Teorema di Radon-Nikodym e Statistica

Il presente elaborato vuole illustrare alcuni risultati matematici di teoria della misura grazie ai quali si sono sviluppate interessanti conseguenze nel campo della statistica inferenziale relativamente al concetto di statistica sufficiente. Il primo capitolo riprende alcune nozioni preliminari e si espone il teorema di Radon-Nikodym, sulle misure assolutamente continue, con conseguente dimostrazione. Il secondo capitolo dal titolo ‘Applicazioni alla statistica sufficiente’ si apre con le definizioni degli oggetti di studio e con la presentazione di alcune loro proprietà matematiche. Nel secondo paragrafo si espongono i concetti di attesa condizionata e probabilità condizionata in relazione agli elementi definiti nel paragrafo iniziale. Si entra nel corpo di questo capitolo con il terzo paragrafo nel quale definiamo gli insiemi di misura, gli insiemi di misura dominati e il concetto di statistica sufficiente. Viene qua presentato un importante teorema di caratterizzazione delle statistiche sufficienti per insiemi dominati e un suo corollario che descrive la relativa proprietà di fattorizzazione. Definiamo poi gli insiemi omogenei ed esponiamo un secondo corollario al teorema, relativo a tali insiemi. Si considera poi l’esempio del controllo di qualità per meglio illustrare la nozione di statistica sufficiente osservando una situazione più concreta. Successivamente viene introdotta la nozione di statistica sufficiente a coppie e viene enunciato un secondo teorema di caratterizzazione in termini di rapporto di verosimiglianza. Si procede quindi ad un confronto tra questi due tipi di sufficienza. Tale confronto viene operato in due situazioni differenti e porta a risultati diversi per ogni caso. Si conclude dunque l’elaborato marcando ancora l’effettiva bontà di una statistica sufficiente in termini di informazioni contenute al suo interno.

Analysis of robot dynamics through complexity measures: an application in automatic design

L'applicazione di misure, derivanti dalla teoria dell'informazione, fornisce un valido strumento per quantificare alcune delle proprietà dei sistemi complessi. Le stesse misure possono essere utilizzate in robotica per favorire l'analisi e la sintesi di sistemi di controllo per robot. In questa tesi si è analizzata la correlazione tra alcune misure di complessità e la capacità dei robot di portare a termine, con successo, tre differenti task. I risultati ottenuti suggeriscono che tali misure di complessità rappresentano uno strumento promettente anche nel campo della robotica, ma che il loro utilizzo può diventare difficoltoso quando applicate a task compositi.

Estimating Willingness to Pay for River Amenities and Safety Measures Associated with Shale Gas Extraction

This paper utilizes a Contingent Valuation Method survey of a random sample of residents to estimate that households are willing to pay an average of $12.00 per month for public projects designed to improve river access and $10.46 per month for additional safety measures that would eliminate risks to local watersheds from drilling for natural gas from underground shale formations. These estimates can be compared to the costs of providing each of these two amenities to help foster the formation of efficient policy decisions.

Feasibility of Wii Fit Training to Improve Clinical Measures of Balance in Older Adults

Background and purpose: Numerous interventions have been proposed to improve balance in older adults with varying degrees of success. A novel approach may be to use an off-the-shelf video game system utilizing real-time force feedback to train older adults. The purpose of this study is to investigate the feasibility of using Nintendo's Wii Fit for training to improve clinical measures of balance in older adults and to retain the improvements after a period of time. Methods: Twelve healthy older adults (aged >70 years) were randomly divided into two groups. The experimental group completed training using Nintendo's Wii Fit game three times a week for 3 weeks while the control group continued with normal activities. Four clinical measures of balance were assessed before training, 1 week after training, and 1 month after training: Berg Balance Scale (BBS), Fullerton Advanced Balance (FAB) scale, Functional Reach (FR), and Timed Up and Go (TUG). Friedman two-way analysis of variance by ranks was conducted on the control and experimental group to determine if training using the Wii Balance Board with Wii Fit had an influence on clinical measures of balance. Results: Nine older adults completed the study (experimental group n = 4, control group n = 5). The experimental group significantly increased their BBS after training while the control group did not. There was no significant change for either group with FAB, FR, and TUG. Conclusion: Balance training with Nintendo's Wii Fit may be a novel way for older adults to improve balance as measured by the BBS.

Electroencephalographic topography measures of experienced utility

Economic theory distinguishes two concepts of utility: decision utility, objectively quantifiable by choices, and experienced utility, referring to the satisfaction by an obtainment. To date, experienced utility is typically measured with subjective ratings. This study intended to quantify experienced utility by global levels of neuronal activity. Neuronal activity was measured by means of electroencephalographic (EEG) responses to gain and omission of graded monetary rewards at the level of the EEG topography in human subjects. A novel analysis approach allowed approximating psychophysiological value functions for the experienced utility of monetary rewards. In addition, we identified the time windows of the event-related potentials (ERP) and the respective intracortical sources, in which variations in neuronal activity were significantly related to the value or valence of outcomes. Results indicate that value functions of experienced utility and regret disproportionally increase with monetary value, and thus contradict the compressing value functions of decision utility. The temporal pattern of outcome evaluation suggests an initial (∼250 ms) coarse evaluation regarding the valence, concurrent with a finer-grained evaluation of the value of gained rewards, whereas the evaluation of the value of omitted rewards emerges later. We hypothesize that this temporal double dissociation is explained by reward prediction errors. Finally, a late, yet unreported, reward-sensitive ERP topography (∼500 ms) was identified. The sources of these topographical covariations are estimated in the ventromedial prefrontal cortex, the medial frontal gyrus, the anterior and posterior cingulate cortex and the hippocampus/amygdala. The results provide important new evidence regarding “how,” “when,” and “where” the brain evaluates outcomes with different hedonic impact.

Depressive symptoms, perceived social support, and prothrombotic measures in patients with venous thromboembolism

Psychosocial factors have been associated with both a prothrombotic state and an increased risk of venous thromboembolism (VTE). We examined the relation of depressive symptoms and social support with D-dimer, an integrative measure of enhanced coagulation activity, and several additional prothrombotic measures in patients with VTE.