Dissertations / Theses on the topic 'Bayesian Information Criterion'

This paper intend to find the proper hypothesis and test statistic for testing existence of bilaterally contamination when there exists nuisance parameter. The test statistic is based on method of moments estimators. Union-Intersection test is used for testing if the distribution of population can be implemented by a bilaterally contaminated normal model with unknown variance. This paper also developed a hierarchical normal mixture model (HNM) and applied it to birth weight data. EM algorithm is employed for parameter estimation and a singular Bayesian information criterion (sBIC) is applied to choose the number components. We also proposed a singular flexible information criterion which in addition involves a data-driven penalty.

This thesis was a step forward in gaining insight into falls in people with early stages of Parkinson's disease (PD), and in monitoring the disease progression based on clinical assessments. This research contributes new knowledge by providing new insights into utilizing information provided by the clinically administered instruments used routinely for the assessment of PD severity. The novel approach to modelling the progression of PD symptoms using multi-variable clinical assessment measurements for longitudinal data provides a new perspective into disease progression.

The processes of evaluation of environmental stimuli and decision are common in everyday life and in many social and economic situations. These processes are generally described in scientific literature using multi-attribute choice models. These models assume that evaluation of a stimulus described by several attributes results from a multi-stage process (Anderson, 1981; Lynch, 1985): evaluation of the attributes, integration of the values of the attributes and explicit evaluation of the stimulus. Commonly, in this field, experimental settings require the evaluation of a set of stimuli built combining some attributes. A subject evaluator examines the attributes of each stimulus; using her “mental” model of choice (Oral & Kettani, 1989), it assigns a value to attributes and formulate an overall judgment. Finally, subject expresses his opinion in terms of order-ranking, pairwise preference comparisons, values in a rating scale, and so on. This so-called multi-attribute evaluation suffers of a fundamental difficulty to measure the values of each attribute of a stimulus starting by the overall evaluation of each subject. Basically, the problem is to derive each value decomposing the overall judgment (i.e. the response output). This difficulty in measuring is typical in most of the often complementary multi-attribute models traditions, as those of Conjoint Analysis (Luce & Tukey, 1964; Krantz & Tversky, 1971; Green & Rao, 1971) or Information Integration Theory (IIT: Anderson, 1970, 1981, 1982). According to Anderson’s IIT, cognitive system give a subjective value to each characteristic of a stimulus, and the values are put together in a overall judgment using a specific integration function. IIT describe integration modalities using different mathematical rules, and functional measurement is the methodology proposed to determine and measure the integration function. Functional measurement use factorial experiments, selecting some attributes of a stimulus and combining them in factorial plans. Usually, subject’s evaluations for each cell of experimental design are reported on a category scale, and each subject replicates each evaluation for more trials. Starting from subject’s evaluations, functional measurement aims to quantify the value of each level of factors and its importance in the global judgment, for each subject evaluator or group of subjects. Anderson’s theory suggests that the most widely used integration rules are of three fundamental and simple kinds: additive, multiplicative and weighted average. Statistical techniques as the analysis of variance can be used to detect the integration rule on the basis of the goodness of fit. The averaging rule in particular can account for interaction effects between factors, splitting evaluation in two components: scale value and weight, which can be identified and measured separately (Zalinski & Anderson, 1989). If scale value represents the location of the level of attribute on the response scale, the weight represents his importance into global judgment. Averaging model provides a useful way to manage interaction between factors, surpassing the assumption of independence on which most applications of multi-attribute choice models are based. However, the model presents some critical points about the estimation issue, and for this motivation it potential is not fully exploited up until now. In this research work, a new method for parameter estimation for averaging model is proposed. The method provides a way to select the best set of parameters to fit data, and aims to overcome some problems that have limited the use of the model. According to this new method, named R-Average (Vidotto & Vicentini, 2007; Vidotto, Massidda & Noventa, 2010), the choice of optimal model is made according to so-called “principle of parsimony”: the best model is the “simplest” one which found the best compromise between explanation of phenomenon (explained variance) and structural complexity (number of different weight parameters). Selection process use in combination two goodness-of-fit indexes: Akaike Information Criterion (AIC; Akaike, 1974) and Bayesian Information Criterion (BIC; Schwarz, 1978). Both indexes are derived starting from the logarithm of the residual variance weighted for the number of observations, and by penalizing the models with additional parameters. AIC and BIC differ in penalty function - since the BIC imposes a larger penalty for complex models than the AIC does - and are very useful for model comparison. In this research work, two version of R-Average method are presented. This two versions are one evolution of the other, and both methods are structured in some procedures to perform estimation. Basically, R-Average consists of three procedures: EAM Procedure, DAM Procedure and Information Criteria (IC) Procedure. EAM, DAM and IC differ in constraints imposed on weights during the optimization process. EAM Procedure constrains all the weight within each factor to be equal, estimating an Equal-weight Averaging Model. This model is the optimum in terms of parsimony, because it presents the smallest number of parameters (one single weight for all levels of each factor). In fact, it is defined as “parsimonious” a simple model, in which the weights are equal. Differently, DAM Procedure does not impose constraints on the weights, leaving their free to vary. Thus, this procedure may converge to a complete Differential-weight Averaging Model, which is the less parsimonious model (i.e. all the weights of each level of each factor are different). The core of R-Average method is the Information Criteria Procedure. This procedure is based on idea that, from a psychological point of view, a simple model is more plausible than a complex model. For this reason, estimation algorithm is not oriented to search parameters that explain the greater proportion of variance, but search a compromise between explained variance and model complexity. A complex model will be evaluated as better than a simpler one only if the allows a significantly higher degree of explanation of phenomenon. IC Procedure search the model, trying to keep (in the “forward” version) or to make (in the “backward” version) all the weights equal. In the forward version, the procedure starts from the EAM model and spans all the possible combination of weights, modifying it: initially one by one, then two by two, then three by three and so on. For each combination, the procedure tries to diversifies weights. From time to time, using BIC and AIC indexes, the procedure selects the best set of parameters and assume the selected model as reference for the following step (if an evidence of improvement is found). In the backward version, the procedure starts from the DAM model and spans all the possible combinations of weights, trying to equalize them. BIC and AIC are used to compare the new models with the reference model: if a new model is detected as better than the reference one, it will used as new reference for following steps. Finally, all the estimated models by the procedures are compared, and the best model based on information criteria is preferred. The original formulation of the averaging model was modified in the evolution of the basic R-Average method. This reformulation considers the weight not as simply w parameters but as w = exp(t). This exponential transformation leads to a solution for classical problem of uniqueness which affect averaging formulation (Vidotto, 2011). Furthermore, this reformulation justifies the application of cluster analysis algorithms on weight values, necessary for the clustering procedure of experimental subjects on the basis of their similarity. In fact, the distance between two t values can be evaluated in terms of simply difference. Differently, the distance between two w values can be evaluated only in terms of ratio between them. This allows to use clustering algorithms of subjects based on matrices of proximity between parameters. The performance of R-Average was tested using Monte Carlo studies and practical applications in three different research fields: in marketing, in economic decision theory and in interpersonal trust. Results of Monte Carlo studies show a good capability of the method to identify parameters of averaging model. Scale parameters are in general well estimated. Differently, weight estimation is a bit more critical. Punctual estimation of the real value of weights are not precise as the estimation of scale values, in particular as the standard deviation of the error component in observed data increases. However, estimations appears reliable, and equalities between weights are identified. The increasing of the number of experimental trials can help model selection when the errors present a greater standard deviation. In summary, R-Average appear as an useful instrument to select the best model within the family of averaging models, allowing to manage particular multi-attribute conditions in functional measurement experiments. R-Average method was applied in a first study in marketing field. In buying a product, people express a preference for particular products: understanding cognitive processes underlying the formulation of consumers’ preferences is an important issue. The study was conducted in collaboration with a local pasta manufacturer, the Sgambaro company. The aims of research were three: understand the consumer’s judgment formulation about a market product, test the R-Average method in real conditions, and provide to Sgambaro company useful information for a good marketing of its product. Two factors was manipulated: the packaging of the Sgambaro’s pasta (Box with window, Box without window and Plastic bag) and the price (0.89€, 0.99€, 1.09€). Analyses started considering evaluations of the product express by participants: for each subject, parameters of averaging model was estimated. Since the consumers population is presumably not homogeneous in preferences, the overall sample has been split in three clusters (simply named A, B and C) by an cluster analysis algorithm. For both Price and Packaging factors, different clusters showed different ratings. Cluster A express judgments that are positioned on the center of scale, suggesting as participants are not particularly attracted by this products. By contrast, Cluster B express positive judgments, and Cluster C express globally negative with the exception of the package “box with window”. For packaging, it observes that the box with window, although is not the preferred one in the three clusters, has always positive evaluations, while judgments on other packaging are inconsistent across groups. Therefore, if the target of potential consumers for the product is the general population, the box with window can be considered the most appreciated packaging. Moreover, in Cluster C ANOVA shows a significant interaction between Price and Packaging. In fact, estimated parameters of averaging model show that Cluster C is greatly affected by a high price. In this cluster the highest price had a double weight in the final ratings, therefore the positive influence on the judgment of the “box with window” packaging could be invalidated. It’s important to notice that the group which is more sensitive to the high price is also that one which gave the lowest ratings compared to the other clusters. In a second experiment, the R-Average method has been applied in a study in the field of economic decision marking under risk. The assumption that moved the study is that, when a person must evaluate an economic bet in a risky situation, person integrates cognitively the economic value of bet and the probability to win. In the past, Shanteau (1974) shown that integration between value and probability is made according a multiplicative rule. The study, as Lynch (1979), highlighted that when the situation concern two simultaneous bets, each one composed from a value and a probability, judgments for double bet is different to the sum of judgments for single bets. This observation, named subadditivity effect, violate the assumptions of Expected Utility Theory. The proposed study analyze the convenience/satisfaction associated with single and duplex bets. The study proposed to participants two kind of bets. A first group of bets involved a good (Mobile Phones), and the other one, a service (free SMS per day); to each good/service was associated the a probability to obtained him. Two experimental conditions was defined. In the first condition, subjects judge bets considering that phones come from a good company, and SMS service came from a untrustworthy provider. In the reverse condition, subjects judge bets considering that phones was made with low-quality and come from a untrustworthy company, and SMS service come from a strong and trustworthy provider. For duplex bets, the presence of averaging integration model was hypnotized, and the parameters of model was estimated using R-Average on each subject. Results show that the integration in presence of a duplex bet is fully compatible with an averaging model: the averaging and not adding appear the correct integration rule. In the last experiment, averaging model and R-Average methodology were applied to study trust beliefs in three contexts of everyday life: interpersonal, institutional and organizational. Trusting beliefs are a solid persuasion that trustee has favorable attributes to induce trusting intentions. Trusting beliefs are relevant factors in making an individual to consider another individual as trustworthy. They modulate the extent to which a trustor feels confident in believing that a trustee is trustworthy. According to McKnight, Cummings & Chervany (1998), the most cited trusting beliefs are: benevolence, competence, honesty/integrity and predictability. The basic idea under the proposed study is that beliefs might be cognitive integrated in the concept of trustworthiness with some weighting processes. The R-Average method was used to identify parameters of averaging model for each participant. As main result, analysis shown that, according to McKnight, Cummings & Chervany (1998), the four main beliefs play a fundamental role in judging trust. Moreover, agreeing with information integration theory and functional measurement, an averaging model seems to explain individual responses. The great majority of participants could be referred to the differential-weight case. While scale values show a neat linear trend with higher slopes for honesty and competence, weights show differences with higher mean values, still, for honesty and competence. These results are coherent with the idea that different attributes play a different role in the final judgment: indeed, honesty and competence seem to play the major role while predictability seems less relevant. Another interesting conclusion refers to the high weight of the low level of honesty; it seems to show how a belief related to low integrity play the most important role for a final negative judgment. Finally, the different tilt of the trend for the levels of the attributes in the three situational contexts suggests a prominent role of the honesty in the interpersonal scenarios and of the competence in the institutional scenarios. In conclusion, information integration theory and functional measurement seem to represent an interesting approach to comprehend the human judgment formulation. This research work proposes a new method to estimate parameters of averaging models. The method shows a good capability to identify parameters and opens new scenarios in information integration theory, providing a good instrument to understand more in detail the averaging integration of attributes<br>I processi di valutazione degli stimoli ambientali e di decisione sono comuni nella vita quotidiana e in tante situazioni di carattere sociale ed economico. Questi processi sono generalmente descritti dalla letteratura scientifica utilizzando modelli di scelta multi-attributo. Tali modelli assumono che la valutazione di uno stimolo descritto da più attributi sia il risultato di un processo a più stadi (Anderson, 1981; Lynch, 1985): valutazione degli attributi, integrazione dei valori e valutazione esplicita dello stimolo. Comunemente, in questo campo, le situazioni sperimentali richiedono la valutazione di un set di stimoli costruiti combinando diversi attributi. Un soggetto valutatore esamina gli attributi di ogni stimolo; usando il solo modello “mentale” di scelta (Oral e Kettani, 1989), assegna un valore agli attributi e formula un giudizio globale. Infine, il soggetto esprime la sua opinione in termini di ordinamento, preferenze a coppie, valori su una scala numerica e così via. Questa cosiddetta valutazione multi-attributo soffre di una fondamentale difficoltà nel misurare i valori di ogni attributo di uno stimolo partendo dalle valutazioni complessive di ogni soggetto. Fondamentalmente, il problema è derivare ogni valore decomponendo il giudizio complessivo (cioè la risposta in output). Questa difficoltà di misurazione è tipica di molte delle spesso complementari tradizioni dei modelli multi-attributo, come la Conjoint Analysis (Luce e Tukey, 1964; Krantz e Tversky, 1971; Green e Rao, 1971) o la Teoria dell’Integrazione delle Informazioni (IIT: Anderson, 1970, 1981, 1982). Secondo la IIT di Anderson, il sistema cognitivo fornisce un valore soggettivo a ogni caratteristica di uno stimolo, e tali valori vengono combinati in un giudizio complessivo utilizzando una specifica funzione d’integrazione. La IIT descrive le modalità d’integrazione utilizzando differenti regole matematiche, e la misurazione funzionale è la metodologia proposta per determinare e misurare la funzione d’integrazione. La misurazione funzionale si serve di esperimenti fattoriali, selezionando alcuni attributi di uno stimolo e combinandoli in piani fattoriali. Solitamente, le valutazioni dei soggetti per ogni cella del disegno sperimentale sono riportate su una category scale, e ogni soggetto ripete la valutazione per più prove. Partendo dalle valutazioni soggettive, la misurazione funzionale mira a quantificare il valore di ogni livello dei fattori e la sua importanza nel giudizio complessivo, per ogni soggetto valutatore o gruppo di soggetti. La teoria di Anderson suggerisce che le regole d’integrazione più ampiamente utilizzate sono di tre fondamentali e semplici tipologie: additiva, moltiplicativa e di media ponderata (averaging). Tecniche statistiche come l’analisi della varianza possono essere utilizzare per individuare la regola d’integrazione sulla base della bontà dell’adattamento. La regola averaging in particolare è in grado di tenere in considerazione gli effetti d’interazione tra i fattori, scindendo la valutazione in due componenti: valore di scala e peso, che possono essere identificati e misurati separatamente (Zalisnki e Anderson, 1989). Se il valore di scala rappresenta il posizionamento del livello del fattore sulla scala di risposta, il peso rappresenta la sua importanza nel giudizio complessivo. Il modello averaging fornisce una via molto utile per gestire gli effetti d’interazione tra i fattori, superando l’assunto d’indipendenza sul quale molte applicazioni dei modelli di scelta multi-attributo sono basate. Tuttavia, il modello presenta alcuni punti critici relativi alla questione della stima, e per questo motivo il suo potenziale non è stato pienamente sfruttano fin’ora. In questo lavoro di ricerca viene proposto un nuovo metodo per la stima dei parametri del modello averaging. Il metodo consente di selezionare il miglior set di parametri per adattare i dati, e mira a superare alcuni problemi che ne hanno limitato l’uso. Secondo questo nuovo metodo, chiamato R-Average (Vidotto e Vicentini, 2007; Vidotto, Massidda e Noventa, 2010), la scelta del miglior modello è fatta in accordo al cosiddetto “principio di parsimonia”: il miglior modello è quello più “semplice”, che trova il miglior compromesso tra spiegazione del fenomeno (varianza spiegata) e complessità strutturale (numero di parametri di peso diversi). Il processo di selezione usa in combinazione due indici di bontà dell’adattamento: l’Akaike Information Criterion (AIC; Akaike, 1974) e il Bayesian Information Criterion (BIC; Schwartz, 1978). Entrambi gli indici sono ricavati partendo dal logaritmo della varianza residua pesata per il numero di osservazioni, e penalizzando i modelli con parametri aggiuntivi. AIC e BIC differiscono nella funzione di penalizzazione – dato che il BIC impone una penalità maggiore ai modelli con più parametri – e sono molto utili per la comparazione fra modelli. In questo lavoro di ricerca vengono presentate due versioni del metodo R-Average. Queste due versioni sono una l’evoluzione dell’altra, ed entrambi i metodi sono strutturati in diverse procedure per eseguire la stima. Fondamentalmente, R-Average consta di tre procedure: procedura EAM, procedura DAM e procedura Information Criteria (IC). EAM, DAM e IC differiscono nei vincoli imposti sui pesi durante il processo di ottimizzazione. La procedura EAM vincola tutti i pesi all’interno di ogni fattore a essere uguali, stimando un modello a pesi uguali. Questo modello è il migliore in termini di parsimonia, perché presenta il minor numero di parametri (uno unico per ogni fattore). Infatti, si definisce come “parsimonioso” un modello semplice, nel quale i pesi sono uguali. Diversamente, la procedura DAM non impone alcun vincolo sui pesi, lasciandoli liberi di variare. Così, questa procedura può potenzialmente convergere verso un modello averaging a pesi completamente diversi (dove cioè tutti i pesi dei livelli di ogni fattore sono diversi). Il cuore del metodo R-Average è la procedura Information Criteria. Questa procedura è basata sull’idea che, da un punto di vista psicologico, un modello semplice è più plausibile di un modello complesso. Per questo motivo, l’algoritmo di stima non è volto alla ricerca dei parametri che spiegano la maggior quota di varianza, ma cerca un compromesso tra varianza spiegata e complessità del modello. Un modello complesso sarà valutato come migliore di uno più semplice solo se permette di ottenere un grado significativamente superiore di spiegazione del fenomeno. La procedura IC cerca il modello provando a tenere (nella versione “forward”) o a rendere (nella versione “backward”) tutti i pesi uguali. Nella versione forward, la procedura parte dal modello EAM e passa in rassegna tutte le possibili combinazioni di pesi, modificandole: inizialmente uno a uno, poi due a due, poi tre a tre e così via. Per ogni combinazione, la procedura prova a diversificare i pesi. Di volta in volta, utilizzando gli indici BIC e AIC, la procedura seleziona il miglior set di parametri e assume il modello selezionato come rifermento per il passo successivo (se un’evidenzia di miglioramento viene trovata). Nella versione backward, la procedura parte dal modello DAM e passa in rassegna tutte le possibili combinazioni di pesi, provando a renderli uguali. Gli indici BIC e AIC sono utilizzati per comparare i nuovi modelli con quelli di riferimento: se un nuovo modello viene individuato come migliore di quello di riferimento, sarà utilizzato come nuovo riferimento per i passi successivi. Infine, tutti i modelli stimati dalle procedure vengono comparati, e il quello migliore sulla base dei criteri dell’informazione viene scelto. La formulazione originale del modello averaging è stata modificata nell’evoluzione del metodo R-Average di base. Questa riformulazione considera il peso non come semplice parametro w ma come w = exp(t). Questa trasformazione esponenziale conduce a una soluzione del classico problema di unicità che affligge la formulazione averaging (Vidotto, 2011). Inoltre, essa giustifica l’applicazione di algoritmi di cluster analysis sui parametri di peso, necessari per le procedure di raggruppamento dei soggetti sperimentali sulla base delle loro similarità. Infatti, la distanza tra due valori t può essere valutata in termini di semplice differenza. Diversamente, la distanza tra due valori w può essere valutata solo in termini di rapporto tra loro. Ciò consente l’uso di algoritmi di raggruppamento dei soggetti basati su matrici di prossimità fra i parametri. La performance di R-Average è stata testata utilizzando studi Monte Carlo e applicazioni pratiche in tre differenti campi di ricerca: nel marketing, nella teoria delle decisioni economiche e nella fiducia interpersonale. I risultati degli studi Monte Carlo mostrano una buona capacità del metodo di identificare i parametri del modello averaging. I parametri di scala sono in generale ben stimati. Diversamente, la stima dei pesi è un po’ più critica. La stima puntuale del valore reale del peso non è precisa come quella dei valori di scala, in particolare all’aumento della deviazione standard della componente d’errore dei dati. Nonostante questo, le stime appaiono attendibili, e le uguaglianze fra i pesi sono identificate. L’aumento del numero di replicazioni sperimentali può aiutare la selezione del modello quando gli errori presentano una grande deviazione standard. In sintesi, R-Average si configura come uno strumento molto utile per selezionare il miglior modello all’interno della famiglia dei modelli averaging, permettendo di gestire particolari condizioni multi-attributo negli esperimenti di misurazione funzionale. Il metodo R-Average è stato applicato in un primo studio nel campo del marketing. Nell’acquistare un prodotto, le persone esprimono una preferenza per particolari prodotti: comprendere i processi cognitivi sottostanti la formulazione delle preferenze dei consumatori risulta quindi un punto importante. Lo studio è stato condotto in accordo con un produttore locale di pasta, l’azienda Sgambaro. Gli scopi della ricerca erano tre: comprendere la formulazione dei giudizi dei consumatori su un prodotto di mercato, testare il metodo R-Aveage in condizioni reali e fornire all’azienda Sgambaro utili informazioni per un’ottimale commercializzazione del prodotto. Sono stati manipolati due fattori: la confezione della pasta Sgambaro (scatola con finestra, scatola senza finestra e busta di plastica) e il prezzo (0.89€, 0.99€, 1.09€). Le analisi sono partite considerando le valutazioni del prodotto espresse dai partecipanti: per ogni soggetto sono stati stimati i parametri del modello averaging. Dato che la popolazione dei consumatori presumibilmente non è omogenea in quanto a preferenze, il campione complessivo è stato diviso in tre gruppi (chiamati semplicemente Cluster A, Cluster B e Cluster C) attraverso un algoritmo di cluster analysis. Per entrambi i fattori Prezzo e Confezione, i diversi raggruppamenti mostrano punteggi differenti. Il Cluster A esprime giudizi che si posizionano nel centro scala, indicando come questi partecipanti non fossero particolarmente attratti dai prodotti. All’opposto, il Cluster B esprime giudizi positivi, e il Cluster C esprime giudizi generalmente negativi con l’eccezione della confezione “scatola con finestra”. Per quanto concerne la confezione, si osserva che la scatola con finestra, sebbene non sia quella preferita in tutti e tre i gruppi, ha sempre valutazione positive, mentre i giudizi per le altre confezioni variano tra i gruppi. Inoltre, se il target di potenziali consumatori per il prodotto è la popolazione generale, la scatola con finestra può essere considerata la confezione più apprezzata. Inoltre, nel Cluster C l’ANOVA mostra un’interazione significativa tra Prezzo e Confezione. Difatti, i parametri stimati per il modello averaging mostrano che il Cluster C è generalmente influenzato da un prezzo elevato. In questo gruppo il prezzo più alto ha un peso doppio rispetto agli altri nel punteggio finale, e ciò potrebbe invalidare l’influenza positiva della confezione “scatola con finestra”. È importante notare che il gruppo che è più sensibile a un prezzo alto è anche quello che presenta i punteggi di preferenza più bassi rispetto agli altri gruppi. In un secondo esperimento, il metodo R-Average è stato applicato in uno studio nel campo delle decisioni economiche in condizioni di rischio. L’assunzione che ha mosso lo studio è che, quando una persona deve valutare una scommessa a carattere economico in una situazione rischiosa, la persona integra cognitivamente il valore economico della scommessa con quello della probabilità di vittoria. In passato, Shanteau (1974) ha mostrato che l’integrazione tra valore e probabilità è realizzata attraverso una regola moltiplicativa. Lo studio, come quello di Lynch (1979), ha sottolineato che quando la situazione concerne due scommesse simultanee, ognuna composta da un valore e una probabilità, i giudizi per la scommessa doppia sono diversi dalla somma dei giudizi espressi per le scommesse singole. Questa osservazione, denominata effetto di subadditività, viola le assunzioni della Teoria dell’Utilità Attesa. Lo studio proposto analizza la convenienza/soddisfazione associata alle scommesse singole e doppie. Lo studio ha proposto ai partecipanti due tipologie di scommessa. Un primo gruppo di scommesse riguardava un bene (telefono cellulare) e l’altro un servizio (messaggi SMS gratis per giorno); a ogni bene/servizio era associata la probabilità di ottenerlo. Sono state definite due condizioni sperimentali. Nella prima condizione, i soggetti giudicano le scommesse considerando che i telefoni cellulari sono prodotti da una buona compagnia, e il servizio SMS è fornito da un provider inaffidabile. Nella condizione inversa, i soggetti giudicano le scommesse considerando che i telefoni cellulari sono prodotti con bassa qualità da una compagnia inaffidabile, e il servizio SMS è fornito da un provider robusto e affidabile. Per le scommesse doppie, è stata ipotizzata la presenza di un modello d’integrazione averaging, e i parametri del modello sono stati stimati utilizzando R-Average per ogni soggetto. I risultati mostrano che, in presenza di una scommessa doppia, l’integrazione è pienamente compatibile con un modello averaging: la corretta regola d’integrazione sembra essere quella a media ponderata e non quella additiva. Nell’ultimo esperimento, il modello averaging e la metodologia R-Average sono state applicate a uno studio sulle credenze di fiducia in tre contesti di vita quotidiana: interpersonale, istituzionale e organizzativo. Le credenze di fiducia sono attributi positivi che si ritiene una persona debba possedere affinché ci si possa fidare di lei. Le credenze di fiducia sono fattori rilevanti perché un individuo ne consideri un altro affidabile. Esse definiscono fino a che punto chi ripone fiducia si sente sicuro nel credere che la persona su cui ripone fiducia sia affidabile. Secondo McKnight, Cummings e Chervany (1998), le credenze di fiducia più citate sono: benevolenza, competenza, onestà e prevedibilità. L’idea sottostante lo studio proposto è che le credenze potrebbero essere integrate cognitivamente nel concetto di affidabilità attraverso un processo di ponderazione. Il metodo R-Average è stato utilizzato per identificare i parametri del modello averaging per ogni partecipante. Come principale risultato, l’analisi mostra che, in accordo con McKnight, Cummings e Chervany (1998), le quattro credenze principali giocano un ruolo fondamentale nel giudicare la fiducia. Inoltre, in accordo con la teoria dell’integrazione delle informazioni, un modello averaging sembra spiegare le risposte individuali. La grande maggioranza dei partecipanti potrebbe essere inquadrata come caso a pesi diversi. Mentre i valori di scala mostrano un netto andamento lineare con slopes più elevati per onestà e competenza, i pesi mostrano differenze con valori medi più elevati anche per onestà e competenza. Questi risultati sono coerenti con l’idea che attributi diversi giochino un ruolo diverso nel giudizio finale: infatti, onestà e competenza sembrano rivestire un ruolo preminente, mentre la prevedibilità sembra meno rilevante. Un’altra interessante conclusione riguarda l’elevato peso assunto da un basso livello di onestà; ciò sembra mostrare come una credenza connessa alla bassa onestà giochi il principale ruolo all’interno di un giudizio finale negativo. Infine, la differente inclinazione dell’andamento dei livelli degli attributi nei tre contesti situazionali suggerisce un ruolo preminente dell’onestà nelle situazioni interpersonali e della competenza nelle situazioni istituzionali. In conclusione, la teoria dell’integrazione delle informazioni e la misurazione funzionale sembrano rappresentare un approccio interessante per comprendere la formulazione del giudizio umano. Questo lavoro di ricerca propone un nuovo metodo per stimare i parametri dei modelli averaging. Il metodo mostra una buona capacità di identificare i parametri e apre nuovi scenari nella teoria dell’integrazione delle informazioni, fornendo un buon strumento per comprendere più nel dettaglio l’integrazione averaging degli attributi

La Modélisation spatio-temporelle permet la prédiction d’une variable régionalisée à des sites non observés du domaine d’étude, basée sur l’observation de cette variable en quelques sites du domaine à différents temps t donnés. Dans cette thèse, l’approche que nous avons proposé consiste à coupler des modèles numériques et statistiques. En effet en privilégiant l’approche bayésienne nous avons combiné les différentes sources d’information : l’information spatiale apportée par les observations, l’information temporelle apportée par la boîte noire ainsi que l’information a priori connue du phénomène. Ce qui permet une meilleure prédiction et une bonne quantification de l’incertitude sur la prédiction. Nous avons aussi proposé un nouveau critère d’optimalité de plans d’expérience incorporant d’une part le contrôle de l’incertitude en chaque point du domaine et d’autre part la valeur espérée du phénomène<br>Spatio-temporal modeling allows to make the prediction of a regionalized variable at unobserved points of a given field, based on the observations of this variable at some points of field at different times. In this thesis, we proposed a approach which combine numerical and statistical models. Indeed by using the Bayesian methods we combined the different sources of information : spatial information provided by the observations, temporal information provided by the black-box and the prior information on the phenomenon of interest. This approach allowed us to have a good prediction of the variable of interest and a good quantification of incertitude on this prediction. We also proposed a new method to construct experimental design by establishing a optimality criterion based on the uncertainty and the expected value of the phenomenon

In this thesis we propose to use a penalized maximum conditional likelihood criterion to estimate the graph of a general discrete Markov random field. We prove the almost sure convergence of the estimator of the graph in the case of a finite or countable infinite set of variables. Our method requires minimal assumptions on the probability distribution and contrary to other approaches in the literature, the usual positivity condition is not needed. We present several examples with a finite set of vertices and study the performance of the estimator on simulated data from theses examples. We also introduce an empirical procedure based on k-fold cross validation to select the best value of the constant in the estimators definition and show the application of this method in two real datasets.<br>Nesta tese propomos um critério de máxima verossimilhança penalizada para estimar o grafo de dependência condicional de um campo aleatório Markoviano discreto. Provamos a convergência quase certa do estimador do grafo no caso de um conjunto finito ou infinito enumerável de variáveis. Nosso método requer condições mínimas na distribuição de probabilidade e contrariamente a outras abordagens da literatura, a condição usual de positividade não é necessária. Introduzimos alguns exemplos com um conjunto finito de vértices e estudamos o desempenho do estimador em dados simulados desses exemplos. Também propomos um procedimento empírico baseado no método de validação cruzada para selecionar o melhor valor da constante na definição do estimador, e mostramos a aplicação deste procedimento em dois conjuntos de dados reais.

In this thesis Generalized Additive Neural Networks (GANNs) are studied in the context of predictive Data Mining. A GANN is a novel neural network implementation of a Generalized Additive Model. Originally GANNs were constructed interactively by considering partial residual plots. This methodology involves subjective human judgment, is time consuming, and can result in suboptimal results. The newly developed automated construction algorithm solves these difficulties by performing model selection based on an objective model selection criterion. Partial residual plots are only utilized after the best model is found to gain insight into the relationships between inputs and the target. Models are organized in a search tree with a greedy search procedure that identifies good models in a relatively short time. The automated construction algorithm, implemented in the powerful SAS® language, is nontrivial, effective, and comparable to other model selection methodologies found in the literature. This implementation, which is called AutoGANN, has a simple, intuitive, and user-friendly interface. The AutoGANN system is further extended with an approximation to Bayesian Model Averaging. This technique accounts for uncertainty about the variables that must be included in the model and uncertainty about the model structure. Model averaging utilizes in-sample model selection criteria and creates a combined model with better predictive ability than using any single model. In the field of Credit Scoring, the standard theory of scorecard building is not tampered with, but a pre-processing step is introduced to arrive at a more accurate scorecard that discriminates better between good and bad applicants. The pre-processing step exploits GANN models to achieve significant reductions in marginal and cumulative bad rates. The time it takes to develop a scorecard may be reduced by utilizing the automated construction algorithm.<br>Thesis (Ph.D. (Computer Science))--North-West University, Potchefstroom Campus, 2006.

Le critère de l'information k-means étend le critère des k-means en utilisant la divergence de Kullback comme fonction de perte. La fragmentation est une généralisation supplémentaire permettant l'approximation de chaque signal par une combinaison de fragments. Nous proposons un nouvel algorithme de fragmentation pour les signaux numériques se présentant comme un algorithme de compression avec perte. A l'issue de ce traitement, chaque signal est représenté par un ensemble aléatoires de labels, servant d'entrée à une procédure d'analyse syntaxique, conçue comme un algorithme de compression sans perte. Nous avons testé la méthode sur des images en niveaux de gris sur lesquelles il a été possible de détecter des configurations translatées ou transformées par une rotation. Ceci donne l'espoir d'apporter une réponse à la reconnaissance invariante par transformations fondée sur un critère de compression très général. D'un point de vue mathématique, nous avons prouvé deux types de bornes. Tout d'abord, nous avons relié notre algorithme de compression à un estimateur implicite d'un modèle statistique lui aussi implicite, à travers un lemme, prouvant que le taux de compression et le niveau de distorsion de l'un sont reliés à l'excès de risque de l'autre. Ce résultat contribue à expliquer la pertinence de nos arbres syntaxiques. Ensuite, nous établissons des bornes de généralisation non asymptotiques et indépendantes de la dimension pour les différents critères des k-means et critères de fragmentation que nous avons introduits. Nous utilisons pour cela des inégalités PAC-Bayésiennes appliquées dans des espaces de Hilbert à noyau reproduisant. Par exemple dans le cas des k-means classiques, nous obtenons une borne en O(k log(k) / n)^{1/4}) qui fournit la meilleure condition suffisante de consistance, à savoir que l'excès de risque tend vers zéro quand O(k log(k) / n) tend vers zéro. Grâce à une nouvelle méthode de chaînage PAC-Bayésien, nous prouvons aussi une borne en O(log(n/k) sqrt{k log(k)/n})<br>Information k-means is a new mathematical framework that extends the classical k-means criterion, using the Kullback divergence as a distortion measure. The fragmentation criterion is an even broader extension where each signal is approximated by a combination of fragments instead of a single center. Using the fragmentation criterion as a distortion measure, we propose a new fragmentation algorithm for digital signals, conceived as a lossy data compression scheme. Our syntax analysis is based on two principles: factorization and relabeling of frequent patterns. It is an iterative scheme, decreasing at each step as much as possible the length of the representation of the training set. It produces for each signal a syntax tree, providing a multi-level classification of the signal components. We tested the method on grey level digital images, where it was possible to label successfully translated patterns and rotated patterns. This lets us hope that transformation invariant pattern recognition could be approached in a flexible way using a general purpose data compression criterion. From a mathematical point of view, we derived two kinds of generalization bounds. First we defined an implicit estimator based on an implicit statistical model, related to our lossy data compression scheme. We proved a lemma relating the data compression rate and the distortion level of the compression algorithm with the excess risk of the statistical estimator. This explains why our syntax trees may be meaningful. Second, combining PAC-Bayesian lemmas with the kernel trick, we proved non asymptotic dimension-free generalization bounds for the various information k-means and information fragmentation criteria we introduced. For instance, in the special case of the classical k-means criterion, we get a non asymptotic dimension free generalization bound of order O( k log(k) / n )^{1/4}) that gives the best sufficient consistency condition, namely that the excess risk goes to zero when (k log(k) / n) goes to zero. Using a new kind of PAC-Bayesian chaining, we also proved a bound of order O( log(n/k) sqrt{k log(k)/n} )

This thesis proposes three novel models which extend the statistical methodology for motor unit number estimation, a clinical neurology technique. Motor unit number estimation is important in the treatment of degenerative muscular diseases and, potentially, spinal injury. Additionally, a recent and untested statistic to enable statistical model choice is found to be a practical alternative for larger datasets. The existing methods for dose finding in dual-agent clinical trials are found to be suitable only for designs of modest dimensions. The model choice case-study is the first of its kind containing interesting results using so-called unit information prior distributions.

Genetic research of complex diseases is a challenging, but exciting, area of research. The early development of the research was limited, however, until the completion of the Human Genome and HapMap projects, along with the reduction in the cost of genotyping, which paves the way for understanding the genetic composition of complex diseases. In this thesis, we focus on the statistical methods for two aspects of genetic research: phenotype definition for diseases with complex etiology and methods for identifying potentially associated Single Nucleotide Polymorphisms (SNPs) and SNP-SNP interactions. With regard to phenotype definition for diseases with complex etiology, we firstly investigated the effects of different statistical phenotyping approaches on the subsequent analysis. In light of the findings, and the difficulties in validating the estimated phenotype, we proposed two different methods for reconciling phenotypes of different models using Bayesian model averaging as a coherent mechanism for accounting for model uncertainty. In the second part of the thesis, the focus is turned to the methods for identifying associated SNPs and SNP interactions. We review the use of Bayesian logistic regression with variable selection for SNP identification and extended the model for detecting the interaction effects for population based case-control studies. In this part of study, we also develop a machine learning algorithm to cope with the large scale data analysis, namely modified Logic Regression with Genetic Program (MLR-GEP), which is then compared with the Bayesian model, Random Forests and other variants of logic regression.

We investigated the neuronal processes which occur during a decision- making task based on a perceptual classi cation judgment. For this purpose we have analysed three di erent experimental paradigms (somatosensory, visual, and auditory) in two di erent species (monkey and rat), with the common goal of shedding light into the information carried by neurons. In particular, we focused on how the information content is preserved in the underlying neuronal activity over time. Furthermore we considered how the decision, the stimuli, and the con dence are encoded in memory and, when the experimental paradigm allowed it, how the attention modulates these features. Finally, we went one step further, and we investigated the interactions between brain areas that arise during the process of decision- making.<br>Durant aquesta tesi hem investigat els processos neuronals que es pro- dueixen durant tasques de presa de decisions, tasques basades en un ju- dici l ogic de classi caci o perceptual. Per a aquest prop osit hem analitzat tres paradigmes experimentals diferents (somatosensorial, visual i auditiu) en dues espcies diferents (micos i rates), amb l'objectiu d'il.lustrar com les neurones codi quen informaci on referents a les t asques. En particular, ens hem centrat en com certes informacions estan cod- i cades en l'activitat neuronal al llarg del temps. Concretament, com la informaci o sobre: la decisi o comportamental, els factors externs, i la con- ana en la resposta, b e codi cada en la mem oria. A m es a m es, quan el paradigma experimental ens ho va permetre, com l'atenci o modula aquests aspectes. Finalment, hem anat un pas m es enll a, i hem analitzat la comu- nicaci o entre les diferents arees corticals, mentre els subjectes resolien una tasca de presa de decisions.

Роботу виконано в Інституті прикладного системного аналізу Національного технічного університету України «Київський політехнічний інститут імені Ігоря Сікорського».<br>У дисертаційній роботі розроблено системну методологію аналізу та оцінювання фінансових ризиків, яка ґрунтується на принципах системного аналізу та менеджменту ризиків, а також запропонованих принципах адаптивного та динамічного менеджменту ризиків. Методологія включає: комбінований метод обробки неповних та втрачених даних, ймовірнісно-статистичний метод оцінювання ризику фінансових втрат, динамічний метод оцінювання ризиків, який передбачає побудову різних типів моделей виживання, метод структурно-параметричної адаптації, застосування скорингової карти до аналізу ризиків фінансових систем і нейро-нечіткий метод доповнення вибірки відхиленими заявками. Містить критерії урахування інформаційного ризику, оцінки якості даних, прогнозів та рішень, квадратичний критерій якості опрацювання ризику та інтегральну характеристику оцінювання ефективності методів менеджменту ризиків. Практична цінність одержаних результатів полягає у створенні розширеної інформаційної технології та інформаційної системи підтримки прийняття рішень на основі запропонованої системної методології.

碩士<br>淡江大學<br>資訊管理學系<br>91<br>In this paper, we study on applying Bayesian Information Criterion (BIC) for speaker segmentation and selection of optimum model order of Gaussian Mixture Model (GMM). In the former part, we introduce the BIC-based speaker segmentation algorithm and explore the segmentation effects in window sizes, sampling rates and dimensions of voice feature. The experiment results reveal that when we set window size at 4 seconds, sampling rate at 10K Hz and 13 feature dimensions of Mel Frequency Cepstrum Coefficient, we can get better segmentation effects. After that we compare BIC-based segmentation method with the improved methods proposed by Tritshler[3], Zhou[4] and Cettolo[5]. We found BIC-based segmentation method is better than Zhou’s. Trishler’s and Cettolo’s effects are the same as BIC-based method, except they have less computation time. In the second part, we discuss how to select the optimum mixture component of Gaussian Mixture Model. We also apply Bayesian Information Criterion to select optimum mixture component of Gaussian Mixture Model. In addition, we introduce the concept of Adaptive Mixture Component. This concept is derived from the difference of statistical distribution of speech keyword corpus. We should construct the corresponding keyword model based on this kind of difference. Moreover, speech keywords are rarely to be repeated. We propose GMM based speech keyword recognition method under this hypothesis. We use this recognition method to test Adaptive Mixture Component. Finally, we find the experiment reflect the recognition rates always upper 90% when applying Adaptive Mixture Component. Although, the results are not better than the optimum results caused among different Fixed Model Order settings, they differs only less than 2%. However, the total mixture components of Gaussian Mixture Model produced by Adaptive Mixture Component are much less than total mixture components produced by optimum Fixed Mixture Component setting. The means that we use less computation time when applying Adaptive Mixture Component. Besides, BIC-based selection method is setting-free method. As a result, we can view the BIC-based selection method along with the proposed Adaptive Mixture Component is a good, fast, and automatic method in Gaussian Mixture Model.

This thesis aims to identify main driving market risk factors of different strategies implemented by hedge funds by looking at correlation coefficients, implementing Principal Component Analysis and analyzing "loadings" for first three principal components, which explain the largest portion of the variation of hedge funds' returns. In the next step, a stepwise regression through iteration process includes and excludes market risk factors for each strategy, searching for the combination of risk factors which will offer a model with the best "fit", based on The Akaike Information Criterion - AIC and Bayesian Information Criterion - BIC. Lastly, to avoid counterfeit results and overcome model uncertainty issues a Bayesian Model Average - BMA approach was taken. Key words: Hedge Funds, hedge funds' strategies, market risk, principal component analysis, stepwise regression, Akaike Information Criterion, Bayesian Information Criterion, Bayesian Model Averaging Author's e-mail: aleksaradosavcevic@gmail.com Supervisor's e-mail: mp.princ@seznam.cz

This thesis contributes to the field of Gaussian Graphical Models by exploring either numerically or theoretically various topics of Bayesian Methods in Gaussian Graphical Models and by providing a number of interesting results, the further exploration of which would be promising, pointing to numerous future research directions. Gaussian Graphical Models are statistical methods for the investigation and representation of interdependencies between components of continuous random vectors. This thesis aims to investigate some issues related to the application of Bayesian methods for Gaussian Graphical Models. We adopt the popular $G$-Wishart conjugate prior $W_G(\delta,D)$ for the precision matrix. We propose an efficient sampling method for the $G$-Wishart distribution based on the Metropolis Hastings algorithm and show its validity through a number of numerical experiments. We show that this method can be easily used to estimate the Deviance Information Criterion, providing a computationally inexpensive approach for model selection. In addition, we look at the marginal likelihood of a graphical model given a set of data. This is proportional to the ratio of the posterior over the prior normalizing constant. We explore methods for the estimation of this ratio, focusing primarily on applying the Monte Carlo simulation method of path sampling. We also explore numerically the effect of the completion of the incomplete matrix $D^{\mathcal{V}}$, hyperparameter of the $G$-Wishart distribution, for the estimation of the normalizing constant. We also derive a series of exact and approximate expressions for the Bayes Factor between two graphs that differ by one edge. A new theoretical result regarding the limit of the normalizing constant multiplied by the hyperparameter $\delta$ is given and its implications to the validity of an improper prior and of the subsequent Bayes Factor are discussed.

Many databases involve ordered discrete responses in a temporal and spatial context, including, for example, land development intensity levels, vehicle ownership, and pavement conditions. An appreciation of such behaviors requires rigorous statistical methods, recognizing spatial effects and dynamic processes. This dissertation develops a dynamic spatial ordered probit (DSOP) model in order to capture patterns of spatial and temporal autocorrelation in ordered categorical response data. This model is estimated in a Bayesian framework using Gibbs sampling and data augmentation, in order to generate all autocorrelated latent variables. The specifications, methodologies, and applications undertaken here advance the field of spatial econometrics while enhancing our understanding of land use and air quality changes. The proposed DSOP model incorporates spatial effects in an ordered probit model by allowing for inter-regional spatial interactions and heteroskedasticity, along with random effects across regions (where "region" describes any cluster of observational units). The model assumes an autoregressive, AR(1), process across latent response values, thereby recognizing time-series dynamics in panel data sets. The model code and estimation approach is first tested on simulated data sets, in order to reproduce known parameter values and provide insights into estimation performance. Root mean squared errors (RMSE) are used to evaluate the accuracy of estimates, and the deviance information criterion (DIC) is used for model comparisons. It is found that the DSOP model yields much more accurate estimates than standard, non-spatial techniques. As for model selection, even considering the penalty for using more parameters, the DSOP model is clearly preferred to standard OP, dynamic OP and spatial OP models. The model and methods are then used to analyze both land use and air quality (ozone) dynamics in Austin, Texas. In analyzing Austin's land use intensity patterns over a 4-point panel, the observational units are 300 m × 300 m grid cells derived from satellite images (at 30 m resolution). The sample contains 2,771 such grid cells, spread among 57 clusters (zip code regions), covering about 10% of the overall study area. In this analysis, temporal and spatial autocorrelation effects are found to be significantly positive. In addition, increases in travel times to the region's central business district (CBD) are estimated to substantially reduce land development intensity. The observational units for the ozone variation analysis are 4 km × 4 km grid cells, and all 132 observations falling in the study area are used. While variations in ozone concentration levels are found to exhibit strong patterns of temporal autocorrelation, they appear strikingly random in a spatial context (after controlling for local land cover, transportation, and temperature conditions). While transportation and land cover conditions appear to influence ozone levels, their effects are not as instantaneous, nor as practically significant as the impact of temperature. The proposed and tested DSOP model is felt to be a significant contribution to the field of spatial econometrics, where binary applications (for discrete response data) have been seen as the cutting edge. The Bayesian framework and Gibbs sampling techniques used here permit such complexity, in world of two-dimensional autocorrelation.<br>text

Several studies point out different causes of performance degradation in supervised machine learning. Problems such as class imbalance, overlapping, small-disjuncts, noisy labels, and sparseness limit accuracy in classification algorithms. Even though a number of approaches either in the form of a methodology or an algorithm try to minimize performance degradation, they have been isolated efforts with limited scope. This research consists of three main parts: In the first part, a novel probabilistic diagnostic model based on identifying signs and symptoms of each problem is presented. Secondly, the behavior and performance of several supervised algorithms are studied when training sets have such problems. Therefore, prediction of success for treatments can be estimated across classifiers. Finally, a probabilistic sampling technique based on training set diagnosis for avoiding classifier degradation is proposed<br>