Exercise sheet 2

Exercises and solutions in LaTex

MA348exam 1998 pdf

Exam questions and solutions in PDF

Exercise sheet 1

Exercises and solutions in LaTex

MA167exam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

Aplicación de colas de Poisson en procesos de ‘toma de decisiones’ en la gestión de servicios médicos

En este documento se revisa teóricamente la distribución de probabilidad de Poisson como función que asigna a cada suceso definido, sobre una variable aleatoria discreta, la probabilidad de ocurrencia en un intervalo de tiempo o región del espacio disjunto. Adicionalmente se revisa la distribución exponencial negativa empleada para modelar el intervalo de tiempo entre eventos consecutivos de Poisson que ocurren de manera independiente; es decir, en los cuales la probabilidad de ocurrencia de los eventos sucedidos en un intervalo de tiempo no depende de los ocurridos en otros intervalos de tiempo, por esta razón se afirma que es una distribución que no tiene memoria. El proceso de Poisson relaciona la función de Poisson, que representa un conjunto de eventos independientes sucedidos en un intervalo de tiempo o región del espacio con los tiempos dados entre la ocurrencia de los eventos según la distribución exponencial negativa. Los anteriores conceptos se usan en la teoría de colas, rama de la investigación de operaciones que describe y brinda soluciones a situaciones en las que un conjunto de individuos o elementos forman colas en espera de que se les preste un servicio, por lo cual se presentan ejemplos de aplicación en el ámbito médico.

Determinants of demand for antenatal care in Colombia

Even though antenatal care is universally regarded as important, determinants of demand for antenatal care have not been widely studied. Evidence concerning which and how socioeconomic conditions influence whether a pregnant woman attends or not at least one antenatal consultation or how these factors affect the absences to antenatal consultations is very limited. In order to generate this evidence, a two-stage analysis was performed with data from the Demographic and Health Survey carried out by Profamilia in Colombia during 2005. The first stage was run as a logit model showing the marginal effects on the probability of attending the first visit and an ordinary least squares model was performed for the second stage. It was found that mothers living in the pacific region as well as young mothers seem to have a lower probability of attending the first visit but these factors are not related to the number of absences to antenatal consultation once the first visit has been achieved. The effect of health insurance was surprising because of the differing effects that the health insurers showed. Some familiar and personal conditions such as willingness to have the last children and number of previous children, demonstrated to be important in the determination of demand. The effect of mother’s educational attainment was proved as important whereas the father’s educational achievement was not. This paper provides some elements for policy making in order to increase the demand inducement of antenatal care, as well as stimulating research on demand for specific issues on health.

Geoadditive models for regional count data: an application to industrial location

We propose a geoadditive negative binomial model (Geo-NB-GAM) for regional count data that allows us to address simultaneously some important methodological issues, such as spatial clustering, nonlinearities, and overdispersion. This model is applied to the study of location determinants of inward greenfield investments that occurred during 2003–2007 in 249 European regions. After presenting the data set and showing the presence of overdispersion and spatial clustering, we review the theoretical framework that motivates the choice of the location determinants included in the empirical model, and we highlight some reasons why the relationship between some of the covariates and the dependent variable might be nonlinear. The subsequent section first describes the solutions proposed by previous literature to tackle spatial clustering, nonlinearities, and overdispersion, and then presents the Geo-NB-GAM. The empirical analysis shows the good performance of Geo-NB-GAM. Notably, the inclusion of a geoadditive component (a smooth spatial trend surface) permits us to control for spatial unobserved heterogeneity that induces spatial clustering. Allowing for nonlinearities reveals, in keeping with theoretical predictions, that the positive effect of agglomeration economies fades as the density of economic activities reaches some threshold value. However, no matter how dense the economic activity becomes, our results suggest that congestion costs never overcome positive agglomeration externalities.

Physical disability, recent illnesses and health self-assessment in a population-based study in Sao Paulo, Brazil

Objectives. To investigate health self-assessment and to estimate the prevalence of chronic diseases and recent illnesses in people with and without physical disabilities (PD) in the state of Sao Paulo, southeastern Brazil. Study design. A Cross-sectional study comprising two population-based health surveys conducted in 2002 and 2003. Methods. A total of 8317 persons (165 with PD) were interviewed in the two studies. Variables concerning to health self-assessment; chronic disease and recent illness were compared in the people with and without PD. Negative binomial regression was used in the analysis. Results. Subjects with PD more often assessed their health as poor/very poor compared to non-disabled ones. They reported more illnesses in the 15 days prior to interview as well as more chronic diseases (skin conditions, anaemia, chronic kidney disease, stroke, depression/anxiety, migraine/headache, pulmonary diseases, hypertension, diabetes, arthritis/arthrosis/rheumatic conditions and heart disease). This higher disease prevalence can be either attributed to disability itself or be associated to gender, age and schooling. Conclusions. Subjects with PD had more recent illnesses and chronic diseases and poorer health self-assessment than non-disabled ones. Age, gender, schooling and disability have individual roles in disease development among disabled people.

Random sums of exchangeable variables and actuarial applications

In this paper we study the accumulated claim in some fixed time period, skipping the classical assumption of mutual independence between the variables involved. Two basic models are considered: Model I assumes that any pair of claims are equally correlated which means that the corresponding square-integrable sequence is exchangeable one. Model 2 states that the correlations between the adjacent claims are the same. Recurrence and explicit expressions for the joint probability generating function are derived and the impact of the dependence parameter (correlation coefficient) in both models is examined. The Markov binomial distribution is obtained as a particular case under assumptions of Model 2. (C) 2007 Elsevier B.V. All rights reserved.

Amostragem seqüencial (presença-ausência) para Bemisia tabaci (Genn.) biótipo B (Hemiptera: Aleyrodidae) em feijoeiro (Phaseolus vulgaris L.)

A amostragem seqüencial (presença-ausência) vem sendo utilizada no manejo integrado de pragas pela rapidez e eficiência, principalmente, para pragas que são difíceis de serem quantificadas. Para o manejo de Bemisia tabaci (Genn.) biótipo B foi desenvolvido um plano de amostragem seqüencial, com base na presença ou ausência da praga em plantas de feijoeiro (Phaseolus vulgaris L.), independente do seu número. Os experimentos foram conduzidos nas épocas de semeadura das águas (2000/01) e da seca (2002), em Jaboticabal - SP, utilizando-se área de 1 ha, subdividida em 100 parcelas iguais de 100 m² (10 x 10 m). em cada parcela foram avaliadas 10 plantas ao acaso, considerando-se somente se a mosca-branca estava ou não presente. O nível de dano econômico adotado foi de 10% de infestação. A partir dos dados analisados, foram obtidas duas retas: uma superior (S1= 2,7095 + 0,1452n), a partir da qual recomenda-se o controle; e outra inferior (S0= -2,7095 + 0,1452n), até a qual o controle não é recomendado. Pelos resultados verifica-se que a amostragem seqüencial é eficiente na indicação ou não do controle da B. tabaci biótipo B na cultura do feijão.

Distribuição espacial de Bemisia tabaci (Genn.) biótipo B (Hemiptera: Aleyrodidae) em feijoeiro (Phaseolus vulgaris L.)

O estudo da distribuição espacial de pragas é fundamental para elaboração de planos de amostragem que possam propiciar maior adoção do manejo integrado de pragas. Para Bemisia tabaci (Genn.) biótipo B em feijoeiro Phaseolus vulgaris L., foram conduzidos ensaios de campo em uma área de 10.000 m², dividida em 100 parcelas iguais de 10 x 10 m, nas épocas de semeadura das águas e da seca. As amostragens foram realizadas semanalmente, em 10 plantas por parcela. Coletou-se um folíolo por planta e avaliou-se a presença-ausência de ninfas da mosca-branca na página abaxial. Para adultos, observou-se visualmente a presença-ausência da praga nas plantas. em todas as amostragens obtiveram-se valores menores que a unidade para a relação variância/média, indicando disposição regular da mosca-branca no campo, confirmada pelos valores significativos da estatística ½d½, do teste de afastamento da aleatoriedade, assim como pelos valores inferiores à unidade do índice de Morisita. A distribuição binomial positiva foi o modelo mais adequado para representar a distribuição espacial da B. tabaci biótipo B na cultura do feijão.

Physical disability, recent illnesses and health self-assessment in a population-based study in São Paulo, Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Choosing between Cox proportional hazards and logistic models for interval-censored data via bootstrap

This work develops a new methodology in order to discriminate models for interval-censored data based on bootstrap residual simulation by observing the deviance difference from one model in relation to another, according to Hinde (1992). Generally, this sort of data can generate a large number of tied observations and, in this case, survival time can be regarded as discrete. Therefore, the Cox proportional hazards model for grouped data (Prentice & Gloeckler, 1978) and the logistic model (Lawless, 1982) can befitted by means of generalized linear models. Whitehead (1989) considered censoring to be an indicative variable with a binomial distribution and fitted the Cox proportional hazards model using complementary log-log as a link function. In addition, a logistic model can be fitted using logit as a link function. The proposed methodology arises as an alternative to the score tests developed by Colosimo et al. (2000), where such models can be obtained for discrete binary data as particular cases from the Aranda-Ordaz distribution asymmetric family. These tests are thus developed with a basis on link functions to generate such a fit. The example that motivates this study was the dataset from an experiment carried out on a flax cultivar planted on four substrata susceptible to the pathogen Fusarium oxysoprum. The response variable, which is the time until blighting, was observed in intervals during 52 days. The results were compared with the model fit and the AIC values.

Catch-per-unit-effort: which estimator is best?

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Sum rules in the oscillator radiation processes

We consider the problem of a harmonic oscillator coupled to a scalar field in the framework of recently introduced dressed coordinates. We compute all the probabilities associated with the decay process of an excited level of the oscillator. Instead of doing direct quantum mechanical calculations we establish some sum rules from which we infer the probabilities associated to the different decay processes of the oscillator. Thus, the sum rules allows to show that the transition probabilities between excited levels follow a binomial distribution. (c) 2005 Published by Elsevier B.V.