Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, andmargin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

Measuring strategic uncertainty in coordination games

This paper explores three aspects of strategic uncertainty: its relation to risk, predictability of behavior and subjective beliefs of players. In a laboratory experiment we measure subjects certainty equivalents for three coordination games and one lottery. Behavior in coordination games is related to risk aversion, experience seeking, and age.From the distribution of certainty equivalents we estimate probabilities for successful coordination in a wide range of games. For many games, success of coordination is predictable with a reasonable error rate. The best response to observed behavior is close to the global-game solution. Comparing choices in coordination games with revealed risk aversion, we estimate subjective probabilities for successful coordination. In games with a low coordination requirement, most subjects underestimate the probability of success. In games with a high coordination requirement, most subjects overestimate this probability. Estimating probabilistic decision models, we show that the quality of predictions can be improved when individual characteristics are taken into account. Subjects behavior is consistent with probabilistic beliefs about the aggregate outcome, but inconsistent with probabilistic beliefs about individual behavior.

General Equilibrium Long-Run Determinants for Spanish FDI: A Spatial Panel Data Approach

While general equilibrium theories of trade stress the role of third-country effects, little work has been done in the empirical foreign direct investment (FDI) literature to test such spatial linkages. This paper aims to provide further insights into long-run determinants of Spanish FDI by considering not only bilateral but also spatially weighted third-country determinants. The few studies carried out so far have focused on FDI flows in a limited number of countries. However, Spanish FDI outflows have risen dramatically since 1995 and today account for a substantial part of global FDI. Therefore, we estimate recently developed Spatial Panel Data models by Maximum Likelihood (ML) procedures for Spanish outflows (1993-2004) to top-50 host countries. After controlling for unobservable effects, we find that spatial interdependence matters and provide evidence consistent with New Economic Geography (NEG) theories of agglomeration, mainly due to complex (vertical) FDI motivations. Spatial Error Models estimations also provide illuminating results regarding the transmission mechanism of shocks.

Planificación de la producción en sistemas poco complejos. (Algoritmo de planificación de BOLD APS)

BOLD APS es un software diseñado para solventar el problema de la planificación de la producción. Como tal, cuenta con un algoritmo, en continuo desarrollo, cuya función es tomar las decisiones oportunas para obtener una buena programación de tareas. Este proyecto consta de dos fases: la principal comprende el diseño e implementación de una nueva sección dentro del algoritmo de planificación de la producción que utiliza la empresa Global Planning Solution, con el objetivo de ofrecer mejoras en la calidad de las soluciones actuales; la fase secundaria consiste en una labor de depuración, limpieza y ordenación del código, para facilitar su comprensión y posterior modificación.

Breast cancer incidence and overdiagnosis in Catalonia (Spain)

Early detection of breast cancer (BC) with mammography may cause overdiagnosis andovertreatment, detecting tumors which would remain undiagnosed during a lifetime. The aims of this study were: first, to model invasive BC incidence trends in Catalonia (Spain) taking into account reproductive and screening data; and second, to quantify the extent of BC overdiagnosis. We modeled the incidence of invasive BC using a Poisson regression model. Explanatory variables were:age at diagnosis and cohort characteristics (completed fertility rate, percentage of women that use mammography at age 50, and year of birth). This model also was used to estimate the background incidence in the absence of screening. We used a probabilistic model to estimate the expected BC incidence if women in the population usedmammography as reported in health surveys. The difference between the observed and expected cumulative incidences provided an estimate of overdiagnosis.Incidence of invasive BC increased, especially in cohorts born from 1940 to 1955. The biggest increase was observed in these cohorts between the ages of 50 to 65 years, where the final BC incidence rates more than doubled the initial ones. Dissemination of mammography was significantly associated with BC incidence and overdiagnosis. Our estimates of overdiagnosis ranged from 0.4% to 46.6%, for women born around 1935 and 1950, respectively.Our results support the existence of overdiagnosis in Catalonia attributed to mammography usage, and the limited malignant potential of some tumors may play an important role. Women should be better informed about this risk. Research should be oriented towards personalized screening and risk assessment tools

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the studyof tephrochrology. In this paper, DFA is applied to compositional datasets of twodifferent types of tephras from Mountain Ruapehu in New Zealand and MountainRainier in USA. The canonical variables from the analysis are further investigated witha statistical methodology of change-point problems in order to gain a betterunderstanding of the change in compositional pattern over time. Finally, a special caseof segmented regression has been proposed to model both the time of change and thechange in pattern. This model can be used to estimate the age for the unknown tephrasusing Bayesian statistical calibration

Systemic crises and growth

In this paper, we document the fact that countries that have experienced occasional financial crises have on average grown faster than countries with stable financial conditions. We measure the incidence of crisis with the skewness of credit growth, and find that it has a robust negative effect on GDP growth. This link coexists with the negative link between variance and growth typically found in the literature. To explain the link between crises and growth we present a model where weak institutions lead to severe financial constraints and low growth. Financial liberalization policies that facilitaterisk-taking increase leverage and investment. This leads to higher growth, but also toa greater incidence of crises. Conditions are established under which the costs of crises are outweighed by the benefits of higher growth.

Validation procedures in radiological diagnostic models. Neural network and logistic regression

The objective of this paper is to compare the performance of twopredictive radiological models, logistic regression (LR) and neural network (NN), with five different resampling methods. One hundred and sixty-seven patients with proven calvarial lesions as the only known disease were enrolled. Clinical and CT data were used for LR and NN models. Both models were developed with cross validation, leave-one-out and three different bootstrap algorithms. The final results of each model were compared with error rate and the area under receiver operating characteristic curves (Az). The neural network obtained statistically higher Az than LR with cross validation. The remaining resampling validation methods did not reveal statistically significant differences between LR and NN rules. The neural network classifier performs better than the one based on logistic regression. This advantage is well detected by three-fold cross-validation, but remains unnoticed when leave-one-out or bootstrap algorithms are used.

Breast cancer incidence and overdiagnosis in Catalonia (Spain)

Introduction: Early detection of breast cancer (BC) with mammography may cause overdiagnosis and overtreatment, detecting tumors which would remain undiagnosed during a lifetime. The aims of this study were: first, to model invasive BC incidence trends in Catalonia (Spain) taking into account reproductive and screening data; and second, to quantify the extent of BC overdiagnosis. Methods: We modeled the incidence of invasive BC using a Poisson regression model. Explanatory variables were: age at diagnosis and cohort characteristics (completed fertility rate, percentage of women that use mammography at age 50, and year of birth). This model also was used to estimate the background incidence in the absence of screening. We used a probabilistic model to estimate the expected BC incidence if women in the population used mammography as reported in health surveys. The difference between the observed and expected cumulative incidences provided an estimate of overdiagnosis. Results: Incidence of invasive BC increased, especially in cohorts born from 1940 to 1955. The biggest increase was observed in these cohorts between the ages of 50 to 65 years, where the final BC incidence rates more than doubled the initial ones. Dissemination of mammography was significantly associated with BC incidence and overdiagnosis. Our estimates of overdiagnosis ranged from 0.4% to 46.6%, for women born around 1935 and 1950, respectively. Conclusions: Our results support the existence of overdiagnosis in Catalonia attributed to mammography usage, and the limited malignant potential of some tumors may play an important role. Women should be better informed about this risk. Research should be oriented towards personalized screening and risk assessment tools.

Estimation of the viscoelastic properties of vessel walls using a computational model and Doppler ultrasound

Human arteries affected by atherosclerosis are characterized by altered wall viscoelastic properties. The possibility of noninvasively assessing arterial viscoelasticity in vivo would significantly contribute to the early diagnosis and prevention of this disease. This paper presents a noniterative technique to estimate the viscoelastic parameters of a vascular wall Zener model. The approach requires the simultaneous measurement of flow variations and wall displacements, which can be provided by suitable ultrasound Doppler instruments. Viscoelastic parameters are estimated by fitting the theoretical constitutive equations to the experimental measurements using an ARMA parameter approach. The accuracy and sensitivity of the proposed method are tested using reference data generated by numerical simulations of arterial pulsation in which the physiological conditions and the viscoelastic parameters of the model can be suitably varied. The estimated values quantitatively agree with the reference values, showing that the only parameter affected by changing the physiological conditions is viscosity, whose relative error was about 27% even when a poor signal-to-noise ratio is simulated. Finally, the feasibility of the method is illustrated through three measurements made at different flow regimes on a cylindrical vessel phantom, yielding a parameter mean estimation error of 25%.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Rigorous derivation of a nonlinear diffusion equation as fast-reaction limit of a continuous coagulation-fragmentation model with diffusion

Weak solutions of the spatially inhomogeneous (diffusive) Aizenmann-Bak model of coagulation-breakup within a bounded domain with homogeneous Neumann boundary conditions are shown to converge, in the fast reaction limit, towards local equilibria determined by their mass. Moreover, this mass is the solution of a nonlinear diffusion equation whose nonlinearity depends on the (size-dependent) diffusion coefficient. Initial data are assumed to have integrable zero order moment and square integrable first order moment in size, and finite entropy. In contrast to our previous result [CDF2], we are able to show the convergence without assuming uniform bounds from above and below on the number density of clusters.

Convergence of the mass-transport steepest descent scheme for the sub-critical Patlak-Keller-Segel model

Variational steepest descent approximation schemes for the modified Patlak-Keller-Segel equation with a logarithmic interaction kernel in any dimension are considered. We prove the convergence of the suitably interpolated in time implicit Euler scheme, defined in terms of the Euclidean Wasserstein distance, associated to this equation for sub-critical masses. As a consequence, we recover the recent result about the global in time existence of weak-solutions to the modified Patlak-Keller-Segel equation for the logarithmic interaction kernel in any dimension in the sub-critical case. Moreover, we show how this method performs numerically in one dimension. In this particular case, this numerical scheme corresponds to a standard implicit Euler method for the pseudo-inverse of the cumulative distribution function. We demonstrate its capabilities to reproduce easily without the need of mesh-refinement the blow-up of solutions for super-critical masses.

Blow-up, concentration phenomenon and global existence for the Keller-Segel model in high dimension

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