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Recent Advances in Approximate Bayesian Computation Methods
Get PDFThe Bayesian approach to statistical inference in fundamentally probabilistic. Exploiting the internal consistency of the probability framework, the posterior distribution extracts the relevant information in the data, and provides a complete and coherent summary of post data uncertainty. However, summarising the posterior distribution often requires the calculation of awkward multidimensional integrals. A further complication with the Bayesian approach arises when the likelihood functions is unavailable. In this respect, promising advances have been made by theory of Approximate Bayesian Computations (ABC).
This thesis focuses on computational methods for the approximation of posterior distributions, and it discusses six original contributions. The first contribution concerns the approximation of marginal posterior distributions for scalar parameters. By combining higher-order tail area approximation with the inverse transform sampling, we define the HOTA algorithm which draws independent random sample from the approximate marginal posterior. The second discusses the HOTA algorithm with pseudo-posterior distributions, \eg, posterior distributions obtained by the combination of a pseudo-likelihood with a prior within Bayes' rule. The third contribution extends the use of tail-area approximations to contexts with multidimensional parameters, and proposes a method which gives approximate Bayesian credible regions with good sampling coverage properties. The forth presents an improved Laplace approximation which can be used for computing marginal likelihoods. The fifth contribution discusses a model-based procedure for choosing good summary statistics for ABC, by using composite score functions. Lastly, the sixth contribution discusses the choice of a default proposal distribution for ABC that is based on the notion of quasi-likelihood
A Quasi likelihood approximation of posterior distributions for likelihood-intractable complex models
No full textComplex models typically involve intractable likelihood functions which, from a Bayesian perspective, lead to intractable posterior distributions. In this context, Approximate Bayesian computation (ABC) methods can be used in order to obtain a valid posterior
approximation. However, when simulation from the model is computationally demanding, then the ABC approach may be cumbersome. We discuss an alternative method, where the intractable likelihood is approximated by a quasi-likelihood calculated through an algorithm that is reminiscent of the ABC. The proposed approximation method requires less computational effort than ABC. An extension to multiparameter models is also considered and the method is illustrated by several examples
Approximate Bayesian Computation by modelling summary statistics in a quasi-likelihood framework
Get PDFApproximate Bayesian Computation (ABC) is a useful class of methods for Bayesian inference when the likelihood function is computationally intractable. In practice, the basic ABC algorithm may be inefficient in the presence of discrepancy between prior and posterior. Therefore, more elaborate methods, such as ABC with the Markov chain Monte Carlo algorithm (ABC-MCMC), should be used. However, the elaboration of a proposal density for MCMC is a sensitive issue and very difficult in the ABC setting, where the likelihood is intractable. We discuss an automatic proposal distribution useful for ABC-MCMC algorithms. This proposal is inspired by the theory of quasi-likelihood (QL) functions and is obtained by modelling the distribution of the summary statistics as a function of the parameters. Essentially, given a real-valued vector of summary statistics, we reparametrize the model by means of a regression function of the statistics on parameters, obtained by sampling from the original model in a pilot-run simulation study. The QL theory is well established for a scalar parameter, and it is shown that when the conditional variance of the summary statistic is assumed constant, the QL has a closed-form normal density. This idea of constructing proposal distributions is extended to non constant variance and to real-valued parameter vectors. The method is illustrated by several examples and by an application to a real problem in population genetics
Analysis of MRI data in patients with anosmia from COVID-19 by high-dimensional cumulative logit model
No full textreservedLa sindrome respiratoria acuta grave Coronavirus-2 (SARS-CoV-2) è stata responsabile della pandemia globale di COVID-19, caratterizzata principalmente da sintomi respiratori ma con la capacità di diffondersi anche ad altri distretti del corpo umano, come il sistema nervoso centrale e periferico, e provocare danni ai muscoli scheletrici. In particolare, il COVID-19 può causare la perdita del senso dell'olfatto (anosmia) e del gusto (ageusia) in una percentuale significativa di pazienti. La tesi si concentra sul ruolo della morfologia del nervo olfattivo e del bulbo, analizzati tramite risonanza magnetica, nella formulazione di una prognosi sul possibile recupero olfattivo post-riabilitazione. Il dataset utilizzato proviene da pazienti affetti da COVID-19 e con anosmia e ageusia, sottoposti a riabilitazione, e presenta un elevato numero di variabili. Sono state utilizzate tecniche di analisi statistica descrittiva e un modello logit cumulativo ad elevata dimensionalità per analizzare i dati derivanti dalle risonanze magnetiche e predire il recupero olfattivo dei pazienti
Allergic contact dermatitis in the elderly compared over time with the young people
No full textopenLa dermatite allergica da contatto (DAC) è una reazione infiammatoria cutanea derivante dal contatto con sostanze allergeniche in grado di stimolare una risposta immunologica. Il patch test è il principale metodo diagnostico per identificare gli allergeni responsabili di tali reazioni. Tuttavia, le reazioni di ipersensibilità ritardata possono variare con l'età. Da un lato, l'invecchiamento è associato a un declino delle funzioni immunitarie, il che potrebbe ridurre la frequenza delle reazioni allergiche nei pazienti anziani rispetto ai più giovani. D'altro canto, gli anziani sono maggiormente esposti all'influenza di fattori ambientali e all'uso prolungato di farmaci, il che potrebbe aumentare la probabilità di sviluppare sensibilizzazioni cutanee.
Lo studio mira a valutare la reattività al patch test negli anziani, analizzando retrospettivamente i dati della Clinica Dermatologica dell'Università di Padova tra il 2006 e il 2019. Sono confrontati 709 pazienti di età pari o superiore a 65 con un gruppo di controllo di 1668 adulti tra i 18 e i 40 anni. Inoltre, si propone un modello di regressione per stimare la probabilità che un paziente sia positivo ad almeno un allergene durante il patch test, tenendo conto delle caratteristiche individuali e della storia personale e familiare di malattie atopiche. Infine, i risultati dell'analisi sono comparati con quelli ottenuti da uno studio simile condotto dalla Clinica Dermatologica di Padova e altri centri facenti parte del Gruppo Dermatite da Contatto Nord-Est Italia (NEICDG) nel periodo 1997-2001.Allergic contact dermatitis (ACD) is an inflammatory skin reaction resulting from contact with allergenic substances that can stimulate an immunologic response. Patch testing is the main diagnostic method to identify the allergens responsible for such reactions. However, delayed hypersensitivity reactions may vary with age. On one hand, aging is associated with a decline in immune function, which may reduce the frequency of allergic reactions in elderly patients compared with younger patients. On the other hand, the elderly are more exposed to the influence of environmental factors and prolonged use of medications, which could increase the likelihood of developing skin sensitization.
The study aims to assess patch test reactivity in the elderly by retrospectively analyzing data from the Dermatology Clinic of the University of Padua between 2006 and 2019. It compares 709 patients aged 65 and older with a control group of 1668 adults aged 18 to 40 years. In addition, a regression model is proposed to estimate the probability of a patient being positive for at least one allergen during patch testing, taking into account individual characteristics and personal and family history of atopic diseases. Finally, the results of the analysis are compared with those obtained from a similar study conducted by the Padua Dermatology Clinic and other centers that are part of the Northeast Italy Contact Dermatitis Group (NEICDG) during 1997-2001
Analysis of air pollution starting from the data coming from the control units located in the province of Padua
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Statistical study on asthmatic patients suffering from small airway dysfunction
No full textreservedQuesto studio si propone di valutare l'impatto delle disfunzioni delle piccole vie aeree sul controllo dell'asma nei pazienti affetti da asma intermittente, trattati con monoterapia SABA(agonisti beta-adrenergici a breve durata d'azione). L'obiettivo principale è analizzare i principali fattori che influenzano la presenza delle disfunzioni delle piccole vie aeree (SAD).This study aims to evaluate the impact of small airway dysfunction on asthma control in patients with intermittent asthma treated with SABA (short-acting beta-adrenergic agonist) monotherapy. The main objective is to analyze the main factors that influence the presence of small airway dysfunction (SAD)
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