Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

"Water users must be efficient producers". Women's access to and use of land in Chókwè irrigation scheme, Mozambique

The irrigation scheme Eduardo Mondlane, situated in Chókwè District - in the Southern part of the Gaza province and within the Limpopo River Basin - is the largest in the country, covering approximately 30,000 hectares of land. Built by the Portuguese colonial administration in the 1950s to exploit the agricultural potential of the area through cash-cropping, after Independence it became one of Frelimo’s flagship projects aiming at the “socialization of the countryside” and at agricultural economic development through the creation of a state farm and of several cooperatives. The failure of Frelimo’s economic reforms, several infrastructural constraints and local farmers resistance to collective forms of production led to scheme to a state of severe degradation aggravated by the floods of the year 2000. A project of technical rehabilitation initiated after the floods is currently accompanied by a strong “efficiency” discourse from the managing institution that strongly opposes the use of irrigated land for subsistence agriculture, historically a major livelihood strategy for smallfarmers, particularly for women. In fact, the area has been characterized, since the end of the XIX century, by a stable pattern of male migration towards South African mines, that has resulted in an a steady increase of women-headed households (both de jure and de facto). The relationship between land reform, agricultural development, poverty alleviation and gender equality in Southern Africa is long debated in academic literature. Within this debate, the role of agricultural activities in irrigation schemes is particularly interesting considering that, in a drought-prone area, having access to water for irrigation means increased possibilities of improving food and livelihood security, and income levels. In the case of Chókwè, local governments institutions are endorsing the development of commercial agriculture through initiatives such as partnerships with international cooperation agencies or joint-ventures with private investors. While these business models can sometimes lead to positive outcomes in terms of poverty alleviation, it is important to recognize that decentralization and neoliberal reforms occur in the context of financial and political crisis of the State that lacks the resources to efficiently manage infrastructures such as irrigation systems. This kind of institutional and economic reforms risk accelerating processes of social and economic marginalisation, including landlessness, in particular for poor rural women that mainly use irrigated land for subsistence production. The study combines an analysis of the historical and geographical context with the study of relevant literature and original fieldwork. Fieldwork was conducted between February and June 2007 (where I mainly collected secondary data, maps and statistics and conducted preliminary visit to Chókwè) and from October 2007 to March 2008. Fieldwork methodology was qualitative and used semi-structured interviews with central and local Government officials, technical experts of the irrigation scheme, civil society organisations, international NGOs, rural extensionists, and water users from the irrigation scheme, in particular those women smallfarmers members of local farmers’ associations. Thanks to the collaboration with the Union of Farmers’ Associations of Chókwè, she has been able to participate to members’ meeting, to education and training activities addressed to women farmers members of the Union and to organize a group discussion. In Chókwè irrigation scheme, women account for the 32% of water users of the familiar sector (comprising plot-holders with less than 5 hectares of land) and for just 5% of the private sector. If one considers farmers’ associations of the familiar sector (a legacy of Frelimo’s cooperatives), women are 84% of total members. However, the security given to them by the land title that they have acquired through occupation is severely endangered by the use that they make of land, that is considered as “non efficient” by the irrigation scheme authority. Due to a reduced access to marketing possibilities and to inputs, training, information and credit women, in actual fact, risk to see their right to access land and water revoked because they are not able to sustain the increasing cost of the water fee. The myth of the “efficient producer” does not take into consideration the characteristics of inequality and gender discrimination of the neo-liberal market. Expecting small-farmers, and in particular women, to be able to compete in the globalized agricultural market seems unrealistic, and can perpetuate unequal gendered access to resources such as land and water.

Eco-Management and Audit Scheme (EMAS): An evaluation of success factors in the agricultural sector. The case of Italy's Emilia Romagna region.

Different tools have been used to set up and adopt the model for the fulfillment of the objective of this research. 1. The Model The base model that has been used is the Analytical Hierarchy Process (AHP) adapted with the aim to perform a Benefit Cost Analysis. The AHP developed by Thomas Saaty is a multicriteria decision - making technique which decomposes a complex problem into a hierarchy. It is used to derive ratio scales from both discreet and continuous paired comparisons in multilevel hierarchic structures. These comparisons may be taken from actual measurements or from a fundamental scale that reflects the relative strength of preferences and feelings. 2. Tools and methods 2.1. The Expert Choice Software The software Expert Choice is a tool that allows each operator to easily implement the AHP model in every stage of the problem. 2.2. Personal Interviews to the farms For this research, the farms of the region Emilia Romagna certified EMAS have been detected. Information has been given by EMAS center in Wien. Personal interviews have been carried out to each farm in order to have a complete and realistic judgment of each criteria of the hierarchy. 2.3. Questionnaire A supporting questionnaire has also been delivered and used for the interviews . 3. Elaboration of the data After data collection, the data elaboration has taken place. The software support Expert Choice has been used . 4. Results of the Analysis The result of the figures above (vedere altro documento) gives a series of numbers which are fractions of the unit. This has to be interpreted as the relative contribution of each element to the fulfillment of the relative objective. So calculating the Benefits/costs ratio for each alternative the following will be obtained: Alternative One: Implement EMAS Benefits ratio: 0, 877 Costs ratio: 0, 815 Benfit/Cost ratio: 0,877/0,815=1,08 Alternative Two: Not Implement EMAS Benefits ratio: 0,123 Costs ration: 0,185 Benefit/Cost ratio: 0,123/0,185=0,66 As stated above, the alternative with the highest ratio will be the best solution for the organization. This means that the research carried out and the model implemented suggests that EMAS adoption in the agricultural sector is the best alternative. It has to be noted that the ratio is 1,08 which is a relatively low positive value. This shows the fragility of this conclusion and suggests a careful exam of the benefits and costs for each farm before adopting the scheme. On the other part, the result needs to be taken in consideration by the policy makers in order to enhance their intervention regarding the scheme adoption on the agricultural sector. According to the AHP elaboration of judgments we have the following main considerations on Benefits: - Legal compliance seems to be the most important benefit for the agricultural sector since its rank is 0,471 - The next two most important benefits are Improved internal organization (ranking 0,230) followed by Competitive advantage (ranking 0, 221) mostly due to the sub-element Improved image (ranking 0,743) Finally, even though Incentives are not ranked among the most important elements, the financial ones seem to have been decisive on the decision making process. According to the AHP elaboration of judgments we have the following main considerations on Costs: - External costs seem to be largely more important than the internal ones (ranking 0, 857 over 0,143) suggesting that Emas costs over consultancy and verification remain the biggest obstacle. - The implementation of the EMS is the most challenging element regarding the internal costs (ranking 0,750).

Automated Segmentation and Non-Rigid Registration for the Quantitative Evaluation of Myocardial Perfusion from Magnetic Resonance Images

Myocardial perfusion quantification by means of Contrast-Enhanced Cardiac Magnetic Resonance images relies on time consuming frame-by-frame manual tracing of regions of interest. In this Thesis, a novel automated technique for myocardial segmentation and non-rigid registration as a basis for perfusion quantification is presented. The proposed technique is based on three steps: reference frame selection, myocardial segmentation and non-rigid registration. In the first step, the reference frame in which both endo- and epicardial segmentation will be performed is chosen. Endocardial segmentation is achieved by means of a statistical region-based level-set technique followed by a curvature-based regularization motion. Epicardial segmentation is achieved by means of an edge-based level-set technique followed again by a regularization motion. To take into account the changes in position, size and shape of myocardium throughout the sequence due to out of plane respiratory motion, a non-rigid registration algorithm is required. The proposed non-rigid registration scheme consists in a novel multiscale extension of the normalized cross-correlation algorithm in combination with level-set methods. The myocardium is then divided into standard segments. Contrast enhancement curves are computed measuring the mean pixel intensity of each segment over time, and perfusion indices are extracted from each curve. The overall approach has been tested on synthetic and real datasets. For validation purposes, the sequences have been manually traced by an experienced interpreter, and contrast enhancement curves as well as perfusion indices have been computed. Comparisons between automatically extracted and manually obtained contours and enhancement curves showed high inter-technique agreement. Comparisons of perfusion indices computed using both approaches against quantitative coronary angiography and visual interpretation demonstrated that the two technique have similar diagnostic accuracy. In conclusion, the proposed technique allows fast, automated and accurate measurement of intra-myocardial contrast dynamics, and may thus address the strong clinical need for quantitative evaluation of myocardial perfusion.

Iterative regularization methods for ill-posed problems

This Ph.D thesis focuses on iterative regularization methods for regularizing linear and nonlinear ill-posed problems. Regarding linear problems, three new stopping rules for the Conjugate Gradient method applied to the normal equations are proposed and tested in many numerical simulations, including some tomographic images reconstruction problems. Regarding nonlinear problems, convergence and convergence rate results are provided for a Newton-type method with a modified version of Landweber iteration as an inner iteration in a Banach space setting.