L'estadística i els nous mitjans de càlcul

Aquesta exposició vol presentar breument el ventall d'eines disponibles, la terminologia utilitzada i, en general, el marc metodològic de l'estadística exploratoria i de l'analisi de dades, el paradigma de la disciplina.En el decurs dels darrers anys, la disciplina no ha estat pas capgirada, però de tota manera sí que cal una actualització permanent.S'han forjat i provat algunes eines gairebé només esbossades, han aparegut nous dominis d'aplicació. Cal precisar la relació amb els competidors i dinamics veïns (intel·ligencia artificial, xarxes neurals, Data Mining). La perspectiva que presento dels mètodes d'anàlisi de dades emana evidentment d'un punt de vista particular; altres punts de vista poden ser igualment vàlids

Bayes linear spaces

Linear spaces consisting of σ-finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended

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.

Motion estimation using higher-order statistics

The objective of this paper is to introduce a fourth-order cost function of the displaced frame difference (DFD) capable of estimatingmotion even for small regions or blocks. Using higher than second-orderstatistics is appropriate in case the image sequence is severely corruptedby additive Gaussian noise. Some results are presented and compared to those obtained from the mean kurtosis and the mean square error of the DFD.

Growth variability of Scots pine (Pinus sylvestris) along a West-East gradient across northern Fennoscandia: a dendroclimatic approach

We performed a spatiotemporal analysis of a network of 21 Scots pine (Pinus sylvestris) ring-width chronologies in northern Fennoscandia by means of chronology statistics and multivariate analyses. Chronologies are located on both sides (western and eastern) of the Scandes Mountains (67°N-70°N, 15°E-29°E). Growth relationships with temperature, precipitation, and North Atlantic Oscillation (NAO) indices were calculated for the period 1880-1991. We also assessed their temporal stability. Current July temperature and, to a lesser degree, May precipitation are the main growth limiting factors in the whole area of study. However, Principal Component Analysis (PCA) and mean interseries correlation revealed differences in radial growth between both sides of the Scandes Mountains, attributed to the Oceanic-Continental climatic gradient in the area. The gradient signal is temporally variable and has strengthened during the second half of the 20th century. Northern Fennoscandia Scots pine growth is positively related to early winter NAO indices previous to the growth season and to late spring NAO. NAO/growth relationships are unstable and have dropped in the second half of the 20th century. Moreover, they are noncontinuous through the range of NAO values: for early winter, only positive NAO indices enhance tree growth in the next growing season, while negative NAO does not. For spring, only negative NAO is correlated with radial growth.

All-sky search algorithms for monochromatic signals in bar gravitational wave detector data

In this paper we design and develop several filtering strategies for the analysis of data generated by a resonant bar gravitational wave (GW) antenna, with the goal of assessing the presence (or absence) therein of long-duration monochromatic GW signals, as well as the eventual amplitude and frequency of the signals, within the sensitivity band of the detector. Such signals are most likely generated in the fast rotation of slightly asymmetric spinning stars. We develop practical procedures, together with a study of their statistical properties, which will provide us with useful information on the performance of each technique. The selection of candidate events will then be established according to threshold-crossing probabilities, based on the Neyman-Pearson criterion. In particular, it will be shown that our approach, based on phase estimation, presents a better signal-to-noise ratio than does pure spectral analysis, the most common approach.

Quantifying Social Asymmetric Structures

Many social phenomena involve a set of dyadic relations among agents whose actions may be dependent. Although individualistic approaches have frequently been applied to analyze social processes, these are not generally concerned with dyadic relations nor do they deal with dependency. This paper describes a mathematical procedure for analyzing dyadic interactions in a social system. The proposed method mainly consists of decomposing asymmetric data into their symmetrical and skew-symmetrical parts. A quantification of skew-symmetry for a social system can be obtained by dividing the norm of the skew-symmetrical matrix by the norm of the asymmetric matrix. This calculation makes available to researchers a quantity related to the amount of dyadic reciprocity. Regarding agents, the procedure enables researchers to identify those whose behavior is asymmetric with respect to all agents. It is also possible to derive symmetric measurements among agents and to use multivariate statistical techniques.

Measuring and making decisions for social reciprocity

Social reciprocity may explain certain emerging psychological processes, which are likely to be founded on dyadic relations. Although some indices and statistics have been proposed to measure and make statistical decisions regarding social reciprocity in groups, these were generally developed to identify association patterns rather than to quantify the discrepancies between what each individual addresses to his/her partners and what is received from them in return. Additionally, social researchers are not only interested in measuring groups at the global level, since dyadic and individual measurements are also necessary for a proper description of social interactions. This study is concerned with a new statistic for measuring social reciprocity at the global level and with decomposing it in order to identify those dyads and individuals which account for a significant part of asymmetry in social interactions. In addition to a set of indices some exact analytical results are derived and a way of making statistical decisions is proposed.

Simulated Annealing, High-Order Statistics and Mutual Information for Separation of Sources

In this article, the fusion of a stochastic metaheuristic as Simulated Annealing (SA) with classical criteria for convergence of Blind Separation of Sources (BSS), is shown. Although the topic of BSS, by means of various techniques, including ICA, PCA, and neural networks, has been amply discussed in the literature, to date the possibility of using simulated annealing algorithms has not been seriously explored. From experimental results, this paper demonstrates the possible benefits offered by SA in combination with high order statistical and mutual information criteria for BSS, such as robustness against local minima and a high degree of flexibility in the energy function.

The Barcelona International Conference on Advances in Statistics (BAS 2012) : Abstracts of communications

Conferència Organitzada per l'Escola Politècnica Superior, Universitat de Vic en col·laboració amb Servei d'Estadística de la Universitat Autònoma de Barcelona i CosmoCaixa Barcelona. Celebrada del 18 al 22 de juny de 2012 a Barcelona

Testing reciprocity in social interactions: A comparison between the Directional consistency and Skew symmetry statistics

In the present work we focus on two indices that quantify directionality and skew-symmetrical patterns in social interactions as measures of social reciprocity: the Directional consistency (DC) and Skew symmetry indices. Although both indices enable researchers to describe social groups, most studies require statistical inferential tests. The main aims of the present study are: firstly, to propose an overall statistical technique for testing null hypotheses regarding social reciprocity in behavioral studies, using the DC and Skew symmetry statistics (Φ) at group level; and secondly, to compare both statistics in order to allow researchers to choose the optimal measure depending on the conditions. In order to allow researchers to make statistical decisions, statistical significance for both statistics has been estimated by means of a Monte Carlo simulation. Furthermore, this study will enable researchers to choose the optimal observational conditions for carrying out their research, as the power of the statistical tests has been estimated.

Exploring Compositional Data with the CoDa-Dendrogram

Within the special geometry of the simplex, the sample space of compositional data, compositional orthonormal coordinates allow the application of any multivariate statistical approach. The search for meaningful coordinates has suggested balances (between two groups of parts)—based on a sequential binary partition of a D-part composition—and a representation in form of a CoDa-dendrogram. Projected samples are represented in a dendrogram-like graph showing: (a) the way of grouping parts; (b) the explanatory role of subcompositions generated in the partition process; (c) the decomposition of the variance; (d) the center and quantiles of each balance. The representation is useful for the interpretation of balances and to describe the sample in a single diagram independently of the number of parts. Also, samples of two or more populations, as well as several samples from the same population, can be represented in the same graph, as long as they have the same parts registered. The approach is illustrated with an example of food consumption in Europe

Building an open social learning community around a Dspace repository on Statistics

LORs, addressing content management and preservation, have the positive collaterals of institutional positioning and dissemination, but their main benefit is the empowerment of interest-centred learning communities, as we recognise that learning is much more than content, which becomes infrastructure: the LOR provides the learner interaction with the LOs, but also with other learners and teachers.

Polyphenol intake and mortality risk: a re-analysis of the PREDIMED trial

Background: Polyphenols may lower the risk of cardiovascular disease (CVD) and other chronic diseases due to their antioxidant and anti-inflammatory properties, as well as their beneficial effects on blood pressure, lipids and insulin resistance. However, no previous epidemiological studies have evaluated the relationship between the intake of total polyphenols intake and polyphenol subclasses with overall mortality. Our aim was to evaluate whether polyphenol intake is associated with all-cause mortality in subjects at high cardiovascular risk. Methods: We used data from the PREDIMED study, a 7,447-participant, parallel-group, randomized, multicenter, controlled five-year feeding trial aimed at assessing the effects of the Mediterranean Diet in primary prevention of cardiovascular disease. Polyphenol intake was calculated by matching food consumption data from repeated food frequency questionnaires (FFQ) with the Phenol-Explorer database on the polyphenol content of each reported food. Hazard ratios (HR) and 95% confidence intervals (CI) between polyphenol intake and mortality were estimated using time-dependent Cox proportional hazard models. Results: Over an average of 4.8 years of follow-up, we observed 327 deaths. After multivariate adjustment, we found a 37% relative reduction in all-cause mortality comparing the highest versus the lowest quintiles of total polyphenol intake (hazard ratio (HR) = 0.63; 95% CI 0.41 to 0.97; P for trend = 0.12). Among the polyphenol subclasses, stilbenes and lignans were significantly associated with reduced all-cause mortality (HR =0.48; 95% CI 0.25 to 0.91; P for trend = 0.04 and HR = 0.60; 95% CI 0.37 to 0.97; P for trend = 0.03, respectively), with no significant associations apparent in the rest (flavonoids or phenolic acids). Conclusions: Among high-risk subjects, those who reported a high polyphenol intake, especially of stilbenes and lignans, showed a reduced risk of overall mortality compared to those with lower intakes. These results may be useful to determine optimal polyphenol intake or specific food sources of polyphenols that may reduce the risk of all-cause mortality.