Lag-one autocorrelation in short series: Estimation and hypothesis testing

In the first part of the study, nine estimators of the first-order autoregressive parameter are reviewed and a new estimator is proposed. The relationships and discrepancies between the estimators are discussed in order to achieve a clear differentiation. In the second part of the study, the precision in the estimation of autocorrelation is studied. The performance of the ten lag-one autocorrelation estimators is compared in terms of Mean Square Error (combining bias and variance) using data series generated by Monte Carlo simulation. The results show that there is not a single optimal estimator for all conditions, suggesting that the estimator ought to be chosen according to sample size and to the information available of the possible direction of the serial dependence. Additionally, the probability of labelling an actually existing autocorrelation as statistically significant is explored using Monte Carlo sampling. The power estimates obtained are quite similar among the tests associated with the different estimators. These estimates evidence the small probability of detecting autocorrelation in series with less than 20 measurement times.

Electric dipole polarizability in 208Pb: insights from the droplet model

We study the electric dipole polarizability α D in 208 Pb based on the predictions of a large and representative set of relativistic and nonrelativistic nuclear mean-field models. We adopt the droplet model as a guide to better understand the correlations between α D and other isovector observables. Insights from the droplet model suggest that the product of α D and the nuclear symmetry energy at saturation density J is much better correlated with the neutron skin thickness r np of 208 Pb than the polarizability alone. Correlations of α D J with r np and with the symmetry energy slope parameter L suggest that α D J is a strong isovector indicator. Hence, we explore the possibility of constraining the isovector sector of the nuclear energy density functional by comparing our theoretical predictions against measurements of both α D and the parity-violating asymmetry in 208 Pb. We find that the recent experimental determination of α D in 208 Pb in combination with the range for the symmetry energy at saturation density J = [31 ± (2) est] MeV suggests r np (208 Pb) = 0 . 165 ± (0 . 009) expt ± (0 . 013) theor ± (0.021) est fm and L = 43 ± (6) expt ± (8) theor ± (12) est MeV

An approach to predicting bowing control parameter contours in violin performance

We present a machine learning approach to modeling bowing control parametercontours in violin performance. Using accurate sensing techniqueswe obtain relevant timbre-related bowing control parameters such as bowtransversal velocity, bow pressing force, and bow-bridge distance of eachperformed note. Each performed note is represented by a curve parametervector and a number of note classes are defined. The principal componentsof the data represented by the set of curve parameter vectors are obtainedfor each class. Once curve parameter vectors are expressed in the new spacedefined by the principal components, we train a model based on inductivelogic programming, able to predict curve parameter vectors used for renderingbowing controls. We evaluate the prediction results and show the potentialof the model by predicting bowing control parameter contours from anannotated input score.

Statistical modeling of violin bowing parameter contours

We present a framework for modeling right-hand gestures in bowed-string instrument playing, applied to violin. Nearly non-intrusive sensing techniques allow for accurate acquisition of relevant timbre-related bowing gesture parameter cues. We model the temporal contour of bow transversal velocity, bow pressing force, and bow-bridge distance as sequences of short segments, in particular B´ezier cubic curve segments. Considering different articulations, dynamics, andcontexts, a number of note classes is defined. Gesture parameter contours of a performance database are analyzed at note-level by following a predefined grammar that dictatescharacteristics of curve segment sequences for each of the classes into consideration. Based on dynamic programming, gesture parameter contour analysis provides an optimal curve parameter vector for each note. The informationpresent in such parameter vector is enough for reconstructing original gesture parameter contours with significant fidelity. From the resulting representation vectors, weconstruct a statistical model based on Gaussian mixtures, suitable for both analysis and synthesis of bowing gesture parameter contours. We show the potential of the modelby synthesizing bowing gesture parameter contours from an annotated input score. Finally, we point out promising applicationsand developments.

Confirmatory factor analysis of an integrated model of psycopathology assessed with MMPI-2-RF and the MCMI-III

We presented an integrated hierarchical model of psychopathology that more accurately captures empirical patterns of comorbidity between clinical syndromes and personality disorders.In order to verify the structural validity of the model proposed, this study aimed to analyze the convergence between the Restructured Clinical (RC) scales and Personality scales (PSY-5) of the MMPI-2-RF and the Clinical Syndrome and Personality Disorder scales of the MCMI-III.The MMPI-2-RF and MCMI-III were administered to a clinical sample of 377 outpatients (167 men and 210 women).The structural hypothesiswas assessed by using a Confirmatory Factor Analytic design with four common superordinate factors. An independent-cluster-basis solution was proposed based on maximum likelihood estimation and the application of several fit indices.The fit of the proposed model can be considered as good and more so if we take into account its complexity.

Partial correlation : Network analysis

The final year project came to us as an opportunity to get involved in a topic which has appeared to be attractive during the learning process of majoring in economics: statistics and its application to the analysis of economic data, i.e. econometrics.Moreover, the combination of econometrics and computer science is a very hot topic nowadays, given the Information Technologies boom in the last decades and the consequent exponential increase in the amount of data collected and stored day by day. Data analysts able to deal with Big Data and to find useful results from it are verydemanded in these days and, according to our understanding, the work they do, although sometimes controversial in terms of ethics, is a clear source of value added both for private corporations and the public sector. For these reasons, the essence of this project is the study of a statistical instrument valid for the analysis of large datasets which is directly related to computer science: Partial Correlation Networks.The structure of the project has been determined by our objectives through the development of it. At first, the characteristics of the studied instrument are explained, from the basic ideas up to the features of the model behind it, with the final goal of presenting SPACE model as a tool for estimating interconnections in between elements in large data sets. Afterwards, an illustrated simulation is performed in order to show the power and efficiency of the model presented. And at last, the model is put into practice by analyzing a relatively large data set of real world data, with the objective of assessing whether the proposed statistical instrument is valid and useful when applied to a real multivariate time series. In short, our main goals are to present the model and evaluate if Partial Correlation Network Analysis is an effective, useful instrument and allows finding valuable results from Big Data.As a result, the findings all along this project suggest the Partial Correlation Estimation by Joint Sparse Regression Models approach presented by Peng et al. (2009) to work well under the assumption of sparsity of data. Moreover, partial correlation networks are shown to be a very valid tool to represent cross-sectional interconnections in between elements in large data sets.The scope of this project is however limited, as there are some sections in which deeper analysis would have been appropriate. Considering intertemporal connections in between elements, the choice of the tuning parameter lambda, or a deeper analysis of the results in the real data application are examples of aspects in which this project could be completed.To sum up, the analyzed statistical tool has been proved to be a very useful instrument to find relationships that connect the elements present in a large data set. And after all, partial correlation networks allow the owner of this set to observe and analyze the existing linkages that could have been omitted otherwise.

ML approaches to channel estimation for pilot-aided multi-rate DS/CDMA systems

This paper analyzes the asymptotic performance of maximum likelihood (ML) channel estimation algorithms in wideband code division multiple access (WCDMA) scenarios. We concentrate on systems with periodic spreading sequences (period larger than or equal to the symbol span) where the transmitted signal contains a code division multiplexed pilot for channel estimation purposes. First, the asymptotic covariances of the training-only, semi-blind conditional maximum likelihood (CML) and semi-blind Gaussian maximum likelihood (GML) channelestimators are derived. Then, these formulas are further simplified assuming randomized spreading and training sequences under the approximation of high spreading factors and high number of codes. The results provide a useful tool to describe the performance of the channel estimators as a function of basicsystem parameters such as number of codes, spreading factors, or traffic to training power ratio.

Asymptotic equivalence between the unconditional maximum likelihood and the square-law nonlinearity symbol timing estimation

This paper provides a systematic approach to theproblem of nondata aided symbol-timing estimation for linearmodulations. The study is performed under the unconditionalmaximum likelihood framework where the carrier-frequencyerror is included as a nuisance parameter in the mathematicalderivation. The second-order moments of the received signal arefound to be the sufficient statistics for the problem at hand and theyallow the provision of a robust performance in the presence of acarrier-frequency error uncertainty. We particularly focus on theexploitation of the cyclostationary property of linear modulations.This enables us to derive simple and closed-form symbol-timingestimators which are found to be based on the well-known squaretiming recovery method by Oerder and Meyr. Finally, we generalizethe OM method to the case of linear modulations withoffset formats. In this case, the square-law nonlinearity is foundto provide not only the symbol-timing but also the carrier-phaseerror.

Unifying Time to Contact Estimation and Collision Avoidance across Species

The -function and the -function are phenomenological models that are widely used in the context of timing interceptive actions and collision avoidance, respectively. Both models were previously considered to be unrelated to each other: is a decreasing function that provides an estimation of time-to-contact (ttc) in the early phase of an object approach; in contrast, has a maximum before ttc. Furthermore, it is not clear how both functions could be implemented at the neuronal level in a biophysically plausible fashion. Here we propose a new framework the corrected modified Tau function capable of predicting both -type ("") and -type ("") responses. The outstanding property of our new framework is its resilience to noise. We show that can be derived from a firing rate equation, and, as , serves to describe the response curves of collision sensitive neurons. Furthermore, we show that predicts the psychophysical performance of subjects determining ttc. Our new framework is thus validated successfully against published and novel experimental data. Within the framework, links between -type and -type neurons are established. Therefore, it could possibly serve as a model for explaining the co-occurrence of such neurons in the brain.

Estimation of age- and stage-specific Catalan breast cancer survival functions using US and Catalan survival data

Background: During the last part of the 1990s the chance of surviving breast cancer increased. Changes in survival functions reflect a mixture of effects. Both, the introduction of adjuvant treatments and early screening with mammography played a role in the decline in mortality. Evaluating the contribution of these interventions using mathematical models requires survival functions before and after their introduction. Furthermore, required survival functions may be different by age groups and are related to disease stage at diagnosis. Sometimes detailed information is not available, as was the case for the region of Catalonia (Spain). Then one may derive the functions using information from other geographical areas. This work presents the methodology used to estimate age- and stage-specific Catalan breast cancer survival functions from scarce Catalan survival data by adapting the age- and stage-specific US functions. Methods: Cubic splines were used to smooth data and obtain continuous hazard rate functions. After, we fitted a Poisson model to derive hazard ratios. The model included time as a covariate. Then the hazard ratios were applied to US survival functions detailed by age and stage to obtain Catalan estimations. Results: We started estimating the hazard ratios for Catalonia versus the USA before and after the introduction of screening. The hazard ratios were then multiplied by the age- and stage-specific breast cancer hazard rates from the USA to obtain the Catalan hazard rates. We also compared breast cancer survival in Catalonia and the USA in two time periods, before cancer control interventions (USA 1975–79, Catalonia 1980–89) and after (USA and Catalonia 1990–2001). Survival in Catalonia in the 1980–89 period was worse than in the USA during 1975–79, but the differences disappeared in 1990–2001. Conclusion: Our results suggest that access to better treatments and quality of care contributed to large improvements in survival in Catalonia. On the other hand, we obtained detailed breast cancer survival functions that will be used for modeling the effect of screening and adjuvant treatments in Catalonia.

Effect of radar rainfall time resolution on the predictive capability of a distributed hydrologic model

The performance of a hydrologic model depends on the rainfall input data, both spatially and temporally. As the spatial distribution of rainfall exerts a great influence on both runoff volumes and peak flows, the use of a distributed hydrologic model can improve the results in the case of convective rainfall in a basin where the storm area is smaller than the basin area. The aim of this study was to perform a sensitivity analysis of the rainfall time resolution on the results of a distributed hydrologic model in a flash-flood prone basin. Within such a catchment, floods are produced by heavy rainfall events with a large convective component. A second objective of the current paper is the proposal of a methodology that improves the radar rainfall estimation at a higher spatial and temporal resolution. Composite radar data from a network of three C-band radars with 6-min temporal and 2 × 2 km2 spatial resolution were used to feed the RIBS distributed hydrological model. A modification of the Window Probability Matching Method (gauge-adjustment method) was applied to four cases of heavy rainfall to improve the observed rainfall sub-estimation by computing new Z/R relationships for both convective and stratiform reflectivities. An advection correction technique based on the cross-correlation between two consecutive images was introduced to obtain several time resolutions from 1 min to 30 min. The RIBS hydrologic model was calibrated using a probabilistic approach based on a multiobjective methodology for each time resolution. A sensitivity analysis of rainfall time resolution was conducted to find the resolution that best represents the hydrological basin behaviour.

Unifying Time to Contact Estimation and Collision Avoidance across Species

The -function and the -function are phenomenological models that are widely used in the context of timing interceptive actions and collision avoidance, respectively. Both models were previously considered to be unrelated to each other: is a decreasing function that provides an estimation of time-to-contact (ttc) in the early phase of an object approach; in contrast, has a maximum before ttc. Furthermore, it is not clear how both functions could be implemented at the neuronal level in a biophysically plausible fashion. Here we propose a new framework- the corrected modified Tau function- capable of predicting both -type ("") and -type ("") responses. The outstanding property of our new framework is its resilience to noise. We show that can be derived from a firing rate equation, and, as , serves to describe the response curves of collision sensitive neurons. Furthermore, we show that predicts the psychophysical performance of subjects determining ttc. Our new framework is thus validated successfully against published and novel experimental data. Within the framework, links between -type and -type neurons are established. Therefore, it could possibly serve as a model for explaining the co-occurrence of such neurons in the brain.

A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement -SCR-, under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

Scale-up model obtained from the rheological analysis of highly concentrated emulsions prepared at three scales

We examine the scale invariants in the preparation of highly concentrated w/o emulsions at different scales and in varying conditions. The emulsions are characterized using rheological parameters, owing to their highly elastic behavior. We first construct and validate empirical models to describe the rheological properties. These models yield a reasonable prediction of experimental data. We then build an empirical scale-up model, to predict the preparation and composition conditions that have to be kept constant at each scale to prepare the same emulsion. For this purpose, three preparation scales with geometric similarity are used. The parameter N¿D^α, as a function of the stirring rate N, the scale (D, impeller diameter) and the exponent α (calculated empirically from the regression of all the experiments in the three scales), is defined as the scale invariant that needs to be optimized, once the dispersed phase of the emulsion, the surfactant concentration, and the dispersed phase addition time are set. As far as we know, no other study has obtained a scale invariant factor N¿Dα for the preparation of highly concentrated emulsions prepared at three different scales, which covers all three scales, different addition times and surfactant concentrations. The power law exponent obtained seems to indicate that the scale-up criterion for this system is the power input per unit volume (P/V).

Estimation of Water Circulation in a Mediterranean Salt Marsh and its Relationship with Flooding Causes

Variations in water volume in small depressions in Mediterranean salt marshes in Girona (Spain) are described and the potential causes for these variations analysed. Although the basins appear to be endorrheic, groundwater circulation is intense, as estimated from the difference between water volume observed and that expected from the balance precipitation / evaporation. The rate of variation in volume (VR = AV / VAt) may be used to estimate groundwater supply ('circulation'), since direct measurements of this parameter are impossible. Volume.conductivity figures can also be used to estimate the quantity of circulation, and to investigate the origin of water supplied to the system. The relationships between variations in the volume of water in the basins and the main causes of flooding are also analysed. Sea storms, rainfall levels and strong, dry northerly winds are suggested as the main causes of the variations in the volumes of basins. The relative importance assigned to these factors has changed, following the recent regulation of freshwater flows entering the system