deposition by insect pollinators

Summary Studies of pollen dispersal in insect-pollinated plants have often documented highly leptokurtic patterns of pollen deposition that can increase the likelihood of long-distance mating. To examine potential causes of highly leptokurtic deposition, we introduce four functions that arise when (1) the duration of pollinator visits to pollen sources is limited, (2) the rate of pollen deposition varies randomly among pollinators and/or among visits, (3) the rate of pollen deposition changes monotonically over time or (4) pollen is carried in layers or compartments on the pollinator's body that differ in deposition rate. Maximum likelihood techniques were used to fit deposition functions to data obtained from honey bees (Apis mellifera L.) visiting mustard plants (Brassica campestris L.) that contained a marker gene. Each of the alternative leptokurtic functions fit the experimental data better than a simple exponential function and the best-fit function predicted a mean pollen dispersal distance more than three times greater than the exponential. We argue that studies of pollen deposition need to test a broader range of deposition models to assess outcrossing distance in plant populations accurately.     

The dose response relationship obtained at constant irradiation times for the induction of chromosome aberrations in human lymphocytes by cobalt-60 gamma rays

Summary The induction of unstable chromosome aberrations in human peripheral blood lymphocytes exposed in vitro to protracted doses of cobalt-60 radiation is presented. Four dose response curves have been produced using constant exposure times of 1, 3, 6, and 12 h. The data fit well to the linear quadratic model and the yield coefficients have been compared with those obtained for acute (< 10 min) exposure. The quadratic coefficient is dependent on irradiation time and decreases approximately as predicted by Lea and Catcheside'sG-function hypothesis. The possibility of a small proportion of much longer lived breaks is discussed. For purposes of biological dosimetry it is sufficient to assume a mean time of 2 h and a single exponential function for the repair of lesions when relating the effects of brief and protracted exposure.     

Modelling effects of habitat fragmentation on the ability of trees to respond to climatic warming

The ability of trees to migrate in response to climatic warming was simulated under various conditions of habitat availability. The model uses Holocene tree migration rates to approximate maximum migration rates in a forested landscape. Habitat availability and local population size was varied systematically under two dispersal and colonization models. These dispersal models varied in the likelihood of long-distance dispersal events. The first model used a negative exponential function that severely limited the probability of long-distance dispersal. The results of this model indicate that migration rate could decline an order of magnitude where the habitat availability is reduced from 80 to 20% of the matrix. The second model, using an inverse power function, carried a higher probability of long-distance dispersal events. The results from this model predict relatively small declines in migration rates when habitat availability is reduced to 50% of the simulation matrix. Below 50% habitat availability, mean migration rate was similar to the negative exponential model. These results predict a failure of many trees to respond to future climatic change through range expansion.     

Asymptotically robust variance estimation for person‐time incidence rates

Person‐time incidence rates are frequently used in medical research. However, standard estimation theory for this measure of event occurrence is based on the assumption of independent and identically distributed (iid) exponential event times, which implies that the hazard function remains constant over time. Under this assumption and assuming independent censoring, observed person‐time incidence rate is the maximum‐likelihood estimator of the constant hazard, and asymptotic variance of the log rate can be estimated consistently by the inverse of the number of events. However, in many practical applications, the assumption of constant hazard is not very plausible. In the present paper, an average rate parameter is defined as the ratio of expected event count to the expected total time at risk. This rate parameter is equal to the hazard function under constant hazard. For inference about the average rate parameter, an asymptotically robust variance estimator of the log rate is proposed. Given some very general conditions, the robust variance estimator is consistent under arbitrary iid event times, and is also consistent or asymptotically conservative when event times are independent but nonidentically distributed. In contrast, the standard maximum‐likelihood estimator may become anticonservative under nonconstant hazard, producing confidence intervals with less‐than‐nominal asymptotic coverage. These results are derived analytically and illustrated with simulations. The two estimators are also compared in five datasets from oncology studies.     

The exponential‐Poisson model for recurrent event data: An application to a set of data on malaria in Brazil

In this paper, we introduce a new model for recurrent event data characterized by a baseline rate function fully parametric, which is based on the exponential‐Poisson distribution. The model arises from a latent competing risk scenario, in the sense that there is no information about which cause was responsible for the event occurrence. Then, the time of each recurrence is given by the minimum lifetime value among all latent causes. The new model has a particular case, which is the classical homogeneous Poisson process. The properties of the proposed model are discussed, including its hazard rate function, survival function, and ordinary moments. The inferential procedure is based on the maximum likelihood approach. We consider an important issue of model selection between the proposed model and its particular case by the likelihood ratio test and score test. Goodness of fit of the recurrent event models is assessed using Cox‐Snell residuals. A simulation study evaluates the performance of the estimation procedure in the presence of a small and moderate sample sizes. Applications on two real data sets are provided to illustrate the proposed methodology. One of them, first analyzed by our team of researchers, considers the data concerning the recurrence of malaria, which is an infectious disease caused by a protozoan parasite that infects red blood cells.     

Estimation of the incubation period of influenza A (H1N1-2009) among imported cases: addressing censoring using outbreak data at the origin of importation

Empirical estimates of the incubation period of influenza A (H1N1-2009) have been limited. We estimated the incubation period among confirmed imported cases who traveled to Japan from Hawaii during the early phase of the 2009 pandemic (n=72). We addressed censoring and employed an infection-age structured argument to explicitly model the daily frequency of illness onset after departure. We assumed uniform and exponential distributions for the frequency of exposure in Hawaii, and the hazard rate of infection for the latter assumption was retrieved, in Hawaii, from local outbreak data. The maximum likelihood estimates of the median incubation period range from 1.43 to 1.64 days according to different modeling assumptions, consistent with a published estimate based on a New York school outbreak. The likelihood values of the different modeling assumptions do not differ greatly from each other, although models with the exponential assumption yield slightly shorter incubation periods than those with the uniform exposure assumption. Differences between our proposed approach and a published method for doubly interval-censored analysis highlight the importance of accounting for the dependence of the frequency of exposure on the survival function of incubating individuals among imported cases. A truncation of the density function of the incubation period due to an absence of illness onset during the exposure period also needs to be considered. When the data generating process is similar to that among imported cases, and when the incubation period is close to or shorter than the length of exposure, accounting for these aspects is critical for long exposure times.     

On hyperbolic discounting and uncertain hazard rates

The value of a future reward should be discounted where there is a risk that the reward will not be realized. If the risk manifests itself at a known, constant hazard rate, a risk-neutral recipient should discount the reward according to an exponential time-preference function. Experimental subjects, however, exhibit short-term time preferences that differ from the exponential in a manner consistent with a hazard rate that falls with increasing delay. It is shown here that this phenomenon can be explained by uncertainty in the underlying hazard. The time-preference function predicted by this analysis can be calculated by means of either (i) a direct superposition method, or (ii) Bayesian updating of the expected hazard rate. The observed hyperbolic time-preference function is consistent with an exponential prior distribution for the underlying hazard rate. Sensitivity of the predicted time-preference function to variation in the probability distribution of the underlying hazard rate is explored.     

Quantification of the mechanical properties of noncontracting canine myocardium under simultaneous biaxial loading

Detailed understanding of cardiac mechanics depends upon accurate and complete characterization of the three-dimensional properties of both normal and diseased myocardial tissue. This, however, can only be obtained by performing multiaxial tests on cardiac tissue. In this study we subjected thin sheets of passive canine left ventricular myocardium to various combinations of simultaneous biaxial stretching. During each stretch the ratio of the orthogonal strains was kept constant and the corresponding stresses remained proportional. We fitted the biaxial stress-strain data both with exponential strain-energy functions with quadratic powers of strains as well as with an alternative function with nonintegral powers of strains. We used our recently developed nonparametric method to assess the reliability of the coefficients for each of these functions. The quadratic strain-energy functions resulted in wide intra- and interspecimen variability in the coefficients. Moreover, both their absolute and relative values demonstrated marked load history dependence such that interpretation of the direction of anisotropy was difficult. Fitting the data with the alternative nonintegral strain-energy function seemed to alleviate these problems. This alternative strain-energy function may provide more self-consistent results than the more commonly used quadratic strain-energy functions.     

Generalized linear models with unspecified reference distribution

We propose a new class of semiparametric generalized linear models. As with existing models, these models are specified via a linear predictor and a link function for the mean of response Y as a function of predictors X. Here, however, the "baseline" distribution of Y at a given reference mean mu(0) is left unspecified and is estimated from the data. The response distribution when the mean differs from mu(0) is then generated via exponential tilting of the baseline distribution, yielding a response model that is a natural exponential family, with corresponding canonical link and variance functions. The resulting model has a level of flexibility similar to the popular proportional odds model. Maximum likelihood estimation is developed for response distributions with finite support, and the new model is studied and illustrated through simulations and example analyses from aging research.     

长白山阔叶红松林冬季雪面蒸发特征

利用2002-2005年冬季积雪期涡度相关水汽通量和微气象观测资料,对长白山阔叶红松林雪面蒸发动态及其与气象因子的关系进行分析.结果表明： 该涡度相关观测系统积雪期能量平衡闭合度为79.9%,潜热通量占净辐射的21.4%.研究期间,该区蒸发日变化呈单峰曲线形式,蒸发速率在融雪期大于稳定积雪期.30 min平均蒸发速率与净辐射呈线性关系,与气温呈二次曲线关系;蒸发日总量与净辐射呈二次曲线关系,与气温呈指数关系.积雪期蒸发日总量呈下降-稳定-上升的动态变化趋势,且上升期>下降期>稳定期,蒸发日总量最大值为0.73 mm·d^-1,最小值为0.004 mm·d^-1.2002-2003、2003-2004和2004-2005年积雪期蒸发总量分别为27.6、25.5和22.9 mm,占同期降水量的37.9%、19.5%和30.0%,平均蒸发日总量分别为0.17、0.19和0.17 mm·d^-1.     

Reconstructing phylogeny by quadratically approximated maximum likelihood

Maximum likelihood (ML) for phylogenetic inference from sequence data remains a method of choice, but has computational limitations. In particular, it cannot be applied for a global search through all potential trees when the number of taxa is large, and hence a heuristic restriction in the search space is required. In this paper, we derive a quadratic approximation, QAML, to the likelihood function whose maximum is easily determined for a given tree. The derivation depends on Hadamard conjugation, and hence is limited to the simple symmetric models of Kimura and of Jukes and Cantor. Preliminary testing has demonstrated the accuracy of QAML is close to that of ML.     

Control of macromolecular synthesis in proliferating and resting Syrian hamster cells in monolayer culture. I. Ribosome function

The rate of protein synthesis per cell in cultured hamster embryo fibroblasts in the stationary growth phase falls to about one third of the rate in the exponential growth phase. This reduction can be entirely accounted for by the following observations: (1) the average cell in stationary phase contains about one-half the number of ribosomes per cell compared to the average cell in exponential phase; (2) only two thirds of the ribosomes are bound to polysomes in stationary phase, while nearly all of the ribosomes are polysome-bound in exponential phase. In stationary phase, ribosomes which are polysome-bound function with the same efficiency and produce proteins of approximately the same average length as in exponential phase. Experimental findings are presented which suggest that the generation of a higher proportion of free ribosomes in stationary phase in not due to a limitation in messenger RNA, but to a decreased attachment probability of ribosomes to messenger RNA.     

A direct optimization approach to hidden Markov modeling for single channel kinetics

Hidden Markov modeling (HMM) provides an effective approach for modeling single channel kinetics. Standard HMM is based on Baum's reestimation. As applied to single channel currents, the algorithm has the inability to optimize the rate constants directly. We present here an alternative approach by considering the problem as a general optimization problem. The quasi-Newton method is used for searching the likelihood surface. The analytical derivatives of the likelihood function are derived, thereby maximizing the efficiency of the optimization. Because the rate constants are optimized directly, the approach has advantages such as the allowance for model constraints and the ability to simultaneously fit multiple data sets obtained at different experimental conditions. Numerical examples are presented to illustrate the performance of the algorithm. Comparisons with Baum's reestimation suggest that the approach has a superior convergence speed when the likelihood surface is poorly defined due to, for example, a low signal-to-noise ratio or the aggregation of multiple states having identical conductances.     

Prediction of genetic gain from quadratic optimisation with constrained rates of inbreeding

There are selection methods available that allow the optimisation of genetic contributions of selection candidates for maximising the rate of genetic gain while restricting the rate of inbreeding. These methods imply selection on quadratic indices as the selection merit of a particular individual is a quadratic function of its estimated breeding value. This study provides deterministic predictions of genetic gain from selection on quadratic indices for a given set of resources (the number of candidates), heritability, and target rate of inbreeding. The rate of gain was obtained as a function of the accuracy of the Mendelian sampling term at the time of convergence of long-term contributions of selected candidates and the theoretical ideal rate of gain for a given rate of inbreeding after an exact allocation of long-term contributions to Mendelian sampling terms. The expected benefits from quadratic indices over traditional linear indices (i.e. truncation selection), both using BLUP breeding values, were quantified. The results clearly indicate higher gains from quadratic optimisation than from truncation selection. With constant rate of inbreeding and number of candidates, the benefits were generally largest for intermediate heritabilities but evident over the entire range. The advantage of quadratic indices was not highly sensitive to the rate of inbreeding for the constraints considered.     

Survival of a mixture of cells of variable linear-quadratic sensitivity to radiation

The experimentally observed survival of a heterogeneous mixture of cells, each component of which obeys a different linear-quadratic survival response to ionizing radiation, is examined. It is shown that the survival relationship for the mixed population approaches a linear-quadratic form for low doses. The linear parameter of the low-dose relationship approached is equal to the average of the distribution of values of the linear parameter (alpha(i)) of the various components of the mixture. The quadratic parameter of the low-dose relationship approached is equal to the average of the distribution of values of the quadratic parameter (beta(i)) of the various components of the mixture minus one-half the variance of the distribution of the values of alpha(i). A numerical example of the survival expected for an exponentially growing population of Chinese hamster V79 cells is presented. From this it can be appreciated that the apparent value of the alpha and beta parameters obtained by fitting an experimentally obtained survival curve will depend on the range of doses over which survival is determined. The apparent value of beta is decreased at higher doses, producing a straightening of the survival curve to approach the exponential decrease in survival commonly observed for the terminal high-dose portion of survival curves. Apparent exponential survival at high doses is not inconsistent with linear-quadratic survival and may not indicate a multitarget or other mechanism of cell killing.     

A model of dynamic quenching of fluorescence in globular proteins

A model is presented for the quenching of a fluorophore in a protein interior. At low quencher concentration the quenching process is determined by the acquisition rate of quencher by the protein, the migration rate of quencher in the protein interior, and the exit rate of quencher from the protein. In cases where the fluorescence emission observed in the absence of quencher could be described by a single exponential decay, the presence of quencher led to doubly exponential decay times, and the aforementioned exit rates of the quencher could be determined from experimental data. At high quencher concentration, the processes became more complex, and the deterministic rate equations used at low quencher concentration had to be modified to take into account the Poisson distribution of quencher molecules throughout the protein ensemble and also by using a migration rate for quencher in the protein interior that is a function of the quencher concentration. Simulations performed for typical fluorescent probes in proteins showed good agreement with experiments.