Sets of probability distributions, independence, and convexity

This paper analyzes concepts of independence and assumptions of convexity in the theory of sets of probability distributions. The starting point is Kyburg and Pittarelli's discussion of "convex Bayesianism" (in particular their proposals concerning E-admissibility, independence, and convexity). The paper offers an organized review of the literature on independence for sets of probability distributions; new results on graphoid properties and on the justification of "strong independence" (using exchangeability) are presented. Finally, the connection between Kyburg and Pittarelli's results and recent developments on the axiomatization of non-binary preferences, and its impact on "complete" independence, are described.

Prediction and probability of neonatal outcome in isolated congenital diaphragmatic hernia using multiple ultrasound parameters

Objectives To evaluate the accuracy and probabilities of different fetal ultrasound parameters to predict neonatal outcome in isolated congenital diaphragmatic hernia (CDH). Methods Between January 2004 and December 2010, we evaluated prospectively 108 fetuses with isolated CDH (82 left-sided and 26 right-sided). The following parameters were evaluated: gestational age at diagnosis, side of the diaphragmatic defect, presence of polyhydramnios, presence of liver herniated into the fetal thorax (liver-up), lung-to-head ratio (LHR) and observed/expected LHR (o/e-LHR), observed/expected contralateral and total fetal lung volume (o/e-ContFLV and o/e-TotFLV) ratios, ultrasonographic fetal lung volume/fetal weight ratio (US-FLW), observed/expected contralateral and main pulmonary artery diameter (o/e-ContPA and o/eMPA) ratios and the contralateral vascularization index (Cont-VI). The outcomes were neonatal death and severe postnatal pulmonary arterial hypertension (PAH). Results Neonatal mortality was 64.8% (70/108). Severe PAH was diagnosed in 68 (63.0%) cases, of which 63 died neonatally (92.6%) (P < 0.001). Gestational age at diagnosis, side of the defect and polyhydramnios were not associated with poor outcome (P > 0.05). LHR, o/eLHR, liver-up, o/e-ContFLV, o/e-TotFLV, US-FLW, o/eContPA, o/e-MPA and Cont-VI were associated with both neonatal death and severe postnatal PAH (P < 0.001). Receiver-operating characteristics curves indicated that measuring total lung volumes (o/e-TotFLV and US-FLW) was more accurate than was considering only the contralateral lung sizes (LHR, o/e-LHR and o/e-ContFLV; P < 0.05), and Cont-VI was the most accurate ultrasound parameter to predict neonatal death and severe PAH (P < 0.001). Conclusions Evaluating total lung volumes is more accurate than is measuring only the contralateral lung size. Evaluating pulmonary vascularization (Cont-VI) is the most accurate predictor of neonatal outcome. Estimating the probability of survival and severe PAH allows classification of cases according to prognosis. Copyright (C) 2011 ISUOG. Published by John Wiley & Sons, Ltd.

PCR colorimetric dot-blot assay and clinical pretest probability for diagnosis of Pulmonary Tuberculosis in Smear-Negative patients

Abstract Background Smear-negative pulmonary tuberculosis (SNPTB) accounts for 30% of Pulmonary Tuberculosis (PTB) cases reported annually in developing nations. Polymerase chain reaction (PCR) may provide an alternative for the rapid detection of Mycobacterium tuberculosis (MTB); however little data are available regarding the clinical utility of PCR in SNPTB, in a setting with a high burden of TB/HIV co-infection. Methods To evaluate the performance of the PCR dot-blot in parallel with pretest probability (Clinical Suspicion) in patients suspected of having SNPTB, a prospective study of 213 individuals with clinical and radiological suspicion of SNPTB was carried out from May 2003 to May 2004, in a TB/HIV reference hospital. Respiratory specialists estimated the pretest probability of active disease into high, intermediate, low categories. Expectorated sputum was examined by direct microscopy (Ziehl-Neelsen staining), culture (Lowenstein Jensen) and PCR dot-blot. Gold standard was based on culture positivity combined with the clinical definition of PTB. Results In smear-negative and HIV subjects, active PTB was diagnosed in 28.4% (43/151) and 42.2% (19/45), respectively. In the high, intermediate and low pretest probability categories active PTB was diagnosed in 67.4% (31/46), 24% (6/25), 7.5% (6/80), respectively. PCR had sensitivity of 65% (CI 95%: 50%–78%) and specificity of 83% (CI 95%: 75%–89%). There was no difference in the sensitivity of PCR in relation to HIV status. PCR sensitivity and specificity among non-previously TB treated and those treated in the past were, respectively: 69%, 43%, 85% and 80%. The high pretest probability, when used as a diagnostic test, had sensitivity of 72% (CI 95%:57%–84%) and specificity of 86% (CI 95%:78%–92%). Using the PCR dot-blot in parallel with high pretest probability as a diagnostic test, sensitivity, specificity, positive and negative predictive values were: 90%, 71%, 75%, and 88%, respectively. Among non-previously TB treated and HIV subjects, this approach had sensitivity, specificity, positive and negative predictive values of 91%, 79%, 81%, 90%, and 90%, 65%, 72%, 88%, respectively. Conclusion PCR dot-blot associated with a high clinical suspicion may provide an important contribution to the diagnosis of SNPTB mainly in patients that have not been previously treated attended at a TB/HIV reference hospital.

Clinical judgment to estimate pretest probability in the diagnosis of Cushing's syndrome under a Bayesian perspective

OBJECTIVE: To estimate the pretest probability of Cushing's syndrome (CS) diagnosis by a Bayesian approach using intuitive clinical judgment. MATERIALS AND METHODS: Physicians were requested, in seven endocrinology meetings, to answer three questions: "Based on your personal expertise, after obtaining clinical history and physical examination, without using laboratorial tests, what is your probability of diagnosing Cushing's Syndrome?"; "For how long have you been practicing Endocrinology?"; and "Where do you work?". A Bayesian beta regression, using the WinBugs software was employed. RESULTS: We obtained 294 questionnaires. The mean pretest probability of CS diagnosis was 51.6% (95%CI: 48.7-54.3). The probability was directly related to experience in endocrinology, but not with the place of work. CONCLUSION: Pretest probability of CS diagnosis was estimated using a Bayesian methodology. Although pretest likelihood can be context-dependent, experience based on years of practice may help the practitioner to diagnosis CS. Arq Bras Endocrinol Metab. 2012;56(9):633-7

Frequency of human platelet antigens in oncohematological patients with thrombocytopenia and the probability of incompatibility to platelet transfusions

OBJECTIVE: The objective of this study was to evaluate the frequencies of human platelet antigens in oncohematological patients with thrombocytopenia and to analyze the probability of their incompatibility with platelet transfusions. METHODS: Platelet antigen genotyping was performed by sequence-specific primer polymerase chain reaction (SSP-PCR) for the HPA-1a, HPA-1b, HPA-2a, HPA-2b, HPA-3a, HPA-3b, HPA-4a, HPA-4b, HPA-5a, HPA-5b; HPA-15a, HPA-15b alleles in 150 patients of the Hematology Service of the Hospital das Clínicas (FMUSP). RESULTS: The allele frequencies found were: HPA-1a: 0.837; HPA-1b: 0.163; HPA-2a: 0.830; HPA-2b: 0.170; HPA-3a: 0.700; HPA-3b: 0.300; HPA-4a: 1; HPA-4b: 0; HPA-5a: 0.887; HPA-5b: 0.113; HPA-15a: 0.457 and HPA-15b: 0.543. CONCLUSIONS: Data from the present study showed that the A allele is more common in the population than the B allele, except for HPA-15. This suggests that patients homozygous for the B allele are more predisposed to present alloimmunization and refractoriness to platelet transfusions by immune causes. Platelet genotyping could be of great value in the diagnosis of alloimmune thrombocytopenia and to provide compatible platelet concentrates for these patients.

Stochastic lattice model describing a vector-borne disease

We employ the approach of stochastic dynamics to describe the dissemination of vector-borne diseases such as dengue, and we focus our attention on the characterization of the threshold of the epidemic. The coexistence space comprises two representative spatial structures for both human and mosquito populations. The human population has its evolution described by a process that is similar to the Susceptible-Infected-Recovered (SIR) dynamics. The population of mosquitoes follows a dynamic of the type of the Susceptible Infected-Susceptible (SIS) model. The coexistence space is a bipartite lattice constituted by two structures representing the human and mosquito populations. We develop a truncation scheme to solve the evolution equations for the densities and the two-site correlations from which we get the threshold of the disease and the reproductive ratio. We present a precise deØnition of the reproductive ratio which reveals the importance of the correlations developed in the early stage of the disease. According to our deØnition, the reproductive rate is directed related to the conditional probability of the occurrence of a susceptible human (mosquito) given the presence in the neighborhood of an infected mosquito (human). The threshold of the epidemic as well as the phase transition between the epidemic and the non-epidemic states are also obtained by performing Monte Carlo simulations. References: [1] David R. de Souza, T^ania Tom∂e, , Suani R. T. Pinho, Florisneide R. Barreto and M∂ario J. de Oliveira, Phys. Rev. E 87, 012709 (2013). [2] D. R. de Souza, T. Tom∂e and R. M. ZiÆ, J. Stat. Mech. P03006 (2011).

3D probability tomography: theoretical developments and applications to high-resolution geophysical prospecting

The theory of the 3D multipole probability tomography method (3D GPT) to image source poles, dipoles, quadrupoles and octopoles, of a geophysical vector or scalar field dataset is developed. A geophysical dataset is assumed to be the response of an aggregation of poles, dipoles, quadrupoles and octopoles. These physical sources are used to reconstruct without a priori assumptions the most probable position and shape of the true geophysical buried sources, by determining the location of their centres and critical points of their boundaries, as corners, wedges and vertices. This theory, then, is adapted to the geoelectrical, gravity and self potential methods. A few synthetic examples using simple geometries and three field examples are discussed in order to demonstrate the notably enhanced resolution power of the new approach. At first, the application to a field example related to a dipole–dipole geoelectrical survey carried out in the archaeological park of Pompei is presented. The survey was finalised to recognize remains of the ancient Roman urban network including roads, squares and buildings, which were buried under the thick pyroclastic cover fallen during the 79 AD Vesuvius eruption. The revealed anomaly structures are ascribed to wellpreserved remnants of some aligned walls of Roman edifices, buried and partially destroyed by the 79 AD Vesuvius pyroclastic fall. Then, a field example related to a gravity survey carried out in the volcanic area of Mount Etna (Sicily, Italy) is presented, aimed at imaging as accurately as possible the differential mass density structure within the first few km of depth inside the volcanic apparatus. An assemblage of vertical prismatic blocks appears to be the most probable gravity model of the Etna apparatus within the first 5 km of depth below sea level. Finally, an experimental SP dataset collected in the Mt. Somma-Vesuvius volcanic district (Naples, Italy) is elaborated in order to define location and shape of the sources of two SP anomalies of opposite sign detected in the northwestern sector of the surveyed area. The modelled sources are interpreted as the polarization state induced by an intense hydrothermal convective flow mechanism within the volcanic apparatus, from the free surface down to about 3 km of depth b.s.l..

Studio delle comunicazioni intraspecifiche in Anarsia lineatella Zeller

Sebbene Anarsia lineatella sia un fitofago ormai da anni introdotto e diffuso in Italia, ancora poco si conosce circa le sue abitudini riproduttive. In considerazione della elevata dannosità di A. lineatella nei pescheti del nord Italia e delle scarse conoscenze sulla sua biologia, si è evidenziata la necessità di approfondire la conoscenza di questo fitofago. Pertanto gli scopi di questa ricerca hanno riguardato l’approfondimento delle conoscenze sui sistemi di comunicazione intraspecifici utilizzati da A. lineatella; la valutazione dell’efficacia di diverse miscele di feromone sintetico, in laboratorio utilizzando anche densità diverse di popolazioni di anarsia e in campo utilizzando gabbie di accoppiamento appositamente costruite, posizionate in frutteti a conduzione biologica nel nord Italia e messe a confronto con gabbie che utilizzavano come fonte attrattiva femmine vergini di tre giorni di età. Sono state condotte prove sul comportamento di maschi di A. lineatella di differenti età in risposta al feromone emesso da femmine vergini di tre giorni di età e al feromone emesso da erogatori di materiale plastico contenenti differenti miscele di feromone sintetico. Sono stati condotti studi per verificare l’influenza del contenuto di alcol ((E)5-10:OH) nella miscela feromonica sulla capacità di inibizione degli accoppiamenti, sottoponendo gli insetti a differenti concentrazioni di feromone in modo da verificare eventuali differenze di attività delle diverse miscele, differenze che emergerebbero con evidenza maggiore alle minori concentrazioni. Alcune prove sono state effettuate anche con differenti densità di popolazione, poiché una maggiore densità di popolazione determina una maggiore probabilità di accoppiamento, evidenziando più chiaramente i limiti di efficacia della miscela utilizzata. Inoltre sono state effettuate prove di campo per confrontare due modelli di erogatore per la confusione sessuale di anarsia contenenti miscele con differenti percentuali di alcol Inoltre, poiché nei pescheti la presenza di A. lineatella è pressoché sempre associata a quella di Cydia molesta e l’applicazione del metodo della confusione deve spesso essere applicato per controllare entrambi gli insetti, può risultare vantaggioso disporre di un unico erogatore contenente entrambi i feromoni; è stato quindi valutato un erogatore contenente una miscela dei due feromoni per verificare eventuali interazioni che possano ridurre l’efficacia.

FRAX® assessment of osteoporotic fracture probability in Switzerland

A Swiss-specific FRAX model was developed. Patient profiles at increased probability of fracture beyond currently accepted reimbursement thresholds for bone mineral density (BMD) measurement by dual X-ray absorptiometry (DXA), and osteoporosis treatment were identified.

A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.

A project-oriented course in probability and statistics for undergraduate electrical engineering students

An introductory course in probability and statistics for third-year and fourth-year electrical engineering students is described. The course is centered around several computer-based projects that are designed to achieve two objectives. First, the projects illustrate the course topics and provide hands-on experience for the students. The second and equally important objective of the projects is to convey the relevance and usefulness of probability and statistics to practical problems that undergraduate students can appreciate. The benefit of this course as to motivate electrical engineering students to excel in the study of probability concepts, instead of viewing the subject as one more course requirement toward graduation. The authors co-teach the course, and MATLAB is used for mast of the computer-based projects

New Results Concerning Probability Distributions with Increasing Generalized Failure Rates

The generalized failure rate of a continuous random variable has demonstrable importance in operations management. If the valuation distribution of a product has an increasing generalized failure rate (that is, the distribution is IGFR), then the associated revenue function is unimodal, and when the generalized failure rate is strictly increasing, the global maximum is uniquely specified. The assumption that the distribution is IGFR is thus useful and frequently held in recent pricing, revenue, and supply chain management literature. This note contributes to the IGFR literature in several ways. First, it investigates the prevalence of the IGFR property for the left and right truncations of valuation distributions. Second, we extend the IGFR notion to discrete distributions and contrast it with the continuous distribution case. The note also addresses two errors in the previous IGFR literature. Finally, for future reference, we analyze all common (continuous and discrete) distributions for the prevalence of the IGFR property, and derive and tabulate their generalized failure rates.