Consistency in approximate entropy given by a volumetric estimate

Non-linear methods for estimating variability in time-series are currently of widespread use. Among such methods are approximate entropy (ApEn) and sample approximate entropy (SampEn). The applicability of ApEn and SampEn in analyzing data is evident and their use is increasing. However, consistency is a point of concern in these tools, i.e., the classification of the temporal organization of a data set might indicate a relative less ordered series in relation to another when the opposite is true. As highlighted by their proponents themselves, ApEn and SampEn might present incorrect results due to this lack of consistency. In this study, we present a method which gains consistency by using ApEn repeatedly in a wide range of combinations of window lengths and matching error tolerance. The tool is called volumetric approximate entropy, vApEn. We analyze nine artificially generated prototypical time-series with different degrees of temporal order (combinations of sine waves, logistic maps with different control parameter values, random noises). While ApEn/SampEn clearly fail to consistently identify the temporal order of the sequences, vApEn correctly do. In order to validate the tool we performed shuffled and surrogate data analysis. Statistical analysis confirmed the consistency of the method. (C) 2008 Elsevier Ltd. All rights reserved.

Fluctuating abundance of humpback whales (Megaptera novaeangliae) in a calving ground off coastal Brazil

The humpback whale (Megaptera novaeangliae) population that uses Abrolhos Bank, off the east coast of Brazil as a breeding ground is increasing. To describe temporal changes in the relative abundance of humpback whales around Abrolhos, seven years (1998-2004) of whale count data were collected during July through to November. During one-hour-scans, observers determined group size within 9.3 km (5 n.m.) of a land-based observing station. A total Of 930 scans, comprising 7996 sightings of adults and 2044 calves were analysed using generalized linear models that included variables for time of day, day of the season, years and two-way interactions as possible predictors. The pattern observed was the gradual build-up and decline in whale counts within seasons. Patterns and peaks of adult and calf counts varied among years. Although fluctuation was observed, there was generally an increasing trend in adult counts among years. Calf counts increased only in 2004. These fluctuations may have been caused by some environmental conditions in humpback whales` summering grounds and also by changes in spatial-temporal concentrations in Abrolhos Bank. The general pattern observed within the study area mirrored what was observed in the whole Abrolhos Bank. Knowledge of the consistency with which humpback whales use this important nursing area should prove beneficial for designing future monitoring programmes especially related to whale watching activities around Abrolhos Archipelago.

The sleep-wake cycle in adult rats following pilocarpine-induced temporal lobe epilepsy

The relationship between sleep and epilepsy is both complex and clinically significant. Temporal lobe epilepsy (TLE) influences sleep architecture, while sleep plays an important role in facilitating and/or inhibiting possible epileptic seizures. The pilocarpine experimental model reproduces several features of human temporal lobe epilepsy and is one of the most widely used models in basic research. The aim of the present study was to characterize, behaviorally and electrophysiologically, the phases of sleep-wake cycles (SWC) in male rats with pilocarpine-induced epilepsy. Epileptic rats presented spikes in all phases of the SWC as well as atypical cortical synchronization during attentive wakefulness and paradoxical sleep. The architecture of the sleep-wake phases was altered in epileptic rats, as was the integrity of the SWC. Because our findings reproduce many relevant features observed in patients with epilepsy, this model is suitable to study sleep dysfunction in epilepsy. (C) 2009 Elsevier Inc. All rights reserved.

Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. journal of Applied Statistics 14 (2),117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality. (C) 2009 Elsevier B.V. All rights reserved.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Asymptotic Skewness in Exponential Family Nonlinear Models

In this article, we give an asymptotic formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in exponencial family nonlinear models. We generalize the result by Cordeiro and Cordeiro ( 2001). The formula is given in matrix notation and is very suitable for computer implementation and to obtain closed form expressions for a great variety of models. Some special cases and two applications are discussed.

Systematic risk estimation in symmetric models

The aim of this article is to discuss the estimation of the systematic risk in capital asset pricing models with heavy-tailed error distributions to explain the asset returns. Diagnostic methods for assessing departures from the model assumptions as well as the influence of observations on the parameter estimates are also presented. It may be shown that outlying observations are down weighted in the maximum likelihood equations of linear models with heavy-tailed error distributions, such as Student-t, power exponential, logistic II, so on. This robustness aspect may also be extended to influential observations. An application in which the systematic risk estimate of Microsoft is compared under normal and heavy-tailed errors is presented for illustration.

Skovgaard`s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-321] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as X(2) with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. journal of the Royal Statistical Society B49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265]. (C) 2008 Elsevier B.V. All rights reserved.

Influence diagnostics in Birnbaum-Saunders nonlinear regression models

We consider the issue of assessing influence of observations in the class of Birnbaum-Saunders nonlinear regression models, which is useful in lifetime data analysis. Our results generalize those in Galea et al. [8] which are confined to Birnbaum-Saunders linear regression models. Some influence methods, such as the local influence, total local influence of an individual and generalized leverage are discussed. Additionally, the normal curvatures for studying local influence are derived under some perturbation schemes. We also give an application to a real fatigue data set.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

Digital spiral analysis for objective assessment of fine motor timing variability in Parkinson's disease

OBJECTIVES: To develop a method for objective assessment of fine motor timing variability in Parkinson’s disease (PD) patients, using digital spiral data gathered by a touch screen device. BACKGROUND: A retrospective analysis was conducted on data from 105 subjects including65 patients with advanced PD (group A), 15 intermediate patients experiencing motor fluctuations (group I), 15 early stage patients (group S), and 10 healthy elderly subjects (HE) were examined. The subjects were asked to perform repeated upper limb motor tasks by tracing a pre-drawn Archimedes spiral as shown on the screen of the device. The spiral tracing test was performed using an ergonomic pen stylus, using dominant hand. The test was repeated three times per test occasion and the subjects were instructed to complete it within 10 seconds. Digital spiral data including stylus position (x-ycoordinates) and timestamps (milliseconds) were collected and used in subsequent analysis. The total number of observations with the test battery were as follows: Swedish group (n=10079), Italian I group (n=822), Italian S group (n = 811), and HE (n=299). METHODS: The raw spiral data were processed with three data processing methods. To quantify motor timing variability during spiral drawing tasks Approximate Entropy (APEN) method was applied on digitized spiral data. APEN is designed to capture the amount of irregularity or complexity in time series. APEN requires determination of two parameters, namely, the window size and similarity measure. In our work and after experimentation, window size was set to 4 and similarity measure to 0.2 (20% of the standard deviation of the time series). The final score obtained by APEN was normalized by total drawing completion time and used in subsequent analysis. The score generated by this method is hence on denoted APEN. In addition, two more methods were applied on digital spiral data and their scores were used in subsequent analysis. The first method was based on Digital Wavelet Transform and Principal Component Analysis and generated a score representing spiral drawing impairment. The score generated by this method is hence on denoted WAV. The second method was based on standard deviation of frequency filtered drawing velocity. The score generated by this method is hence on denoted SDDV. Linear mixed-effects (LME) models were used to evaluate mean differences of the spiral scores of the three methods across the four subject groups. Test-retest reliability of the three scores was assessed after taking mean of the three possible correlations (Spearman’s rank coefficients) between the three test trials. Internal consistency of the methods was assessed by calculating correlations between their scores. RESULTS: When comparing mean spiral scores between the four subject groups, the APEN scores were different between HE subjects and three patient groups (P=0.626 for S group with 9.9% mean value difference, P=0.089 for I group with 30.2%, and P=0.0019 for A group with 44.1%). However, there were no significant differences in mean scores of the other two methods, except for the WAV between the HE and A groups (P<0.001). WAV and SDDV were highly and significantly correlated to each other with a coefficient of 0.69. However, APEN was not correlated to neither WAV nor SDDV with coefficients of 0.11 and 0.12, respectively. Test-retest reliability coefficients of the three scores were as follows: APEN (0.9), WAV(0.83) and SD-DV (0.55). CONCLUSIONS: The results show that the digital spiral analysis-based objective APEN measure is able to significantly differentiate the healthy subjects from patients at advanced level. In contrast to the other two methods (WAV and SDDV) that are designed to quantify dyskinesias (over-medications), this method can be useful for characterizing Off symptoms in PD. The APEN was not correlated to none of the other two methods indicating that it measures a different construct of upper limb motor function in PD patients than WAV and SDDV. The APEN also had a better test-retest reliability indicating that it is more stable and consistent over time than WAV and SDDV.

Predicting spatio-temporal distribution for eastern Australian birds using birds Australia's atlas data : survey method, habitat and seasonal effects

Faunal atlases are landscape-level survey collections that can be used for describing spatial and temporal patterns of distribution and densities. They can also serve as a basis for quantitative analysis of factors that may influence the distributions of species. We used a subset of Birds Australia’s Atlas of Australian Birds data (January 1998 to December 2002) to examine the spatio-temporal distribution patterns of 280 selected species in eastern Australia (17–37°S and 136–152°E). Using geographical information systems, this dataset was converted into point coverage and overlaid with a vegetation polygon layer and a half-degree grid. The exploratory data analysis involved calculating species-specific reporting rates spatially, per grid and per vegetation unit, and also temporally, by month and year. We found high spatio-temporal variability in the sampling effort. Using generalised linear models on unaggregated point data, the influences of four factors – survey method and month, geographical location and habitat type – were analysed for each species. When counts of point data were attributed to grid-cells, the total number of species correlated with the total number of surveys, while the number of records per species was highly variable. Surveys had high interannual location fidelity. The predictive values of each of the four factors were species-dependent. Location and habitat were correlated and highly predictive for species with restricted distribution and strong habitat preference. Month was only of importance for migratory species. The proportion of incidental sightings was important for extremely common or extremely rare species. In conclusion, behaviour of species differed sufficiently to require building a customized model for each species to predict distribution. Simple models were effective for habitat specialists with restricted ranges, but for generalists with wide distributions even complex models gave poor predictions.

Stable isotopes reveal inter-annual and inter-individual variation in the diet of female Australian fur seals

Understanding the temporal and spatial variation of foraging habits of apex predators is central to understanding their role in marine ecosystems and how their populations may respond to environmental variability. In the present study, stable isotope analysis (C and N) of blood was used to investigate inter-individual and inter-annual differences in the diet of adult female Australian fur seals Arctocephalus pusillus doriferus. Positive correlations were observed between red cell and plasma values for δ¹³C and δ¹⁵N (r² = 0.47 and r² = 0.66, respectively, p < 0.001 in both cases), suggesting relatively consistent individual prey choices over 3 or 4 foraging trips. Mean δ¹⁵N values (12.8 to 17.5%) confirm the species occupies the highest marine trophic niche in the region. A significant decrease in plasma δ¹⁵N values, corresponding to two-thirds of a trophic level (ca. 2%), was observed between the 1998 to 2000 and 2003 to 2005 sampling periods. This was associated with a significant decrease in adult female body condition and is consistent with a decline, previously documented by faecal analysis, of the proportion of red cod Pseudophysis bachus, barracouta Thyrsites atun and Gould's squid Nototodarus gouldi in the diet and an increase in redbait Emmelichthys nitidus. While substantial variation in δ¹⁵N was observed within each age cohort, a significant decrease was observed with age, suggesting individual specialisation for particular prey types is evident early in adulthood, but that its composition changes as females age. In addition, generalized linear models indicated body mass had a negative influence on δ¹⁵N, which may reflect larger total body oxygen stores, facilitating individuals hunting cryptic prey of lower trophic level (e.g. octopus) on the sea floor.

Probabilistic models over ordered partitions with applications in document ranking and collaborative filtering

Ranking is an important task for handling a large amount of content. Ideally, training data for supervised ranking would include a complete rank of documents (or other objects such as images or videos) for a particular query. However, this is only possible for small sets of documents. In practice, one often resorts to document rating, in that a subset of documents is assigned with a small number indicating the degree of relevance. This poses a general problem of modelling and learning rank data with ties. In this paper, we propose a probabilistic generative model, that models the process as permutations over partitions. This results in super-exponential combinatorial state space with unknown numbers of partitions and unknown ordering among them. We approach the problem from the discrete choice theory, where subsets are chosen in a stagewise manner, reducing the state space per each stage significantly. Further, we show that with suitable parameterisation, we can still learn the models in linear time. We evaluate the proposed models on two application areas: (i) document ranking with the data from the recently held Yahoo! challenge, and (ii) collaborative filtering with movie data. The results demonstrate that the models are competitive against well-known rivals.

Predicting avian distributions to evaluate spatiotemporal overlap with locust control operations in eastern Australia.

Locusts and grasshoppers cause considerable economic damage to agriculture worldwide. The Australian Plague Locust Commission uses multiple pesticides to control locusts in eastern Australia. Avian exposure to agricultural pesticides is of conservation concern, especially in the case of rare and threatened species. The aim of this study was to evaluate the probability of pesticide exposure of native avian species during operational locust control based on knowledge of species occurrence in areas and times of application. Using presence-absence data provided by the Birds Australia Atlas for 1998 to 2002, we developed a series of generalized linear models to predict avian occurrences on a monthly basis in 0.5 degrees grid cells for 280 species over 2 million km2 in eastern Australia. We constructed species-specific models relating occupancy patterns to survey date and location, rainfall, and derived habitat preference. Model complexity depended on the number of observations available. Model output was the probability of occurrence for each species at times and locations of past locust control operations within the 5-year study period. Given the high spatiotemporal variability of locust control events, the variability in predicted bird species presence was high, with 108 of the total 280 species being included at least once in the top 20 predicted species for individual space-time events. The models were evaluated using field surveys collected between 2000 and 2005, at sites with and without locust outbreaks. Model strength varied among species. Some species were under- or over-predicted as times and locations of interest typically did not correspond to those in the prediction data set and certain species were likely attracted to locusts as a food source. Field surveys demonstrated the utility of the spatially explicit species lists derived from the models but also identified the presence of a number of previously unanticipated species. These results also emphasize the need for special consideration of rare and threatened species that are poorly predicted by presence-absence models. This modeling exercise was a useful a priori approach in species risk assessments to identify species present at times and locations of locust control applications, and to discover gaps in our knowledge and need for further focused data collection.