We propose an alternative resolution of Simpson's paradox in multiple classification experiments, using a different maximum likelihood estimator. In the center of our analysis is a formal representation of free choice and randomization that is based on the notion of incompatible measurements.We first introduce a representation of incompatible measurements as a collection of sets of outcomes. This leads to a natural generalization of Kolmogoroff's axioms of probability. We then discuss the existence and uniqueness of the maximum (...) class='Hi'>likelihood estimator for a probability weight on such a generalized sample space, given absolute frequency data.As a first example, we discuss an estimation problem with censured data that classically admits only biased ad hoc estimators.Next, we derive an explicit solution of the maximum likelihood estimation problem for a large class of experiments that arise from various kids of compositions of sample spaces. We identify the (categorical) direct sum of sample spaces as a representation of “free choice,” and the (categorical) direct product as a representation of “randomization.”Finally, we apply the foregoing discussion to the case of multiple classification experiments in order to show that there is no Simpson's paradox if the difference between free choice and randomization is recognized in the structure of the experiment.A comparison between our new estimator and the “usual” calculation can be summarized as follows: Pooling the data over one classification factor in the “usual” way in fact destroys or ignores the information contained in it, whereas our proposed maximum likelihood estimator is a proper marginal over this factor that “averages out” the information contained in it. The estimators agree with each other in the case of proportional sample sizes. (shrink)

With small to modest sample sizes and complex models, maximum likelihood estimation of confirmatory factor analysis models can show serious estimation problems such as non-convergence or parameter estimates outside the admissible parameter space. In this article, we distinguish different Bayesian estimators that can be used to stabilize the parameter estimates of a CFA: the mode of the joint posterior distribution that is obtained from penalized maximum likelihood estimation, and the mean, median, or mode (...) of the marginal posterior distribution that are calculated by using Markov Chain Monte Carlo methods. In two simulation studies, we evaluated the performance of the Bayesian estimators from a frequentist point of view. The results show that the EAP produced more accurate estimates of the latent correlation in many conditions and outperformed the other Bayesian estimators in terms of root mean squared error. We also argue that it is often advantageous to choose a parameterization in which the main parameters of interest are bounded, and we suggest the four-parameter beta distribution as a prior distribution for loadings and correlations. Using simulated data, we show that selecting weakly informative four-parameter beta priors can further stabilize parameter estimates, even in cases when the priors were mildly misspecified. Finally, we derive recommendations and propose directions for further research. (shrink)

The notion that an independent central bank reduces a country’s inflation is a controversial hypothesis. To date, it has not been possible to satisfactorily answer this question because the complex macroeconomic structure that gives rise to the data has not been adequately incorporated into statistical analyses. We develop a causal model that summarizes the economic process of inflation. Based on this causal model and recent data, we discuss and identify the assumptions under which the effect of central bank independence on (...) inflation can be identified and estimated. Given these and alternative assumptions, we estimate this effect using modern doubly robust effect estimators, i.e., longitudinal targeted maximum likelihood estimators. The estimation procedure incorporates machine learning algorithms and is tailored to address the challenges associated with complex longitudinal macroeconomic data. We do not find strong support for the hypothesis that having an independent central bank for a long period of time necessarily lowers inflation. Simulation studies evaluate the sensitivity of the proposed methods in complex settings when certain assumptions are violated and highlight the importance of working with appropriate learning algorithms for estimation. (shrink)

Gauss’ 1809 discussion of least squares, which can be viewed as the beginning of mathematical statistics, is reviewed. The general consensus seems to be that Gauss’ arguments are at fault, but we show that his reasoning is in fact correct, given his self-imposed restrictions, and persuasive without these restrictions.

Categorical loudness scaling (CLS) measures provide useful information about an individual’s loudness perception across the dynamic range of hearing. A probability model of CLS categories has previously been described as a multi-category psychometric function (MCPF). In the study, a representative “catalog” of potential listener MCPFs was used in conjunction with maximum-likelihood estimation to derive CLS functions for participants with normal hearing and with hearing loss. The approach of estimating MCPFs for each listener has the potential to improve (...) the accuracy of the CLS measurements, particularly when a relatively low number of data points are available. The present study extends the MCPF approach by using Bayesian inference to select stimulus parameters that are predicted to yield maximum expected information (MEI) during data collection. The accuracy and reliability of the MCPF-MEI approach were compared to the standardized CLS measurement procedure (ISO16832:2006). A non-adaptive, fixed-level, paradigm served as a “gold-standard” for this comparison. The test time required to obtain measurements in the standard procedure is a major barrier to its clinical uptake. Test time was reduced from approximately 15 minutes to approximately 3 minutes with the MEI-adaptive procedure. Results indicated that the test-retest reliability and accuracy of the MCPF-MEI adaptive procedures were similar to the standardized CLS procedure. Computer simulations suggest that the reliability and accuracy of the MEI procedure were limited by intrinsic uncertainty of the listeners represented in the MCPF catalog. In other words, the MCPF provided insufficient predictive power to significantly improve adaptive-tracking efficiency under practical conditions. Concurrent optimization of both the MCPF catalog and the MEI-adaptive procedure have the potential to produce better results. Regardless of the adaptive-tracking method used in the CLS procedure, the MCPF catalog remains clinically useful for enabling maximum-likelihood determination of loudness categories. (shrink)

Recent metaphor research has revealed that metaphor comprehension involves both categorization and comparison processes. This finding has triggered the following central question: Which property determines the choice between these two processes for metaphor comprehension? Three competing views have been proposed to answer this question: the conventionality view (Bowdle & Gentner, 2005), aptness view (Glucksberg & Haught, 2006b), and interpretive diversity view (Utsumi, 2007); these views, respectively, argue that vehicle conventionality, metaphor aptness, and interpretive diversity determine the choice between the categorization (...) and comparison processes. This article attempts to answer the question regarding which views are plausible by using cognitive modeling and computer simulation based on a semantic space model. In the simulation experiment, categorization and comparison processes are modeled in a semantic space constructed by latent semantic analysis. These two models receive word vectors for the constituent words of a metaphor and compute a vector for the metaphorical meaning. The resulting vectors can be evaluated according to the degree to which they mimic the human interpretation of the same metaphor; the maximum likelihood estimation determines which of the two models better explains the human interpretation. The result of the model selection is then predicted by three metaphor properties (i.e., vehicle conventionality, aptness, and interpretive diversity) to test the three views. The simulation experiment for Japanese metaphors demonstrates that both interpretive diversity and vehicle conventionality affect the choice between the two processes. On the other hand, it is found that metaphor aptness does not affect this choice. This result can be treated as computational evidence supporting the interpretive diversity and conventionality views. (shrink)

The essential objective of this research is to develop a linear exponential loss function to estimate the parameters and reliability function of the Weibull distribution based on upper record values when both shape and scale parameters are unknown. We perform this by merging a weight into LINEX to produce a new loss function called the weighted linear exponential loss function. Then, we utilized WLINEX to derive the parameters and reliability function of the WD. Next, we compared the performance of the (...) proposed method in this work with Bayesian estimation using the LINEX loss function, Bayesian estimation using the squared-error loss function, and maximum likelihood estimation. The evaluation depended on the difference between the estimated parameters and the parameters of completed data. The results revealed that the proposed method is the best for estimating parameters and has good performance for estimating reliability. (shrink)

The prevalence of nonpaternity in human societies is difficult to establish. To obtain a current and fairly unbiased estimate of the nonpaternity rate in Germany, we analysed a dataset consisting of 971 children and their parents in whom human leukocyte antigen (HLA) typing had been carried out in the context of bone marrow transplantation. In this sample, nine exclusions (0.93%) could be identified on the basis of more than 300 HLA-haplotypes defined by four HLA genes. Given this number of exclusions, (...) a maximum likelihood estimate of the nonpaternity rate in the population of 0.94% was obtained with asymptotic 95% confidence limits of 0.33% and 1.55%, respectively. This result is in accordance with recent surveys as well as findings from Switzerland for a comparable sample, and it suggests that earlier estimates of the nonpaternity rate which were often in excess of 10% may have been largely exaggerated. (shrink)

This paper is concerned with the estimation of the Weibull generalized exponential distribution parameters based on the adaptive Type-II progressive censored sample. Maximum likelihood estimation, maximum product spacing, and Bayesian estimation based on Markov chain Monte Carlo methods have been determined to find the best estimation method. The Monte Carlo simulation is used to compare the three methods of estimation based on the ATIIP-censored sample, and also, we made a bootstrap confidence interval (...) estimation. We will analyze data related to the distribution about single carbon fiber and electrical data as real data cases to show how the schemes work in practice. (shrink)

The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as (...) those based on the maximum likelihood solution, e.g., output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters of underidentified models, as we illustrate on a simple errors-in-variables model. (shrink)

Compared to constraint-based causal discovery, causal discovery based on functional causal models is able to identify the whole causal model under appropriate assumptions [Shimizu et al. 2006; Hoyer et al. 2009; Zhang and Hyvärinen 2009b]. Functional causal models represent the effect as a function of the direct causes together with an independent noise term. Examples include the linear non-Gaussian acyclic model, nonlinear additive noise model, and post-nonlinear model. Currently, there are two ways to estimate the parameters in the models: dependence (...) minimization and maximum likelihood. In this article, we show that for any acyclic functional causal model, minimizing the mutual information between the hypothetical cause and the noise term is equivalent to maximizing the data likelihood with a flexible model for the distribution of the noise term. We then focus on estimation of the PNL causal model and propose to estimate it with the warped Gaussian process with the noise modeled by the mixture of Gaussians. As a Bayesian nonparametric approach, it outperforms the previous one based on mutual information minimization with nonlinear functions represented by multilayer perceptrons; we also show that unlike the ordinary regression, estimation results of the PNL causal model are sensitive to the assumption on the noise distribution. Experimental results on both synthetic and real data support our theoretical claims. (shrink)

A new three-parameter extension of the generalized-exponential distribution, which has various hazard rates that can be increasing, decreasing, bathtub, or inverted tub, known as the Marshall-Olkin generalized-exponential distribution has been considered. So, this article addresses the problem of estimating the unknown parameters and survival characteristics of the three-parameter MOGE lifetime distribution when the sample is obtained from progressive type-II censoring via maximum likelihood and Bayesian approaches. Making use of the s-normality of classical estimators, two types of approximate confidence (...) intervals are constructed via the observed Fisher information matrix. Using gamma conjugate priors, the Bayes estimators against the squared-error and linear-exponential loss functions are derived. As expected, the Bayes estimates are not explicitly expressed, thus the Markov chain Monte Carlo techniques are implemented to approximate the Bayes point estimates and to construct the associated highest posterior density credible intervals. The performance of proposed estimators is evaluated via some numerical comparisons and some specific recommendations are also made. We further discuss the issue of determining the optimum progressive censoring plan among different competing censoring plans using three optimality criteria. Finally, two real-life datasets are analyzed to demonstrate how the proposed methods can be used in real-life scenarios. (shrink)

This paper introduces the new novel four-parameter Weibull distribution named as the Marshall–Olkin alpha power Weibull distribution. Some statistical properties of the distribution are examined. Based on Type-I censored and Type-II censored samples, maximum likelihood estimation, maximum product spacing, and Bayesian estimation for the MOAPW distribution parameters are discussed. Numerical analysis using real data sets and Monte Carlo simulation are accomplished to compare various estimation methods. This novel model’s supremacy upon some famous distributions is (...) explained using two real data sets and it is shown that the MOAPW model can achieve better fits than other competitive distributions. (shrink)

This paper proposes a uniform method for constructing tests, confidence regions and point estimates which is called exact since it reduces to Fisher's so-called exact test in the case of the hypothesis of independence in a 2 × 2 contingency table. All the wellknown standard tests based on exact sampling distributions are instances of the exact test in its general form. The likelihood ratio and x2 tests as well as the maximum likelihood estimate appears as asymptotic approximations (...) to the corresponding exact procedures. (shrink)

BackgroundBayesian estimation with informative priors permits updating previous findings with new data, thus generating cumulative knowledge. To reduce subjectivity in the process, the present study emphasizes how to systematically weigh and specify informative priors and highlights the use of different aggregation methods using an empirical example that examined whether observed mother-adolescent positive and negative interaction behavior mediate the associations between maternal and adolescent internalizing symptoms across early to mid-adolescence in a 3-year longitudinal multi-method design.MethodsThe sample consisted of 102 mother-adolescent (...) dyads. Mothers and adolescents reported on their internalizing symptoms and their interaction behaviors were observed during a conflict task. We systematically searched for previous studies and used an expert-informed weighting system to account for their relevance. Subsequently, we aggregated the priors using three methods: linear pooling, logarithmic pooling, and fitting a normal distribution to the linear pool by means of maximum likelihood estimation. We compared the impact of the three differently specified informative priors and default priors on the prior predictive distribution, shrinkage, and the posterior estimates.ResultsThe prior predictive distributions for the three informative priors were quite similar and centered around the observed data mean. The shrinkage results showed that the logarithmic pooled priors were least affected by the data. Most posterior estimates were similar across the different priors. Some previous studies contained extremely specific information, resulting in bimodal posterior distributions for the analyses with linear pooled prior distributions. The posteriors following the fitted normal priors and default priors were very similar. Overall, we found that maternal, but not adolescent, internalizing symptoms predicted subsequent mother-adolescent interaction behavior, whereas negative interaction behavior seemed to predict subsequent internalizing symptoms. Evidence regarding mediation effects remained limited.ConclusionA systematic search for previous information and an expert-built weighting system contribute to a clear specification of power priors. How information from multiple previous studies should be included in the prior depends on theoretical considerations, and may also be affected by pragmatic considerations regarding the impact of the previous results at hand. (shrink)

A new continuous version of the inverse flexible Weibull model is proposed and studied. Some of its properties such as quantile function, moments and generating functions, incomplete moments, mean deviation, Lorenz and Bonferroni curves, the mean residual life function, the mean inactivity time, and the strong mean inactivity time are derived. The failure rate of the new model can be “increasing-constant,” “bathtub-constant,” “bathtub,” “constant,” “J-HRF,” “upside down bathtub,” “increasing,” “upside down-increasing-constant,” and “upside down.” Different copulas are used for deriving many (...) bivariate and multivariate type extensions. Different non-Bayesian well-known estimation methods under uncensored scheme are considered and discussed such as the maximum likelihood estimation, Anderson Darling estimation, ordinary least square estimation, Cramér-von-Mises estimation, weighted least square estimation, and right tail Anderson Darling estimation methods. Simulation studies are performed for comparing these estimation methods. Finally, two real datasets are analyzed to illustrate the importance of the new model. (shrink)

This paper deals with various connections that are found to exist between statistical estimation methods for decision-making and rules of group choice in the social choice area. Initially the aggregation of individual opinions is formulated as a pattern recognition problem; firstly it is shown that individual preferences lead to a natural representation in terms of binary patterns. Then we proceed to show how the search for a group preference pattern can be conducted by classifying the input preference patterns into (...) various ‘pattern classes’ and using the resulting classification boundaries to define the area of mutual agreement over some of the available alternatives. This leads to a decision-theoretic problem which consists in defining a decision rule (for classification) that is least likely to lead to misrecognition of arbitrary preference patterns. A maximum likelihood solution is obtained and compared with some well-known rules of group decision-making. Other solutions are also possible, on the basis of different optimality criteria, and their social choice interpretation is suggested. Finally, a method using Coleman's linear model for attributes is applied to yield group decision rules by feature weighting of election issues. (shrink)

Maximum-likelihood updating is a well-known approach for extending static ambiguity sensitive preferences to dynamic set-ups. This paper develops an example in which MLU induces an ambiguity averse maxmin expected utility decision-maker to prefer a bet on an ambiguous over a risky urn and be more willing to bet on the ambiguous urn compared to an subjective expected utility decision-maker. This is challenging, since prior to observing draws from the urns, the MEU decision-maker actually preferred the risky over the (...) ambiguous bet and was less willing to bet on the ambiguous urn than the SEU decision-maker. The identified switch in betting preferences is not due to a violation of dynamic consistency or consequentialism. Rather, it results from MLU’s selection of extreme priors, causing a violation of the stability of set inclusion over the course of the updating process. (shrink)

In the existing Reinforcement Learning, it is difficult and time consuming to find appropriate the meta-parameters such as learning rate, eligibility traces and temperature for exploration, in particular on a complicated and large-scale problem, the delayed reward often occurs and causes a difficulty in solving the problem. In this paper, we propose a novel method introducing a temperature distribution for reinforcement learning. In addition to the acquirement of policy based on profit sharing, the temperature is given to each state and (...) is trained by hill-climbing method using likelihood function based on success and failure of the task. The proposed method can reduce the parameter setting according to the given problems. We showed the performance on the grid world problem and the control of Acrobot. (shrink)

State generalization problem is a significant issue for the realization of the autonomous agents which are expected to decide and learn the proper behavior with various kinds of sensor information. This paper proposes a new state generalization method based on maximum likelihood estimation of the agent’s behavior outcomes. This provides a general framework for unifying the various conventional heuristic generalization criteria which have been used in the previous works, and a way of adapting the state space gradually (...) to the environment. (shrink)

The COVID-19 pandemic shocked the global economy, with numerous companies suffering losses and shutting down. However, some companies proved to be resilient, being able to sustain their economic performance despite the pandemic. The study aims to explain the sustainable economic performance of companies during the COVID-19 pandemic. The relationships between empowering leadership, innovative work behavior, organizational readiness to change, and sustainable economic performance were assessed. The data were collected via an online questionnaire from January 2021 to March 2021, during the (...) height of the COVID-19 pandemic in Russia. The respondents were Russian companies’ employees holding management positions, competent to objectively assess organizational circumstances during the COVID-19 pandemic. A sample of 337 was used in the analysis. Confirmatory factor analysis (CFA) with maximum likelihood estimation was conducted using SPSS AMOS. The structural model was tested with standardized parameter estimates, standard errors, and p-values calculated. The findings of the study suggest that innovative work behavior and organizational readiness to learn have a direct influence on sustainable economic performance. The findings also suggest that empowering leadership impacts innovative work behavior but not sustainable economic performance. The mediation analysis indicates that innovative work behavior is a mediator between empowering leadership and sustainable economic performance, whereas organizational readiness to learn is not a moderator. The study adds to the leadership and sustainability body of knowledge and contributes to the research on the COVID-19 pandemic in the organizational context. (shrink)

Michael Weisberg’s account of scientific models concentrates on the ways in which models are similar to their targets. He intends not merely to explain what similarity consists in, but also to capture similarity judgments made by scientists. In order to scrutinize whether his account fulfills this goal, I outline one common way in which scientists judge whether a model is similar enough to its target, namely maximum likelihood estimation method. Then I consider whether Weisberg’s account could capture (...) the judgments involved in this practice. I argue that his account fails for three reasons. First, his account is simply too abstract to capture what is going on in MLE. Second, it implies an atomistic conception of similarity, while MLE operates in a holistic manner. Third, Weisberg’s atomistic conception of similarity can be traced back to a problematic set-theoretic approach to the structure of models. Finally, I tentatively suggest how these problems might be solved by a holistic approach in which models and targets are compared in a non-set-theoretic fashion. (shrink)

This paper reports the validation of a 6-item short form of the original 35-item Servant Leadership Behavior Scale, a widely used measure of servant leadership behavior. The holistic perspective of servant leadership and the inclusion of spirituality are two distinctive features of the SLBS relative to other servant leadership measures. Psychometric properties of the SLBS-6 were examined on the basis of seven studies. In the preliminary scale development, the factor structure of the new measure was tested using a combination of (...) all samples. The subsequent seven studies were aimed at building further its construct validity relative to observed variables within the servant leadership nomological network in direct, mediating, and moderating relationships. Analyses of all datasets using MPlus with maximum-likelihood estimation provided support for the 6-item structure and demonstrated its internal consistency reliability, criterion-related validity, and construct validity. As such, the study presents the SLBS-6 as the shortest holistic measure of servant leadership to date that can be used with confidence for research and training purposes. (shrink)

The purpose of this study was to test a causal model of ethical conflict in practice and autonomy in a sample of 254 nurse practitioners working in the primary care areas of family health, pediatrics, adult health and obstetrics/gynecology in the state of Maryland. A test of the model was conducted using a path analytic approach with LISREL 8.30 hypothesizing individual, organizational and societal/market factors influencing ethical conflict in practice and autonomy. Maximum likelihood estimation was used to (...) estimate the parameters most likely to have generated the data. Forty-five percent of the total variance in ethical conflict was explained by the variables of ethical environment and ethical concern. Ethical concern, idealistic philosophy, ethics education in continuing education, percentage of client population enrolled in managed care, and market penetration explained 15% of the total variance in autonomy. The findings of this study indicate that the causal model of ethical conflict in practice and autonomy is consistent with the data and contributed to a fuller understanding of clinical decision making associated with practicing in a managed care environment. The final model supported a conceptual framework that is inclusive of three domains: individual, organizational and societal/market variables. (shrink)

The relationship between the neurobiology of speech and music has been investigated for more than a century. There remains no widespread agreement regarding how (or to what extent) music perception utilizes the neural circuitry that is engaged in speech processing, particularly at the cortical level. Prominent models such as Patel’s Shared Syntactic Integration Resource Hypothesis (SSIRH) and Koelsch’s neurocognitive model of music perception suggest a high degree of overlap, particularly in the frontal lobe, but also perhaps more distinct representations in (...) the temporal lobe with hemispheric asymmetries. The present meta-analysis study used activation likelihood estimate analyses to identify the brain regions consistently activated for music as compared to speech across the functional neuroimaging (fMRI and PET) literature. Eighty music and 91 speech neuroimaging studies of healthy adult control subjects were analyzed. Peak activations reported in the music and speech studies were divided into four paradigm categories: passive listening, discrimination tasks, error/anomaly detection tasks and memory-related tasks. We then compared activation likelihood estimates within each category for music versus speech, and each music condition with passive listening. We found that listening to music and to speech preferentially activate distinct temporo-parietal bilateral cortical networks. We also found music and speech to have shared resources in the left pars opercularis but speech-specific resources in the left pars triangularis. The extent to which music recruited speech-activated frontal resources was modulated by task. While there are certainly limitations to meta-analysis techniques particularly regarding sensitivity, this work suggests that the extent of shared resources between speech and music may be task-dependent and highlights the need to consider how task effects may be affecting conclusions regarding the neurobiology of speech and music. (shrink)

Probability distributions play an essential role in modeling and predicting biomedical datasets. To have the best description and accurate prediction of the biomedical datasets, numerous probability distributions have been introduced and implemented. We investigate a novel family of lifetime probability distributions to represent biological datasets in this paper. The proposed family is called a new flexible logarithmic- X family. The suggested NFLog- X family is obtained by applying the T- X method together with the exponential model having the PDF m (...) t = e − t. Based on the NFLog- X approach, a three parameters probability distribution, namely, a new flexible logarithmic-Weibull distribution is introduced. The method of maximum likelihood estimation is adopted for estimating the parameters of the NFLog- X family. In the end, we examine three different biological datasets in order to give a thorough numerical research that illustrates the NFLog-Wei distribution. Comparisons are made between the analytical goodness-of-fit metrics of the suggested distribution. We made comparison with the alpha power transformed Weibull, exponentiated Weibull, Weibull, flexible reduced logarithmic-Weibull, and Marshall–Olkin Weibull distributions. After performing the analyses, we observe that the proposed method outclassed other competitive distributions. (shrink)

Meditation comprises a series of practices mainly developed in eastern cultures aiming at controlling emotions and enhancing attentional processes. Several authors proposed to divide meditation techniques in focused attention and open monitoring techniques. Previous studies have reported differences in brain networks underlying FA and OM. On the other hand common activations across different meditative practices have been reported. Despite differences between forms of meditation and their underlying cognitive processes, we propose that all meditative techniques could share a central process that (...) would be supported by a core network for meditation since their general common goal is to induce relaxation, regulating attention and developing an attitude of detachment from one’s own thoughts. To test this hypothesis, we conducted a quantitative meta-analysis based on activation likelihood estimation of 10 neuroimaging studies on different meditative techniques to evidence the core cortical network subserving meditation. We showed activation of basal ganglia , limbic system and medial prefrontal cortex . We discuss the functional role of these structures in meditation and we tentatively propose a neurocognitive model of meditation that could guide future research. (shrink)

Case-cohort design is a biased sampling method. Due to its cost-effective and theoretical significance, this design has extensive application value in many large cohort studies. The case-cohort data includes a subcohort sampled randomly from the entire cohort and all the failed subjects outside the subcohort. In this paper, the adjustment for the distorted covariates is considered to case-cohort data in Cox’s model. According to the existing adjustable methods of distorted covariates for linear and nonlinear models, we propose estimating the distorting (...) functions by nonparametrically regressing the distorted covariates on the distorting factors; then, the estimators for the parameters are obtained using the estimated covariates. The proof of consistency and being asymptotically normal is completed. For calculating the maximum likelihood estimates of the regression coefficients subject in Cox’s model, a minorization-maximization algorithm is developed. Simulation studies are performed to compare the estimations with the covariates undistorted, distorted, and adjusted to illustrate the proposed methods. (shrink)

The stratum-specific treatment effect function is a random variable giving the average treatment effect (ATE) for a randomly drawn stratum of potential confounders a clinician may use to assign treatment. In addition to the ATE, the variance of the stratum-specific treatment effect function is fundamental in determining the heterogeneity of treatment effect values. We offer a non-parametric plug-in estimator, the targeted maximum likelihood estimator (TMLE) and the cross-validated TMLE (CV-TMLE), to simultaneously estimate both the average and variance of (...) the stratum-specific treatment effect function. The CV-TMLE is preferable because it guarantees asymptotic efficiency under two conditions without needing entropy conditions on the initial fits of the outcome model and treatment mechanism, as required by TMLE. Particularly, in circumstances where data adaptive fitting methods are very important to eliminate bias but hold no guarantee of satisfying the entropy condition, we show that the CV-TMLE sampling distributions maintain normality with a lower mean squared error than TMLE. In addition to verifying the theoretical properties of TMLE and CV-TMLE through simulations, we highlight some of the challenges in estimating the variance of the treatment effect, which lack double robustness and might be biased if the true variance is small and sample size insufficient. (shrink)

In ecology, if the considered area or space is large, the spatial distribution of individuals of a given plant species is never homogeneous; plants form different patches. The homogeneity change in space or in time (in particular, the related change-point problem) is an important research subject in mathematical statistics. In the paper, for a given data system along a straight line, two areas are considered, where the data of each area come from different discrete distributions, with unknown parameters. In the (...) paper a method is presented for the estimation of the distribution change-point between both areas and an estimate is given for the distributions separated by the obtained change-point. The solution of this problem will be based on the maximum likelihood method. Furthermore, based on an adaptation of the well-known bootstrap resampling, a method for the estimation of the so-called change-interval is also given. The latter approach is very general, since it not only applies in the case of the maximum-likelihood estimation of the change-point, but it can be also used starting from any other change-point estimation known in the ecological literature. The proposed model is validated against typical ecological situations, providing at the same time a verification of the applied algorithms. (shrink)

Using mostly prospective menstrual data from mothers and daughters in the Tremin Trust Menstrual Reproductive History Program, this study produces the first estimates of the genetic correlation between the ages of menarche and menopause. I carried out two separate analyses. Standard regression analysis of 21 mother/daughter dyads with natural menopause yielded a nonsignificant negative mean genetic correlation of r A =−0.139±1.268. Survival analysis/maximum likelihood estimation on a dataset which included an additional 85 dyads with censored observations on (...) daughters yielded a nonsignificant positive genetic correlation of r A =0.613±0.587. Although a substantial non-zero correlation cannot be ruled out, these estimates suggest there is no genetic correlation between menarche and menopause, in agreement with previous phenotypic findings. As inconclusive as they may be, these estimates also contribute to our understanding of the nature of selection working on the reproductive life span of human females. (shrink)

A SEM-based approach using likelihood-based confidence interval has been proposed to form confidence intervals for unstandardized and standardized indirect effect in mediation models. However, when used with the maximum likelihood estimation, this approach requires that the variables are multivariate normally distributed. This can affect the LBCIs of unstandardized and standardized effect differently. In the present study, the robustness of this approach when the predictor is not normally distributed but the error terms are conditionally normal, which does (...) not violate the distributional assumption of ordinary least squares estimation, is compared to four other approaches: nonparametric bootstrapping, two variants of LBCI, LBCI assuming the predictor is fixed and LBCI based on ADF estimation, and Monte Carlo. A simulation study was conducted using a simple mediation model and a serial mediation model, manipulating the distribution of the predictor. The Monte Carlo method performed worst among the methods. LBCI and LBCI-Fixed-X had suboptimal performance when the distributions had high kurtosis and the population indirect effects were medium to large. In some conditions, the problem was severe even when the sample size was large. LBCI-ADF and nonparametric bootstrapping had coverage probabilities close to the nominal value in nearly all conditions, although the coverage probabilities were still suboptimal for the serial mediation model when the sample size was small with respect to the model. Implications of these findings in the context of this special case of nonnormal data were discussed. (shrink)

We briefly review Condorcet's and Young's epistemic interpretations of preference aggregation rules as maximum likelihood estimators. We then develop a general framework for interpreting epistemic social choice rules as maximum likelihood estimators, maximum a posteriori estimators, or expected utility maximizers. We illustrate this framework with several examples. Finally, we critique this program.Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal (...) Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.A STATISTICAL APPROACH TO EPISTEMIC DEMOCRACYVolume 9, Issue 2Marcus PivatoDOI: https://doi.org/10.1017/epi.2012.4Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. A STATISTICAL APPROACH TO EPISTEMIC DEMOCRACYVolume 9, Issue 2Marcus PivatoDOI: https://doi.org/10.1017/epi.2012.4Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. A STATISTICAL APPROACH TO EPISTEMIC DEMOCRACYVolume 9, Issue 2Marcus PivatoDOI: https://doi.org/10.1017/epi.2012.4Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation Request permission. (shrink)

The aim of this study is to evaluate the psychometric properties of the Polish version of the Dispositional Flow Scale-2 and Flow State Scale-2, for use with Polish adults and young adults. Currently, there are no tools that would allow us to study flow among Polish speakers. At the same time, due to the great interest in flow and its potential importance for effectiveness, cooperation, and learning, it is worth ensuring that reliable validated measurement questionnaires are available for people studying (...) the Polish population. Study participants completed 856 questionnaires, of which 496 individuals participated in the DFS-2 study and 360 individuals participated in the FSS-2 study. The maximum likelihood estimator was selected for the CFA analysis. Model fit was assessed using: χ2, comparative fit index, Tucker-Lewis index, and standardized root mean square of residuals, and root mean square of approximation error. For both questionnaires, formative first-level models with nine factors and second-level models with nine factors loaded on a higher-order flow factor were compared using the Satorra-Bentler Scaled difference χ2 test. The ω coefficient was used to estimate the reliability of the FFS-2 and DFS-2 models tested in the CFA method. Confirmatory factor analysis of both DFS-2 structural models showed satisfactory model fit. Most of the fit indices for the hierarchical 2nd order FSS-2 model presented satisfactory values, except for SRMR. Both DFS-2 and FSS-2 factors tested in the analysis showed good reliability. Our findings confirmed the reliability and validity of the Polish versions of DFS-2 and FSS-2 scales. The scales are reliable when applied to Polish adults and young adults. (shrink)

In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. (...) In addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study. (shrink)

BackgroundBoth reducing sitting and increasing physical exercise promote health but exercising more does not necessarily reduce sitting time. One reason for this non-dependency may be that different aspects of exercise motivation are differently related to sitting time. Identifying the type of exercise motivation that would also be associated with sitting time can help to reduce sitting indirectly through increased exercise, thus bringing greater benefits.MethodsThe present study explored the association between quality of motivations toward physical activity with physical activity and sitting (...) time in a total of 373 adults. The short version of international physical activity questionnaire was used for measuring physical activity and sitting time. Reasons for exercising regularly were measured with the Self-Regulated Questionnaire–Exercise, including four regulation subscales to assess regulation styles. Confirmatory factor analysis was used to test the four subscales of SRQ-E with the data obtained using AMOS v.23. Then, structural equation model with maximum likelihood estimates was used to test the hypothesized model.ResultsThe results indicated that only intrinsic motivation, but not identified, introjected or external motivation, toward physical activity predicted both physical activity and sitting time. Higher intrinsic motivation toward physical activity was associated with both higher physical activity and lower sitting time. In addition, physical activity was a mediator for lower sitting time when the source was intrinsic motivation.ConclusionPrevious studies have shown low between and within participant correlation between sitting time and physical activity, and interventions have generally failed to both increase physical activity while decreasing sitting time. The present cross-sectional results suggest that targeting increased physical activity by increased intrinsic motivation has the potential to both increase physical activity and decrease sitting time. (shrink)

This paper shows how to define probability distributions over linguistically realistic syntactic structures in a way that permits us to define language learning and language comprehension as statistical problems. We demonstrate our approach using lexical‐functional grammar (LFG), but our approach generalizes to virtually any linguistic theory. Our probabilistic models are maximum entropy models. In this paper we concentrate on statistical inference procedures for learning the parameters that define these probability distributions. We point out some of the practical problems that (...) make straightforward ways of estimating these distributions infeasible, and develop a “pseudo‐likelihood” estimation procedure that overcomes some of these problems. This method raises interesting questions concerning the nature of the data available to a language learner and the modularity of language learning and processing. (shrink)

Matrix models are widely used in biology to predict the temporal evolution of stage-structured populations. One issue related to matrix models that is often disregarded is the sampling variability. As the sample used to estimate the vital rates of the models are of finite size, a sampling error is attached to parameter estimation, which has in turn repercussions on all the predictions of the model. In this study, we address the question of building confidence bounds around the predictions of (...) matrix models due to sampling variability. We focus on a density-dependent Usher model, the maximum likelihood estimator of parameters, and the predicted stationary stage vector. The asymptotic distribution of the stationary stage vector is specified, assuming that the parameters of the model remain in a set of the parameter space where the model admits one unique equilibrium point. Tests for density-dependence are also incidentally provided. The model is applied to a tropical rain forest in French Guiana. (shrink)

The uses of statistical distributions for modeling real phenomena of nature have received considerable attention in the literature. The recent studies have pointed out the potential of statistical distributions in modeling data in applied sciences, particularly in financial sciences. Among them, the two-parameter Lomax distribution is one of the prominent models that can be used quite effectively for modeling data in management sciences, banking, finance, and actuarial sciences, among others. In the present article, we introduce a new three-parameter extension of (...) the Lomax distribution via using a class of claim distributions. The new model may be called the Lomax-Claim distribution. The parameters of the Lomax-Claim model are estimated using the maximum likelihood estimation method. The behaviors of the maximum likelihood estimators are examined by conducting a brief Monte Carlo study. The potentiality and applicability of the Lomax claim model are illustrated by analyzing a dataset taken from financial sciences representing the vehicle insurance loss data. For this dataset, the proposed model is compared with the Lomax, power Lomax, transmuted Lomax, and exponentiated Lomax distributions. To show the best fit of the competing distributions, we consider certain analytical tools such as the Anderson–Darling test statistic, Cramer–Von Mises test statistic, and Kolmogorov–Smirnov test statistic. Based on these analytical measures, we observed that the new model outperforms the competitive models. Furthermore, a bivariate extension of the proposed model called the Farlie–Gumble–Morgenstern bivariate Lomax-Claim distribution is also introduced, and different shapes for the density function are plotted. An application of the bivariate model to GDP and export of goods and services is provided. (shrink)