Measures of Uncertainty for Pharmacokinetic and Pharmacodynamic Parameter Estimates: A New Computerized Algorithm

Minimax nonhomogeneous linear estimators of scalar linear parameter functions are studied in the paper under restrictions on the parameters and variance-covariance matrix. The variance-covariance matrix of the linear model under consideration is assumed to be unknown but from a specific set R of nonnegativedefinite matrices. It is shown under this assumption that, without any restriction on the parameters, minimax estimators correspond to the least-squares estimators of the parameter functions for the “worst” variance-covariance matrix. Then the minimax mean-square error of the estimator is derived using the Bayes approach, and finally the exact formulas are derived for the calculation of minimax estimators under elliptical restrictions on the parameter space and for two special classes of possible variance-covariance matrices R. For example, it is shown that a special choice of a constant q 0 and a matrixW 0 defining one of the above classes R leads to the well known Kuks—Olman admissible estimator (see [16]) with a known variance-covariance matrixW 0. Bibliography:32 titles.

Many species exhibit sexual dimorphism in a variety of characters, and the underlying genetic architecture of dimorphism potentially involves sex-specific differences in the additive-genetic variance-covariance matrix (G) of dimorphic traits. We investigated the quantitative-genetic structure of dimorphic traits in the dioecious plant Silene latifolia by estimating G (including within-sex matrices, G(m), G(f), and the between-sex variance-covariance matrix, B), and the phenotypic variance-covariance matrix (P) for seven traits. Flower number was the most sexually dimorphic trait, and was significantly genetically correlated with all traits within each sex. Negative genetic correlations between flower size and number suggested a genetic trade-off in investment, but positive environmental correlations between the same traits resulted in no physical evidence for a trade-off in the phenotype. Between-sex genetic covariances for homologous traits were always greater than 0 but smaller than 1, showing that some, but not all, of the variation in traits is caused by genes or alleles with sex-limited expression. Using common principal-components analysis (CPCA), a maximum-likelihood (ML) estimation approach, and element-by-element comparison to compare matrices, we found that G(m) and G(f) differed significantly in eigenstructure because of dissimilarity in covariances involving leaf traits, suggesting the presence of variation in sex-limited genes with pleiotropic effects and/or linkage between sex-limited loci. The sex-specific structure of G is expected to cause differences in the correlated responses to selection within each sex, promoting the further evolution and maintenance of dimorphism.

Likelihood-based inference in temporal hierarchies

SUMMARY We introduce an algorithm for producing simple approximate principal components directly from a variance–covariance matrix. At the heart of the algorithm is a series of ‘simplicity preserving’ linear transformations. Each transformation seeks a direction within a two-dimensional subspace that has maximum variance. However, the choice of directions is limited so that the direction can be represented by a vector of integers whenever the subspace can also be represented by vector if integers. The resulting approximate components can therefore always be represented by integers. Furthermore the elements of these integer vectors are often small, particularly for the first few components. We demonstrate the performance of this algorithm on two data sets and show that good approximations to the principal components that are also clearly simple and interpretable can result.

Subspace distance is an invaluable tool exploited in a wide range of feature selection methods. The power of subspace distance is that it can identify a representative subspace, including a group of features that can efficiently approximate the space of original features. On the other hand, employing intrinsic statistical information of data can play a significant role in a feature selection process. Nevertheless, most of the existing feature selection methods founded on the subspace distance are limited in properly fulfilling this objective. To pursue this void, we propose a framework that takes a subspace distance into account which is called “Variance–Covariance subspace distance”. The approach gains advantages from the correlation of information included in the features of data, thus determines all the feature subsets whose corresponding Variance–Covariance matrix has the minimum norm property. Consequently, a novel, yet efficient unsupervised feature selection framework is introduced based on the Variance–Covariance distance to handle both the dimensionality reduction and subspace learning tasks. The proposed framework has the ability to exclude those features that have the least variance from the original feature set. Moreover, an efficient update algorithm is provided along with its associated convergence analysis to solve the optimization side of the proposed approach. An extensive number of experiments on nine benchmark datasets are also conducted to assess the performance of our method from which the results demonstrate its superiority over a variety of state-of-the-art unsupervised feature selection methods. The source code is available at https://github.com/SaeedKarami/VCSDFS.

Compositional nutrient diagnosis (CND) provides a plant nutrient imbalance index (CND - r2) with assumed χ2 distribution. The Mahalanobis distance D2, which detects outliers in compositional data sets, has a χ2 distribution. The objective of this paper was to compare D2 and CND – r2 nutrient imbalance indexes in corn (Zea mays L.). We measured grain yield as well as N, P, K, Ca, Mg, Cu, Fe, Mn, and Zn concentrations in the ear leaf at silk stage for 210 calibration sites in the St. Lawrence Lowlands [2300–2700 corn thermal units (CTU)] as well as 30 phosphorus (2300–2700 CTU; 10 sites) and 10 nitrogen (1900–2100 CTU; one site) replicated fertilizer treatments for validation. We derived CND norms as mean, standard deviation, and the inverse covariance matrix of centred log ratios (clr) for high yielding specimens (≥9.0 Mg grain ha–1 at 150 g H2O kg–1 moisture content) in the 2300–2700 CTU zone. Using χ2 = 17 (P < 0.05) with nine degrees of freedom (i.e., nine nutrients) as a rejection criterion for outliers and a yield threshold of 8.6 Mg ha–1 after Cate-Nelson partitioning between low- and high-yielders in the P validation data set, D2 misclassified two specimens compared with nine for CND –r2. The D2 classification was not significantly different from a χ2 classification (P > 0.05), but the CND – r2 classification differed significantly from χ2 or D2 (P < 0.001). A threshold value for nutrient imbalance could thus be derived probabilistically for conducting D2 diagnosis, while the CND – r2 nutrient imbalance threshold must be calibrated using fertilizer trials. In the proposed CND –D2 procedure, D2 is first computed to classify the specimen as possible outlier. Thereafter, nutrient indices are ranked in their order of limitation. The D2 norms appeared less effective in the 1900–2100 CTU zone. Key words: Nutrient balance, simplex closure, variance-covariance matrix, χ2 distribution, grain corn, nitrogen and phosphorus fertilization

Meta-studies are often conducted on empirical findings obtained from overlapping samples. Sample overlap is common in research fields that strongly rely on aggregated observational data (eg, economics and finance), where the same set of data may be used in several studies. More generally, sample overlap tends to occur whenever multiple estimates are sampled from the same study. We show analytically how failing to account for sample overlap causes high rates of false positives, especially for large meta-sample sizes. We propose a generalized-weights (GW) meta-estimator, which solves the sample overlap problem by explicitly modeling the variance-covariance matrix that describes the structure of dependence among estimates. We show how this matrix can be constructed from information that is usually available from basic sample descriptions in the primary studies (ie, sample sizes and number of overlapping observations). The GW meta-estimator amounts to weighting each empirical outcome according to its share of independent sampling information. We use Monte Carlo simulations to (a) demonstrate how the GW meta-estimator brings the rate of false positives to its nominal level, and (b) quantify the efficiency gains of the GW meta-estimator relative to standard meta-estimators. The GW meta-estimator is fairly straightforward to implement and can solve any case of sample overlap, within or between studies. HIGHLIGHTS: Meta-analyses are often conducted on empirical outcomes based on samples containing common observations. Sample overlap induces a correlation structure among empirical outcomes that harms the statistical properties of meta-analysis methods. We derive the analytic conditions under which sample overlap causes conventional meta-estimators to exhibit high rates of false positives. We propose a generalized-weights (GW) solution to sample overlap, which involves approximating the variance-covariance matrix that describes the correlation structure between outcomes; we show how to construct this matrix from information typically reported in the primary studies. We conduct Monte Carlo simulations to quantify the efficiency gains of the proposed GW estimator and show how it brings the rate of false positives near its nominal level. Although we focus on meta-analyses of regression coefficients, our approach can, in principle, be modified and extended to effect sizes more commonly used in other research fields, such as Cohen's d or odds ratios.

Independence of observations is often assumed when adjusting geodetic network. Unlike the distance observations, no dependence of environmental conditions is known for horizontal direction observations. In order to determine the dependence of horizontal direction observations, we established test geodetic network of a station and four observation points. Measurements of the highest possible accuracy were carried out using Leica TS30 total station along with precise prisms GPH1P. Two series of hundred sets of angles were measured, with the first one in bad observation conditions. Using different methods, i.e. variance–covariance matrices, χ2 test and analyses of time series, the independence of measured directions, reduced directions and horizontal angles were tested. The results show that the independence of horizontal direction observations is not obvious and certainly not in poor conditions. In this case, it would be appropriate for geodetic network adjustments to use variance–covariance matrix calculat...

It has recently become possible to calculate and represent variation or spread of dioptric power in a meaningful way. This is important for the proper analysis and interpretation of data on dioptric power in a number of areas of the vision sciences. The representation takes the form of a symmetric matrix of six (usually) variances and covariances. Although the matrix is satisfactory for several formal statistical purposes, such as the testing of hypotheses, it does not give an intuitively satisfactory picture of the extent and nature of the variation, nor is it easy to interpret in a way that could be useful to the researcher or clinician. A useful graphical representation of variation can be constructed from the variance-covariance matrix. It consists of curves that show the meridional dependence of the variation. These meridional profiles of variation give a complete and intuitively satisfactory picture of the nature and extent of the variation of power and are potentially of general use to researcher and clinician. A complete theoretical basis is provided for the construction of meridional profiles of variation of dioptric power. An accompanying paper employs the theory to construct profiles for a number of representative samples of dioptric power.

Traditional theoretical calculations, field measurements, and finite element methods sometimes fail to realize life cycle simulations of the temperature field and temperature effect of steel–concrete composite bridge deck systems. In this paper, a simulation method based on a back propagation–long short-term memory (BP-LSTM) network correlation model is proposed to predict the temperature field and temperature effect in a low-cost and highly efficient manner. A bridge was used as the engineering background according to a health monitoring system, and the finite element method based on the principle of heat transfer was used to expand the data sets. Data sets with structural, time, and environmental characteristics as the independent variables and temperature and the temperature effect as the dependent variables were formed. The correlation between the dependent and independent variables was verified using the maximal information coefficient. Thus, the BP-LSTM model was established, and the mean squared error loss function considering the time weight was designed. The data set was read in for training, verification, and testing, and a correlation model representing the relationship between the set’s independent and dependent variables was obtained with relatively high accuracy. Finally, combined with the bridge’s historical meteorological data, the established correlation model was used to simulate the bridge’s temperature field and temperature effect. The results indicated that the finite element calculation results of the structure’s temperature field based on the heat transfer principle were basically consistent with the measured results. The independent variables in the data set were non-linearly related to the dependent variables. The BP-LSTM’s prediction accuracy of the temperature field and temperature effect was above 98.8% and 94.5%, respectively, in good agreement with the target value. The variation law of the temperature field and temperature effect of the steel–concrete composite bridge deck system simulated by combining the historical meteorological statistics was in accordance with reality.

Line transect survey methodology is a commonly used method for estimating the population abundance. Despite recent advances in this regard, parametric models are still widely used among biometricians, mainly because of their simplicity. In this paper, a new two-parameter detection model satisfying the shoulder conditions is proposed for modeling line transect data. We discuss its properties of interest, including the shapes of the model and the corresponding probability density function, moments, and the related sub-detection model. Maximum likelihood estimation of the parameters is considered. Subsequently, an application is carried out to the proposed model based on a practical data set of perpendicular distances. It is compared with some classical and recent models based on the evaluation of some goodness-of-fit statistics. As results, the variance-covariance matrix, confidence intervals of the parameters and estimated population abundance of the data set are obtained under the proposed detection model.

In recent years, a move away from traditional conceptualizations of recovery from severe mental illness has been observed. This has resulted in a more dimensional approach to recovery, with a broader focus on psychological well-being and functional outcomes, as opposed to a sole emphasis on symptom reduction. Much of this development has been stimulated by the recovery movement, a service user-led approach that supports each individual's potential for recovery and emphasizes the importance of hope, meaningful outcomes, and personal experience ( 1 ). The importance of social outcomes is also highlighted in the position statement on recovery by the American Psychiatric Association ( 2 ), which states that "the concept of recovery emphasizes a person's capacity to have hope and lead a meaningful life" and suggests that treatment should be guided by "attention to life goals and ambitions."

In this paper, we analyze a modified Susceptible‐Exposed‐Infectious‐Dead‐Recovered (SEIDR) model in the literature of the Ebola disease with uncertainties. The model is constructed using a van Kampen expansion method to have an Ebola SEIDR stochastic Fokker–Planck equation model. This model has a deterministic equation and noise covariance matrix. The basic reproduction number of the deterministic equation is calculated using the next‐generation matrix method. We prove the uniqueness and existence of the deterministic model using Lipschitz conditions and also show that it is locally asymptotically stable at it endemic equilibrium states. We constructed two equivalent stochastic differential equations (SDEs) models, whereas the Weiner process is equal to (i) the number of model equations and (ii) the number of independent changes in the model. Our aim is to solve (i) computationally using Cholesky decomposition technique with the variance–covariance matrix. Our proposed Cholesky decomposition SEIRD‐SDEs model is compared with (ii) and also with the epidemic data of the 2018 Ebola outbreak in the Democratic Republic of Congo. We also use numerical analyses to show that the importance of post‐death transmission is difficult to identify with noise terms supported by statistical hypothesis testing.

Determination of state-space model uncertainty using bootstrap techniques

The traditional approach for analyzing high-resolution optical spectra involves locating and measuring line frequencies, then assigning and fitting these to an appropriate model for the molecular energy levels. The alternative approach of fitting the spectrum directly is particularly appealing in the case of congested spectra with many overlapped features. The capabilities and limitations of direct fitting are explored in application to the 0–0 band of the OH A→X transition, as recorded on a charge-coupled-device array using a high-pressure Tesla discharge source. Monte Carlo calculations confirm that for Poisson (counting) data, the parameter errors from the variance–covariance matrix are trustworthy, unless weights are neglected, in which case the error estimates can be wildly optimistic. In the fitting of actual spectra, a major barrier is the derivation of a suitable instrumental line-shape function. In particular, the often adopted triangular slit function is grossly inadequate. A systematic procedure has been devised for obtaining the line shape as a sum of Gaussian and Lorentzian components. This method has facilitated the analysis of experimental spectra spanning the region 3071–3103 Å. A model having 46 adjustable parameters determines the temperature (320 K) of the low-N′ levels of the A state with σ < 1 K and corroborates theoretical intensity branching ratios within 2%. It also determines within 10% the contribution to the emission from OD, which is present in natural abundance (H:D≈7000) in the source.