A Bayesian approach for mixed effects state-space models under skewness and heavy tails.

Human immunodeficiency virus (HIV) dynamics have been the focus of epidemiological and biostatistical research during the past decades to understand the progression of acquired immunodeficiency syndrome (AIDS) in the population. Although there are several approaches for modeling HIV dynamics, one of the most popular is based on Gaussian mixed-effects models because of its simplicity from the implementation and interpretation viewpoints. However, in some situations, Gaussian mixed-effects models cannot (a) capture serial correlation existing in longitudinal data, (b) deal with missing observations properly, and (c) accommodate skewness and heavy tails frequently presented in patients' profiles. For those cases, mixed-effects state-space models (MESSM) become a powerful tool for modeling correlated observations, including HIV dynamics, because of their flexibility in modeling the unobserved states and the observations in a simple way. Consequently, our proposal considers an MESSM where the observations' error distribution is a skew-t. This new approach is more flexible and can accommodate data sets exhibiting skewness and heavy tails. Under the Bayesian paradigm, an efficient Markov chain Monte Carlo algorithm is implemented. To evaluate the properties of the proposed models, we carried out some exciting simulation studies, including missing data in the generated data sets. Finally, we illustrate our approach with an application in the AIDS Clinical Trial Group Study 315 (ACTG-315) clinical trial data set.

Hyperscanning fNIRS data analysis using multiregression dynamic models: an illustration in a violin duo.

Introduction: Interpersonal neural synchronization (INS) demands a greater understanding of a brain's influence on others. Therefore, brain synchronization is an even more complex system than intrasubject brain connectivity and must be investigated. There is a need to develop novel methods for statistical inference in this context. Methods: In this study, motivated by the analysis of fNIRS hyperscanning data, which measure the activity of multiple brains simultaneously, we propose a two-step network estimation: Tabu search local method and global maximization in the selected subgroup [partial conditional directed acyclic graph (DAG) + multiregression dynamic model]. We illustrate this approach in a dataset of two individuals who are playing the violin together. Results: This study contributes new tools to the social neuroscience field, which may provide new perspectives about intersubject interactions. Our proposed approach estimates the best probabilistic network representation, in addition to providing access to the time-varying parameters, which may be helpful in understanding the brain-to-brain association of these two players. Discussion: The illustration of the violin duo highlights the time-evolving changes in the brain activation of an individual influencing the other one through a data-driven analysis. We confirmed that one player was leading the other given the ROI causal relation toward the other player.

Estimating the efficiency of Brazilian electricity distribution utilities.

This paper proposes a differing methodology from the Brazilian Electricity Regulatory Agency on the efficiency estimation for the Brazilian electricity distribution sector. Our proposal combines robust state-space models and stochastic frontier analysis to measure the operational cost efficiency in a panel data set from 60 Brazilian electricity distribution utilities. The modeling joins the main literature in energy economics with advanced econometric and statistic techniques in order to estimate the efficiencies. Moreover, the suggested model is able to deal with changes in the inefficiencies across time whilst the Bayesian paradigm - through Markov chain Monte Carlo techniques - facilitates the inference on all unknowns. The method enables a significant degree of flexibility in the resultant efficiencies and a complete photography about the distribution sector.

A non-parametric statistic for testing conditional heteroscedasticity for unobserved component models.

When prediction intervals are constructed using unobserved component models (UCM), problems can arise due to the possible existence of components that may or may not be conditionally heteroscedastic. Accurate coverage depends on correctly identifying the source of the heteroscedasticity. Different proposals for testing heteroscedasticity have been applied to UCM; however, in most cases, these procedures are unable to identify the heteroscedastic component correctly. The main issue is that test statistics are affected by the presence of serial correlation, causing the distribution of the statistic under conditional homoscedasticity to remain unknown. We propose a nonparametric statistic for testing heteroscedasticity based on the well-known Wilcoxon's rank statistic. We study the asymptotic validation of the statistic and examine bootstrap procedures for approximating its finite sample distribution. Simulation results show an improvement in the size of the homoscedasticity tests and a power that is clearly comparable with the best alternative in the literature. We also apply the test on real inflation data. Looking for the presence of a conditionally heteroscedastic effect on the error terms, we arrive at conclusions that almost all cases are different than those given by the alternative test statistics presented in the literature.

BrainWave Nets: Are Sparse Dynamic Models Susceptible to Brain Manipulation Experimentation?

Sparse time series models have shown promise in estimating contemporaneous and ongoing brain connectivity. This paper was motivated by a neuroscience experiment using EEG signals as the outcome of our established interventional protocol, a new method in neurorehabilitation toward developing a treatment for visual verticality disorder in post-stroke patients. To analyze the [complex outcome measure (EEG)] that reflects neural-network functioning and processing in more specific ways regarding traditional analyses, we make a comparison among sparse time series models (classic VAR, GLASSO, TSCGM, and TSCGM-modified with non-linear and iterative optimizations) combined with a graphical approach, such as a Dynamic Chain Graph Model (DCGM). These dynamic graphical models were useful in assessing the role of estimating the brain network structure and describing its causal relationship. In addition, the class of DCGM was able to visualize and compare experimental conditions and brain frequency domains [using finite impulse response (FIR) filter]. Moreover, using multilayer networks, the results corroborate with the susceptibility of sparse dynamic models, bypassing the false positives problem in estimation algorithms. We conclude that applying sparse dynamic models to EEG data may be useful for describing intervention-relocated changes in brain connectivity.

A New Method to Reconstruct Quantitative Food Webs and Nutrient Flows from Isotope Tracer Addition Experiments.

Understanding how nutrients flow through food webs is central in ecosystem ecology. Tracer addition experiments are powerful tools to reconstruct nutrient flows by adding an isotopically enriched element into an ecosystem and tracking its fate through time. Historically, the design and analysis of tracer studies have varied widely, ranging from descriptive studies to modeling approaches of varying complexity. Increasingly, isotope tracer data are being used to compare ecosystems and analyze experimental manipulations. Currently, a formal statistical framework for analyzing such experiments is lacking, making it impossible to calculate the estimation errors associated with the model fit, the interdependence of compartments, and the uncertainty in the diet of consumers. In this article we develop a method based on Bayesian hidden Markov models and apply it to the analysis of N15-NH4+ tracer additions in two Trinidadian streams in which light was experimentally manipulated. Through this case study, we illustrate how to estimate N fluxes between ecosystem compartments, turnover rates of N within those compartments, and the associated uncertainty. We also show how the method can be used to compare alternative models of food web structure, calculate the error around derived parameters, and make statistical comparisons between sites or treatments.

From Chilean Patagonia to Galapagos, Ecuador: novel insights on blue whale migratory pathways along the Eastern South Pacific.

BACKGROUND: The most traditional scheme for migration among baleen whales comprises yearly migrations between productive waters at high latitude summer feeding grounds and warmer waters at lower latitudes where whales calve and mate, but rarely feed. Evidence indicates, however, that large departures from this scheme exist among populations and individuals. Furthermore, for some populations there is virtually no information on migratory pathways and destinations. Such is the case of Chilean blue whales throughout the Eastern South Pacific; hence, the goal of this study was to assess its migratory behavior. METHODS: Dedicated marine surveys and satellite tagging efforts were undertaken during the austral summer and early autumn on blue whale feeding grounds off Chilean Northern Patagonia (CNP) during 2013, 2015 and 2016. Positional data derived from satellite tags regarding movement patterns and behavior were analyzed using Bayesian switching first-difference correlated random walk models. RESULTS: We instrumented 10 CNP blue whales with satellite transmitters and documented individual variation in departure time, northbound migratory routes and potential wintering grounds. The onset of migration occurred from mid/late austral autumn to well into the austral winter. Blue whales moved in various directions, but ultimately converged toward a general NW movement direction along a wide corridor exceeding 2,000 km. Area-Restricted Search behavior was exhibited within fjords and channels of CNP and also South of Galapagos Archipelago (GA) and northern Peru, but never during migration. Interestingly, dive profiles for one whale that reached GA showed a sharp and consistent increase in depth north of 5°S and extreme deep dives of up to 330 m. DISCUSSION: Information derived from satellite tagged blue whales in this study is the first of its kind off the Eastern Southern Pacific. Our results provide valuable information on their migratory timing, routes and behavior on their northbound migration, particularly regarding the varied migratory plasticity for this particular population. Our results also highlight the first record of two complete migratory paths between CNP and GA and strengthen the hypothesis that GA waters correspond to a potential wintering destination for CNP blue whales. We further hypothesize that this area might be selected because of its biological productivity, which could provide feeding opportunities during the breeding season. Our results suggest that special efforts should be put forward to identify blue whale critical areas and understand key behavioral aspects in order to provide the basis for their conservation on a regional context (i.e., reducing potential ship strike and promote Marine Protected Area (MPA) implementation in Chile, Ecuador and Peru). Indeed, we suggest joint blue whale conservation efforts at the regional level in order to identify and determine potential threats and impacts and, most importantly, implement prospective management actions.

Maximum likelihood estimation for stochastic volatility in mean models with heavy-tailed distributions.

In this article, we introduce a likelihood-based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions (Abanto-Valle et al., 2012). Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. The method is based on the proposal of Langrock et al. (2012) and makes explicit the useful link between HMMs and SVM models with SMN distributions. Likelihood-based estimation of the parameters of stochastic volatility models in general, and SVM models with SMN distributions in particular, is usually regarded as challenging as the likelihood is a high-dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, i.e., estimating the volatility of the process.

Bayesian analysis of stochastic volatility-in-mean model with leverage and asymmetrically heavy-tailed error using generalized hyperbolic skew Student's t-distribution.

A stochastic volatility-in-mean model with correlated errors using the generalized hyperbolic skew Student-t (GHST) distribution provides a robust alternative to the parameter estimation for daily stock returns in the absence of normality. An efficient Markov chain Monte Carlo (MCMC) sampling algorithm is developed for parameter estimation. The deviance information, the Bayesian predictive information and the log-predictive score criterion are used to assess the fit of the proposed model. The proposed method is applied to an analysis of the daily stock return data from the Standard & Poor's 500 index (S&P 500). The empirical results reveal that the stochastic volatility-in-mean model with correlated errors and GH-ST distribution leads to a significant improvement in the goodness-of-fit for the S&P 500 index returns dataset over the usual normal model.

State-Space Approach to Structural Representation of Perturbed Pitch Period Sequences in Voice Signals.

OBJECTIVES: The aim of this study was to propose a state space-based approach to model perturbed pitch period sequences (PPSs), extracted from real sustained vowels, combining the principal features of disturbed real PPSs with structural analysis of stochastic time series and state space methods. METHODS: The PPSs were obtained from a database composed of 53 healthy subjects. State space models were developed taking into account different structures and complexity levels. PPS features such as trend, cycle, and irregular structures were considered. Model parameters were calculated using optimization procedures. For each PPS, state estimates were obtained combining the developed models and diffuse initialization with filtering and smoothing methods. Statistical tests were applied to objectively evaluate the performance of this method. RESULTS: Statistical tests demonstrated that the proposed approach correctly represented more than the 75% of the database with a significance value of 0.05. In the analysis, structural estimates suitably characterized the dynamics of the PPSs. Trend estimates proved to properly represent slow long-term dynamics, whereas cycle estimates captured short-term autoregressive dependencies. CONCLUSIONS: The present study demonstrated that the proposed approach is suitable for representing and analyzing real perturbed PPSs, also allowing to extract further information related to the phonation process.

Beyond lifetime reproductive success: the posthumous reproductive dynamics of male Trinidadian guppies.

In semelparous populations, dormant germ banks (e.g. seeds) have been proposed as important in maintaining genotypes that are adaptive at different times in fluctuating environments. Such hidden storage of genetic diversity need not be exclusive to dormant banks. Genotype diversity may be preserved in many iteroparous animals through sperm-storage mechanisms in females. This allows males to reproduce posthumously and increase the effective sizes of seemingly female-biased populations. Although long-term sperm storage has been demonstrated in many organisms, the understanding of its importance in the wild is very poor. We here show the prevalence of male posthumous reproduction in wild Trinidadian guppies, through the combination of mark-recapture and pedigree analyses of a multigenerational individual-based dataset. A significant proportion of the reproductive population consisted of dead males, who could conceive up to 10 months after death (the maximum allowed by the length of the dataset), which is more than twice the estimated generation time. Demographic analysis shows that the fecundity of dead males can play an important role in population growth and selection.