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The concept of self-predictability plays a key role for the analysis of the self-driven dynamics of physiological processes displaying richness of oscillatory rhythms. While time domain measures of self-predictability, as well as time-varying and local extensions, have already been proposed and largely applied in different contexts, they still lack a clear spectral description, which would be significantly useful for the interpretation of the frequency-specific content of the investigated processes. Herein, we propose a novel approach to characterize the linear self-predictability (LSP) of Gaussian processes in the frequency domain. The LSP spectral functions are related to the peaks of the power spectral density (PSD) of the investigated process, which is represented as the sum of different oscillatory components with specific frequency through the method of spectral decomposition. Remarkably, each of the LSP profiles is linked to a specific oscillation of the process, and it returns frequency-specific measures when integrated along spectral bands of physiological interest, as well as a time domain self-predictability measure with a clear meaning in the field of information theory, corresponding to the well-known information storage, when integrated along the whole frequency axis. The proposed measure is first illustrated in a theoretical simulation, showing that it clearly reflects the degree and frequency-specific location of predictability patterns of the analyzed process in both time and frequency domains. Then, it is applied to beat-to-beat time series of arterial compliance obtained in young healthy subjects. The results evidence that the spectral decomposition strategy applied to both the PSD and the spectral LSP of compliance identifies physiological responses to postural stress of low and high frequency oscillations of the process which cannot be traced in the time domain only, highlighting the importance of computing frequency-specific measures of self-predictability in any oscillatory physiologic process.

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Background: Density-dependent regulation is ubiquitous in population dynamics, and its potential interaction with environmental stochasticity complicates the characterization of the random component of population dynamics. Yet, this issue has not received attention commensurate with its relevance for descriptive and predictive modeling of population dynamics. Here we use a Bayesian modeling approach to investigate the contribution of density regulation to population variability in stochastic environments. Methods: We analytically derive a formula linking the stationary variance of population abundance/density under Gompertz regulation in a stochastic environment with constant variance to the environmental variance and the strength of density feedback, to investigate whether and how density regulation affects the stationary variance. We examine through simulations whether the relationship between stationary variance and density regulation inferred analytically under the Gompertz model carries over to the Ricker model, widely used in population dynamics modeling. Results: The analytical decomposition of the stationary variance under stochastic Gompertz dynamics implies higher variability for strongly regulated populations. Simulation results demonstrate that the pattern of increasing population variability with increasing density feedback found under the Gompertz model holds for the Ricker model as well, and is expected to be a general phenomenon with stochastic population models. We also analytically established and empirically validated that the square of the autoregressive parameter of the Gompertz model in AR(1) form represents the proportion of stationary variance due to density dependence. Discussion: Our results suggest that neither environmental stochasticity nor density regulation can alone explain the patterns of population variability in stochastic environments, as these two components of temporal variation interact, with a tendency for density regulation to amplify the magnitude of environmentally induced population fluctuations. This finding has far-reaching implications for population viability. It implies that intense intra-specific resource competition increases the risk of environment-driven population collapse at high density, making opportune harvesting a sensible practice for improving the resistance of managed populations such as fish stocks to environmental perturbations. The separation of density-dependent and density-independent processes will help improve population dynamics modeling, while providing a basis for evaluating the relative importance of these two categories of processes that remains a topic of long-standing controversy among ecologists.

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We present in this paper a global methodology for the spike detection in a biological context of fluorescence recording of GnRH-neurons calcium activity. For this purpose we first propose a simple stochastic model that could mimic experimental time series by considering an autoregressive AR(1) process with a linear trend and specific innovations involving spiking times. Estimators of parameters with asymptotic normality are established and used to set up a statistical test on estimated innovations in order to detect spikes. We compare several procedures and illustrate on biological data the performance of our procedure.

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The inference of causal relations between observable phenomena is paramount across scientific disciplines; however, the means for such enterprise without experimental manipulation are limited. A commonly applied principle is that of the cause preceding and predicting the effect, taking into account other circumstances. Intuitively, when the temporal order of events is reverted, one would expect the cause and effect to apparently switch roles. This was previously demonstrated in bivariate linear systems and used in design of improved causal inference scores, while such behaviour in linear systems has been put in contrast with nonlinear chaotic systems where the inferred causal direction appears unchanged under time reversal. The presented work explores the conditions under which the causal reversal happens-either perfectly, approximately, or not at all-using theoretical analysis, low-dimensional examples, and network simulations, focusing on the simplified yet illustrative linear vector autoregressive process of order one. We start with a theoretical analysis that demonstrates that a perfect coupling reversal under time reversal occurs only under very specific conditions, followed up by constructing low-dimensional examples where indeed the dominant causal direction is even conserved rather than reversed. Finally, simulations of random as well as realistically motivated network coupling patterns from brain and climate show that level of coupling reversal and conservation can be well predicted by asymmetry and anormality indices introduced based on the theoretical analysis of the problem. The consequences for causal inference are discussed.

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Cognitive functioning is a key indicator of overall individual health. Identifying factors related to cognitive status, especially in later life, is of major importance. We concentrate on the analysis of the temporal evolution of cognitive abilities in the elderly population. We propose to model the individual cognitive functioning as a multidimensional latent process that accounts also for the effects of individual-specific characteristics (gender, age, and years of education). The proposed model is specified within the generalized linear latent variable framework, and its efficient estimation is obtained using a recent approximation technique, called dimensionwise quadrature. It provides a fast and streamlined approximate inference for complex models, with better or no degradation in accuracy compared with standard techniques. The methodology is applied to the cognitive assessment data from the Health and Retirement Study combined with the Asset and Health Dynamic study in the years between 2006 and 2010. We evaluate the temporal relationship between two dimensions of cognitive functioning, that is, episodic memory and general mental status. We find a substantial influence of the former on the evolution of the latter, as well as evidence of severe consequences on both cognitive abilities among less-educated and older individuals.

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Cardiac autonomic control is commonly assessed via the analysis of fluctuations of the temporal distance between two consecutive R-waves (RR). Cardiac regulation assessment following high intensity physical exercise is difficult due to RR non-stationarities. The very short epoch following maximal sprint exercise when RR remains close to its lowest value, i.e., the PLATEAU, provides the opportunity to evaluate cardiac regulation from stationary RR sequences. The aim of the study is to evaluate cardiac autonomic control during PLATEAU phase following 60-m maximal sprint and compare the results to those derived from sequences featuring the same length as the PLATEAU and derived from pre-exercise and post-exercise periods. These sequences were referred to as PRE and POST sequences. RR series were recorded in 21 subjects (age: 24.9 ± 5.1 years, 15 men and six women). We applied a symbolic approach due to its ability to deal with very short RR sequences. The symbolic approach classified patterns formed by three RRs according to the sign and number of RR variations. Symbolic markers were compared to more classical time and frequency domain indexes. Comparison was extended to simulated signals to explicitly evaluate the suitability of methods to deal with short variability series. A surrogate test was applied to check the null hypothesis of random fluctuations. Over simulated data symbolic analysis was able to separate dynamics with different spectral profiles provided that the frame length was longer than 10 cardiac beats. Over real data the surrogate test indicated the presence of determinism in PRE, PLATEAU, and POST sequences. We found that the rate of patterns with two variations with unlike sign increased during PLATEAU and in POST sequences and the frequency of patterns with no variations remained unchanged during PLATEAU and decreased in POST compared to PRE sequences. Results indicated a sustained sympathetic control along with an early vagal reactivation during PLATEAU and a shift of the sympathovagal balance toward vagal predominance in POST compared to PRE sequences. Time and frequency domains markers were less powerful because they were dominated by the dramatic decrease of RR variance during PLATEAU.

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In this paper we develop a general framework for how the genetic composition of a structured population with strong migration between its subunits, evolves over time. The dynamics is described in terms of a vector-valued Markov process of allele, genotype or haplotype frequencies that varies on two time scales. The more rapid changes are random fluctuations in terms of a multivariate autoregressive process, around a quasi equilibrium fix point, whereas the fix point itself varies more slowly according to a diffusion process, along a lower-dimensional subspace. Under mild regularity conditions, the fluctuations have a magnitude inversely proportional to the square root of the population size N, and hence can be used to estimate a broad class of genetically effective population sizes Ne, with genetic data from one time point only. In this way we are able to unify a number of existing notions of effective size, as well as proposing new ones, for instance one that quantifies the extent to which genotype frequencies fluctuate around Hardy-Weinberg equilibrium.

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Time-course omics experiments enable the reconstruction of the dynamics of the cellular regulatory network. Here, we describe the means for this reconstruction and the downstream exploitation of the inferred network. It is assumed that one of the various vector-autoregressive models (VAR) models presented here serves as a reasonably accurate description of the time-course omics data. The models are estimated through ridge penalized likelihood maximization, accompanied by functionality for the determination of optimal penalty paramaters. Prior knowledge on the network topology is accommodated by the estimation procedures. Various routes that translate the fitted models into more tangible implications for the medical researcher are described. The network is inferred from the-nonsparse-ridge estimates through empirical Bayes probabilistic thresholding. The influence of a (trait of a) molecular entity at the current time on those at future time points is assessed by mutual information, impulse response analysis, and path decomposition of the covariance. The presented methodology is applied to the omics data from the p53 signaling pathway during HPV-induced cellular transformation. All methodology is implemented in the ragt2ridges package, freely available from the Comprehensive R Archive Network.

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We consider modelling and inference as well as sample size estimation and reestimation for clinical trials with longitudinal count data as outcomes. Our approach is general but is rooted in design and analysis of multiple sclerosis trials where lesion counts obtained by magnetic resonance imaging are important endpoints. We adopt a binomial thinning model that allows for correlated counts with marginal Poisson or negative binomial distributions. Methods for sample size planning and blinded sample size reestimation for randomised controlled clinical trials with such outcomes are developed. The models and approaches are applicable to data with incomplete observations. A simulation study is conducted to assess the effectiveness of sample size estimation and blinded sample size reestimation methods. Sample sizes attained through these procedures are shown to maintain the desired study power without inflating the type I error. Data from a recent trial in patients with secondary progressive multiple sclerosis illustrate the modelling approach.

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Directed connectivity inference has become a cornerstone in neuroscience to analyze multivariate data from neuroimaging and electrophysiological techniques. Here we propose a nonparametric significance method to test the nonzero values of multivariate autoregressive model to infer interactions in recurrent networks. We use random permutations or circular shifts of the original time series to generate the null-hypothesis distributions. The underlying network model is the same as used in multivariate Granger causality, but our test relies on the autoregressive coefficients instead of error residuals. By means of numerical simulation over multiple network configurations, we show that this method achieves a good control of false positives (type 1 error) and detects existing pairwise connections more accurately than using the standard parametric test for the ratio of error residuals. In practice, our method aims to detect temporal interactions in real neuronal networks with nodes possibly exhibiting redundant activity. As a proof of concept, we apply our method to multiunit activity (MUA) recorded from Utah electrode arrays in a monkey and examine detected interactions between 25 channels. We show that during stimulus presentation our method detects a large number of interactions that cannot be solely explained by the increase in the MUA level.

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Many researchers in biology and medicine have focused on trying to understand biological rhythms and their potential impact on disease. A common biological rhythm is circadian, where the cycle repeats itself every 24 hours. However, a disturbance of the circadian pattern may be indicative of future disease. In this article, we develop new statistical methodology for assessing the degree of disturbance or irregularity in a circadian pattern for count sequences that are observed over time in a population of individuals. We develop a latent variable Poisson modeling approach with both circadian and stochastic short-term trend (autoregressive latent process) components that allow for individual variation in the degree of each component. A parameterization is proposed for modeling covariate dependence on the proportion of these two model components across individuals. In addition, we incorporate covariate dependence in the overall mean, the magnitude of the trend, and the phase-shift of the circadian pattern. Innovative Markov chain Monte Carlo sampling is used to carry out Bayesian posterior computation. Several variations of the proposed models are considered and compared using the deviance information criterion. We illustrate this methodology with longitudinal physical activity count data measured in a longitudinal cohort of adolescents.

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Vector autoregressive (VAR) models constitute a powerful and well studied tool to analyze multivariate time series. Since sparseness, crucial to identify and visualize joint dependencies and relevant causalities, is not expected to happen in the standard VAR model, several sparse variants have been introduced in the literature. However, in some cases it might be of interest to control some dimensions of the sparsity, as e.g. the number of causal features allowed in the prediction. To authors extent none of the existent methods endows the user with full control over the different aspects of the sparsity of the solution. In this article, we propose a versatile sparsity-controlled VAR model which enables a proper visualization of potential causalities while allows the user to control different dimensions of the sparsity if she holds some preferences regarding the sparsity of the outcome. The model coefficients are found as the solution to an optimization problem, solvable by standard numerical optimization routines. The tests performed on both simulated and real-life time series show that our approach may outperform a greedy algorithm and different Lasso approaches in terms of prediction errors and sparsity.

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Omics experiments endowed with a time-course design may enable us to uncover the dynamic interplay among genes of cellular processes. Multivariate techniques (like VAR(1) models describing the temporal and contemporaneous relations among variates) that may facilitate this goal are hampered by the high-dimensionality of the resulting data. This is resolved by the presented ridge regularized maximum likelihood estimation procedure for the VAR(1) model. Information on the absence of temporal and contemporaneous relations may be incorporated in this procedure. Its computational efficient implemention is discussed. The estimation procedure is accompanied with an LOOCV scheme to determine the associated penalty parameters. Downstream exploitation of the estimated VAR(1) model is outlined: an empirical Bayes procedure to identify the interesting temporal and contemporaneous relationships, impulse response analysis, mutual information analysis, and covariance decomposition into the (graphical) relations among variates. In a simulation study the presented ridge estimation procedure outperformed a sparse competitor in terms of Frobenius loss of the estimates, while their selection properties are on par. The proposed machinery is illustrated in the reconstruction of the p53 signaling pathway during HPV-induced cellular transformation. The methodology is implemented in the ragt2ridges R-package available from CRAN.

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Although the impact of serial correlation (autocorrelation) in residuals of general linear models for fMRI time-series has been studied extensively, the effect of autocorrelation on functional connectivity studies has been largely neglected until recently. Some recent studies based on results from economics have questioned the conventional estimation of functional connectivity and argue that not correcting for autocorrelation in fMRI time-series results in "spurious" correlation coefficients. In this paper, first we assess the effect of autocorrelation on Pearson correlation coefficient through theoretical approximation and simulation. Then we present this effect on real fMRI data. To our knowledge this is the first work comprehensively investigating the effect of autocorrelation on functional connectivity estimates. Our results show that although FC values are altered, even following correction for autocorrelation, results of hypothesis testing on FC values remain very similar to those before correction. In real data we show this is true for main effects and also for group difference testing between healthy controls and schizophrenia patients. We further discuss model order selection in the context of autoregressive processes, effects of frequency filtering and propose a preprocessing pipeline for connectivity studies.

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The robustness and sensitivity of a test for density dependence in an animal population against departures from the assumed null and alternative model is assessed via simulation. The test is shown to be nonrobust and insensitive to departures from the assumed models.

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This is a comment on a note by Solow (1990). It is shown that Solow's simulation results indicate that Bulmer's test for density dependence is non-robust to a particular kind of second-order Markovity that might well be overlooked by an ecologist. It is suggested that Solow's claim that Bulmer's test is insensitive is not wholly justified. Some scepticism concerning the applicability of statistical testing theory to animal population data is expressed.