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Esperimenti per modelli parzialmente lineari con applicazione ai computer experimentsZagoraiou, Maroussa <1979> 02 April 2008 (has links)
No description available.
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Analyzing the dependence structure of microarray data: a copula–based approachDi Lascio, Francesca Marta Lilja <1979> 02 April 2008 (has links)
The main aim of this Ph.D. dissertation is the study of clustering dependent data by means of copula
functions with particular emphasis on microarray data. Copula functions are a popular multivariate modeling
tool in each field where the multivariate dependence is of great interest and their use in clustering has not
been still investigated.
The first part of this work contains the review of the literature of clustering methods, copula functions
and microarray experiments. The attention focuses on the K–means (Hartigan, 1975; Hartigan and Wong,
1979), the hierarchical (Everitt, 1974) and the model–based (Fraley and Raftery, 1998, 1999, 2000, 2007)
clustering techniques because their performance is compared. Then, the probabilistic interpretation of the
Sklar’s theorem (Sklar’s, 1959), the estimation methods for copulas like the Inference for Margins (Joe and
Xu, 1996) and the Archimedean and Elliptical copula families are presented. In the end, applications of
clustering methods and copulas to the genetic and microarray experiments are highlighted.
The second part contains the original contribution proposed. A simulation study is performed in order to
evaluate the performance of the K–means and the hierarchical bottom–up clustering methods in identifying
clusters according to the dependence structure of the data generating process. Different simulations are
performed by varying different conditions (e.g., the kind of margins (distinct, overlapping and nested) and
the value of the dependence parameter ) and the results are evaluated by means of different measures of
performance.
In light of the simulation results and of the limits of the two investigated clustering methods, a new
clustering algorithm based on copula functions (‘CoClust’ in brief) is proposed. The basic idea, the iterative
procedure of the CoClust and the description of the written R functions with their output are given. The
CoClust algorithm is tested on simulated data (by varying the number of clusters, the copula models, the
dependence parameter value and the degree of overlap of margins) and is compared with the performance
of model–based clustering by using different measures of performance, like the percentage of well–identified
number of clusters and the not rejection percentage of H0 on .
It is shown that the CoClust algorithm allows to overcome all observed limits of the other investigated
clustering techniques and is able to identify clusters according to the dependence structure of the data
independently of the degree of overlap of margins and the strength of the dependence. The CoClust uses
a criterion based on the maximized log–likelihood function of the copula and can virtually account for
any possible dependence relationship between observations. Many peculiar characteristics are shown for the
CoClust, e.g. its capability of identifying the true number of clusters and the fact that it does not require a
starting classification.
Finally, the CoClust algorithm is applied to the real microarray data of Hedenfalk et al. (2001) both to
the gene expressions observed in three different cancer samples and to the columns (tumor samples) of the
whole data matrix.
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Modello multilevel a classi latenti: estensione al modello multidimensionaleDel Giovane, Cinzia <1979> 02 April 2008 (has links)
No description available.
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Topics in econometrics of financial marketsCoroneo, Laura <1980> 16 June 2008 (has links)
No description available.
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Bayesian Analysis of Linear Inverse Problems with Applications in Economics and FinanceSimoni, Anna <1980> 10 June 2009 (has links)
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.
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The wrapping approach for circular data Bayesian modelingFerrari, Clarissa <1976> 19 March 2009 (has links)
No description available.
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Markov exchangeable data and mixtures of Markov ChainsDi Cecco, Davide <1980> 19 March 2009 (has links)
No description available.
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Multiple testing in spatial epidemiology: a Bayesian approachVentrucci, Massimo <1980> 19 March 2009 (has links)
In this work we aim to propose a new approach for preliminary epidemiological
studies on Standardized Mortality Ratios (SMR) collected in many spatial
regions. A preliminary study on SMRs aims to formulate hypotheses to be investigated
via individual epidemiological studies that avoid bias carried on by
aggregated analyses. Starting from collecting disease counts and calculating expected
disease counts by means of reference population disease rates, in each
area an SMR is derived as the MLE under the Poisson assumption on each observation.
Such estimators have high standard errors in small areas, i.e. where
the expected count is low either because of the low population underlying the
area or the rarity of the disease under study. Disease mapping models and other
techniques for screening disease rates among the map aiming to detect anomalies
and possible high-risk areas have been proposed in literature according to
the classic and the Bayesian paradigm. Our proposal is approaching this issue
by a decision-oriented method, which focus on multiple testing control, without
however leaving the preliminary study perspective that an analysis on SMR
indicators is asked to. We implement the control of the FDR, a quantity largely
used to address multiple comparisons problems in the eld of microarray data
analysis but which is not usually employed in disease mapping. Controlling
the FDR means providing an estimate of the FDR for a set of rejected null
hypotheses.
The small areas issue arises diculties in applying traditional methods
for FDR estimation, that are usually based only on the p-values knowledge
(Benjamini and Hochberg, 1995; Storey, 2003). Tests evaluated by a traditional
p-value provide weak power in small areas, where the expected number of disease
cases is small. Moreover tests cannot be assumed as independent when spatial
correlation between SMRs is expected, neither they are identical distributed
when population underlying the map is heterogeneous.
The Bayesian paradigm oers a way to overcome the inappropriateness of
p-values based methods. Another peculiarity of the present work is to propose
a hierarchical full Bayesian model for FDR estimation in testing many null
hypothesis of absence of risk.We will use concepts of Bayesian models for disease
mapping, referring in particular to the Besag York and Mollié model (1991) often
used in practice for its exible prior assumption on the risks distribution across
regions. The borrowing of strength between prior and likelihood typical of a
hierarchical Bayesian model takes the advantage of evaluating a singular test
(i.e. a test in a singular area) by means of all observations in the map under
study, rather than just by means of the singular observation. This allows to
improve the power test in small areas and addressing more appropriately the
spatial correlation issue that suggests that relative risks are closer in spatially
contiguous regions.
The proposed model aims to estimate the FDR by means of the MCMC
estimated posterior probabilities b i's of the null hypothesis (absence of risk) for
each area. An estimate of the expected FDR conditional on data (\FDR) can
be calculated in any set of b i's relative to areas declared at high-risk (where thenull hypothesis is rejected) by averaging the b i's themselves. The\FDR can be
used to provide an easy decision rule for selecting high-risk areas, i.e. selecting
as many as possible areas such that the\FDR is non-lower than a prexed
value; we call them\FDR based decision (or selection) rules. The sensitivity
and specicity of such rule depend on the accuracy of the FDR estimate, the
over-estimation of FDR causing a loss of power and the under-estimation of
FDR producing a loss of specicity. Moreover, our model has the interesting
feature of still being able to provide an estimate of relative risk values as in the
Besag York and Mollié model (1991).
A simulation study to evaluate the model performance in FDR estimation
accuracy, sensitivity and specificity of the decision rule, and goodness of
estimation of relative risks, was set up. We chose a real map from which we
generated several spatial scenarios whose counts of disease vary according to
the spatial correlation degree, the size areas, the number of areas where the
null hypothesis is true and the risk level in the latter areas. In summarizing
simulation results we will always consider the FDR estimation in sets
constituted by all b i's selected lower than a threshold t. We will show graphs of
the\FDR and the true FDR (known by simulation) plotted against a threshold
t to assess the FDR estimation. Varying the threshold we can learn which FDR
values can be accurately estimated by the practitioner willing to apply the model
(by the closeness between\FDR and true FDR). By plotting the calculated
sensitivity and specicity (both known by simulation) vs the\FDR we can
check the sensitivity and specicity of the corresponding\FDR based decision
rules. For investigating the over-smoothing level of relative risk estimates we will
compare box-plots of such estimates in high-risk areas (known by simulation),
obtained by both our model and the classic Besag York Mollié model. All the
summary tools are worked out for all simulated scenarios (in total 54 scenarios).
Results show that FDR is well estimated (in the worst case we get an overestimation,
hence a conservative FDR control) in small areas, low risk levels and
spatially correlated risks scenarios, that are our primary aims. In such scenarios
we have good estimates of the FDR for all values less or equal than 0.10. The
sensitivity of\FDR based decision rules is generally low but specicity is high.
In such scenario the use of\FDR = 0:05 or\FDR = 0:10 based selection rule can
be suggested. In cases where the number of true alternative hypotheses (number
of true high-risk areas) is small, also FDR = 0:15 values are well estimated, and
\FDR = 0:15 based decision rules gains power maintaining an high specicity.
On the other hand, in non-small areas and non-small risk level scenarios the
FDR is under-estimated unless for very small values of it (much lower than
0.05); this resulting in a loss of specicity of a\FDR = 0:05 based decision rule.
In such scenario\FDR = 0:05 or, even worse,\FDR = 0:1 based decision rules
cannot be suggested because the true FDR is actually much higher. As regards
the relative risk estimation, our model achieves almost the same results of the
classic Besag York Molliè model. For this reason, our model is interesting for
its ability to perform both the estimation of relative risk values and the FDR
control, except for non-small areas and large risk level scenarios. A case of study
is nally presented to show how the method can be used in epidemiology.
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Network Externalities in Developing EconomiesComola, Margherita <1979> 16 June 2008 (has links)
This thesis contains three essays on microeconometrics, networks and economic development. In the first two essays I focus on developing country settings (Tanzania and Nepal respectively) to study how rural villagers form their social networks, and how the existence of these informal links impacts their welfare. The third essay focuses on the international trade of arms to investigate whether the political orientation of government in power makes any difference to arms export policy.
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A bayesian model for mixed responses and skew laten variable to measure HRQoL in childrenBroccoli, Serena <1982> 30 March 2010 (has links)
The aim of the thesi is to formulate a suitable Item Response Theory (IRT) based model to measure HRQoL (as latent variable) using a mixed responses questionnaire and relaxing the hypothesis of normal distributed latent variable. The new model is a combination of two models already presented in literature, that is, a latent trait model for mixed responses and an IRT model for Skew Normal latent variable. It is developed in a Bayesian framework, a Markov chain Monte Carlo procedure is used to generate samples of the posterior distribution of the parameters of interest. The proposed model is test on a questionnaire composed by 5 discrete items and one continuous to measure HRQoL in children, the EQ-5D-Y questionnaire. A large sample of children collected in the schools was used. In comparison with a model for only discrete responses and a model for mixed responses and normal latent variable, the new model has better performances, in term of deviance information criterion (DIC), chain convergences times and precision of the estimates.
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