980 resultados para Bayes Formula


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Mathematics Subject Classification 2010: 42C40, 44A12.

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2000 Mathematics Subject Classification: 60H30, 35K55, 35K57, 35B35.

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2000 Mathematics Subject Classification: 30A05, 33E05, 30G30, 30G35, 33E20.

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Following our earlier paper on the subject, we present a general closed formula to value the interest savings due to a multi-firm cash-pool system. Assuming normal distribution of the accounts the total savings can be expressed as the product of three independent factors representing the interest spread, the number and the correlation of the firms, and the time-dependent distribution of the cash accounts. We derive analytic results for two special processes one characterizing the initial build-up period and the other describing the mature period. The value gained in the stationary system can be thought of as the interest, paid at the net interest spread rate on the standard deviation of the account. We show that pooling has substantial value already in the transient period. In order to increase the practical relevance of our analysis we discuss possible extensions of our model and we show how real option pricing technics can be applied here.

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Crash reduction factors (CRFs) are used to estimate the potential number of traffic crashes expected to be prevented from investment in safety improvement projects. The method used to develop CRFs in Florida has been based on the commonly used before-and-after approach. This approach suffers from a widely recognized problem known as regression-to-the-mean (RTM). The Empirical Bayes (EB) method has been introduced as a means to addressing the RTM problem. This method requires the information from both the treatment and reference sites in order to predict the expected number of crashes had the safety improvement projects at the treatment sites not been implemented. The information from the reference sites is estimated from a safety performance function (SPF), which is a mathematical relationship that links crashes to traffic exposure. The objective of this dissertation was to develop the SPFs for different functional classes of the Florida State Highway System. Crash data from years 2001 through 2003 along with traffic and geometric data were used in the SPF model development. SPFs for both rural and urban roadway categories were developed. The modeling data used were based on one-mile segments that contain homogeneous traffic and geometric conditions within each segment. Segments involving intersections were excluded. The scatter plots of data show that the relationships between crashes and traffic exposure are nonlinear, that crashes increase with traffic exposure in an increasing rate. Four regression models, namely, Poisson (PRM), Negative Binomial (NBRM), zero-inflated Poisson (ZIP), and zero-inflated Negative Binomial (ZINB), were fitted to the one-mile segment records for individual roadway categories. The best model was selected for each category based on a combination of the Likelihood Ratio test, the Vuong statistical test, and the Akaike's Information Criterion (AIC). The NBRM model was found to be appropriate for only one category and the ZINB model was found to be more appropriate for six other categories. The overall results show that the Negative Binomial distribution model generally provides a better fit for the data than the Poisson distribution model. In addition, the ZINB model was found to give the best fit when the count data exhibit excess zeros and over-dispersion for most of the roadway categories. While model validation shows that most data points fall within the 95% prediction intervals of the models developed, the Pearson goodness-of-fit measure does not show statistical significance. This is expected as traffic volume is only one of the many factors contributing to the overall crash experience, and that the SPFs are to be applied in conjunction with Accident Modification Factors (AMFs) to further account for the safety impacts of major geometric features before arriving at the final crash prediction. However, with improved traffic and crash data quality, the crash prediction power of SPF models may be further improved.

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Con questa tesi si vuole illustrare e riordinare il lavoro da me svolto sulla progettazione di mozzi ruota e di altri componenti ad esso associati, relativi alla vettura del team di Formula SAE dell’Università di Bologna. Dopo una prima fase di studio del particolare componente tesa a definire quali caratteristiche fossero richieste al fine di raggiungere gli obbiettivi, si è passati allo sviluppo del progetto con lo svolgimento di primi calcoli a mano, per definire in linea di massima le sollecitazioni, per poi affinare il dimensionamento con le simulazioni FEM. Il componente è stato infine realizzato in lega d'alluminio ad elevate prestazioni.

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L’obiettivo di questa tesi è illustrare quali siano stati i metodi di studio e le soluzioni adottate per ottimizzare gli impianti di raffreddamento e lubrificazione della monoposto da competizione sviluppata dal team Unibo Motorsport, in preparazione alla stagione di gara 2016 della Formula SAE®. Inizialmente saranno analizzate le principali problematiche di entrambi gli impianti attraverso simulazioni CFD (Computational Fluid Dynamics) e dati telemetrici degli anni passati. In seguito, saranno mostrati i diversi procedimenti di progettazione e il completamento degli impianti unitamente ad una loro valutazione economica. Infine, per verificare l’effettivo successo delle operazioni svolte a bordo vettura, verranno mostrate acquisizioni telemetriche relative alle gare ed altre simulazioni relative alle nuove geometrie sviluppate. Un altro obiettivo della trattazione è mettere a disposizione dei futuri membri del reparto motore un documento che contenga tutte le considerazioni fatte a riguardo degli impianti studiati. Questo è fondamentale all’interno di un ambiente come un team di Formula SAE®, dove ogni anno si ha il ricambio di una buona parte dei membri. Se gli studi svolti sugli impianti venissero persi, i nuovi arrivati si troverebbero a mettere le mani su un qualcosa di sconosciuto e lo sviluppo della vettura negli anni si troverebbe enormemente rallentato. Il “learning by doing” che ha sempre caratterizzato questo progetto viene infatti affiancato con armonia dalla possibilità di consultare esperienze pregresse relative al caso di studio considerato.

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The challenge of detecting a change in the distribution of data is a sequential decision problem that is relevant to many engineering solutions, including quality control and machine and process monitoring. This dissertation develops techniques for exact solution of change-detection problems with discrete time and discrete observations. Change-detection problems are classified as Bayes or minimax based on the availability of information on the change-time distribution. A Bayes optimal solution uses prior information about the distribution of the change time to minimize the expected cost, whereas a minimax optimal solution minimizes the cost under the worst-case change-time distribution. Both types of problems are addressed. The most important result of the dissertation is the development of a polynomial-time algorithm for the solution of important classes of Markov Bayes change-detection problems. Existing techniques for epsilon-exact solution of partially observable Markov decision processes have complexity exponential in the number of observation symbols. A new algorithm, called constellation induction, exploits the concavity and Lipschitz continuity of the value function, and has complexity polynomial in the number of observation symbols. It is shown that change-detection problems with a geometric change-time distribution and identically- and independently-distributed observations before and after the change are solvable in polynomial time. Also, change-detection problems on hidden Markov models with a fixed number of recurrent states are solvable in polynomial time. A detailed implementation and analysis of the constellation-induction algorithm are provided. Exact solution methods are also established for several types of minimax change-detection problems. Finite-horizon problems with arbitrary observation distributions are modeled as extensive-form games and solved using linear programs. Infinite-horizon problems with linear penalty for detection delay and identically- and independently-distributed observations can be solved in polynomial time via epsilon-optimal parameterization of a cumulative-sum procedure. Finally, the properties of policies for change-detection problems are described and analyzed. Simple classes of formal languages are shown to be sufficient for epsilon-exact solution of change-detection problems, and methods for finding minimally sized policy representations are described.

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Fondo Margaritainés Restrepo

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Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

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Neste trabalho é relatado o processo de projeto de um chassis para um veículo de Formula Student. Ao longo do relatório são abordados aspetos regulamentares, requisitos e objetivos técnicos, a interligação com os diversos sistemas do veículo, os aspetos relacionados com o projeto da estrutura, métodos de modelação para análise com recurso ao método dos elementos finitos, e por fim a análise dos esforços aplicados ao chassis e a validação do mesmo.

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Lo scopo del presente lavoro è quello di determinare una metodologia di analisi vibroacustica di validità generale applicabile a tutti i casi nei quali la forzante sia di tipo vibrazionale. Nello specifico si è analizzato il comportamento strutturale e acustico di un impianto di scarico di una monoposto Formula SAE. Ricorrendo all’analisi FEM (Finite Element Method) è possibile determinare e quantificare gli effetti dannosi causati dalle vibrazioni già nella fase di prototipazione permettendo una sostanziale riduzione dei tempi e costi. La determinazione del comportamento strutturale del modello alle vibrazioni è iniziata dall’analisi modale, grazie alla quale sono state determinate le frequenze naturali e i modi propri dell’impianto di scarico. Successivamente, l’analisi FRF (Frequency Response Function) ha permesso di conoscere la risposta del nostro sistema ad una forzante imposta mettendo in luce le diverse criticità strutturali. Con il presupposto di ottenere delle condizioni di carico che fossero il più vicine possibili alle normali condizioni operative si è impostata un’analisi PSD (Power Spectral Density). Per concludere la prima parte dell’analisi si è reso necessario indagare anche il comportamento a fatica vibrazionale, valutando in questo modo le zone soggette a vita finita e quindi le prime a cedere in fase di esercizio. La parte finale è stata dedicata all’analisi del rumore. Dall’analisi FRF si è determinata la SPL (Sound Pressure Level) ottenendo come output un valore di pressione sonora prodotto dall’effetto della propagazione delle onde di pressione generate dalla vibrazione strutturale dell’impianto di scarico. Infine, l’analisi di Transmission Loss ha permesso di valutare l’efficacia della geometria del silenziatore sulla riduzione del livello acustico generato dal transito dei gas di scarico alle diverse frequenze.

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Following the latest environmental concerns, the importance of minimising the detrimental effect of emissions of terrestrial vehicles has become a major goal for the whole automotive field. The key to achieve an emission-free long term future is the electrification of vehicle fleets; this huge step cannot be taken without intermediate technologies. In this context, hybrid vehicles are fundamental to reach this goal. Specifically, mild hybrid vehicles represent a trade-off between cost and emissions that could act now as a bridge towards electrification. Like the industry, also student engineering competitions are likely to take the same route: Combustion vehicles may well turn into hybrid vehicles. For this reason, a preliminary design overview is necessary to pinpoint the key performance indicators for the prototypes of the future.

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Ochnaceae s.str. (Malpighiales) are a pantropical family of about 500 species and 27 genera of almost exclusively woody plants. Infrafamilial classification and relationships have been controversial partially due to the lack of a robust phylogenetic framework. Including all genera except Indosinia and Perissocarpa and DNA sequence data for five DNA regions (ITS, matK, ndhF, rbcL, trnL-F), we provide for the first time a nearly complete molecular phylogenetic analysis of Ochnaceae s.l. resolving most of the phylogenetic backbone of the family. Based on this, we present a new classification of Ochnaceae s.l., with Medusagynoideae and Quiinoideae included as subfamilies and the former subfamilies Ochnoideae and Sauvagesioideae recognized at the rank of tribe. Our data support a monophyletic Ochneae, but Sauvagesieae in the traditional circumscription is paraphyletic because Testulea emerges as sister to the rest of Ochnoideae, and the next clade shows Luxemburgia+Philacra as sister group to the remaining Ochnoideae. To avoid paraphyly, we classify Luxemburgieae and Testuleeae as new tribes. The African genus Lophira, which has switched between subfamilies (here tribes) in past classifications, emerges as sister to all other Ochneae. Thus, endosperm-free seeds and ovules with partly to completely united integuments (resulting in an apparently single integument) are characters that unite all members of that tribe. The relationships within its largest clade, Ochnineae (former Ochneae), are poorly resolved, but former Ochninae (Brackenridgea, Ochna) are polyphyletic. Within Sauvagesieae, the genus Sauvagesia in its broad circumscription is polyphyletic as Sauvagesia serrata is sister to a clade of Adenarake, Sauvagesia spp., and three other genera. Within Quiinoideae, in contrast to former phylogenetic hypotheses, Lacunaria and Touroulia form a clade that is sister to Quiina. Bayesian ancestral state reconstructions showed that zygomorphic flowers with adaptations to buzz-pollination (poricidal anthers), a syncarpous gynoecium (a near-apocarpous gynoecium evolved independently in Quiinoideae and Ochninae), numerous ovules, septicidal capsules, and winged seeds with endosperm are the ancestral condition in Ochnoideae. Although in some lineages poricidal anthers were lost secondarily, the evolution of poricidal superstructures secured the maintenance of buzz-pollination in some of these genera, indicating a strong selective pressure on keeping that specialized pollination system.