Sensitivity and Bias within the Binary Signal Detection Theory, BSDT

Similar to classic Signal Detection Theory (SDT), recent optimal Binary Signal Detection Theory (BSDT) and based on it Neural Network Assembly Memory Model (NNAMM) can successfully reproduce Receiver Operating Characteristic (ROC) curves although BSDT/NNAMM parameters (intensity of cue and neuron threshold) and classic SDT parameters (perception distance and response bias) are essentially different. In present work BSDT/NNAMM optimal likelihood and posterior probabilities are analytically analyzed and used to generate ROCs and modified (posterior) mROCs, optimal overall likelihood and posterior. It is shown that for the description of basic discrimination experiments in psychophysics within the BSDT a ‘neural space’ can be introduced where sensory stimuli as neural codes are represented and decision processes are defined, the BSDT’s isobias curves can simultaneously be interpreted as universal psychometric functions satisfying the Neyman-Pearson objective, the just noticeable difference (jnd) can be defined and interpreted as an atom of experience, and near-neutral values of biases are observers’ natural choice. The uniformity or no-priming hypotheses, concerning the ‘in-mind’ distribution of false-alarm probabilities during ROC or overall probability estimations, is introduced. The BSDT’s and classic SDT’s sensitivity, bias, their ROC and decision spaces are compared.

Fuzzy Membership Functions in a Fuzzy Decision Making Problem

Authors analyses questions of the subjective uncertainty and inexactness situations in the moment of using expert information and another questions which are connected with expert information uncertainty by fuzzy sets with rough membership functions in this article. You can find information about integral problems of individual expert marks and about connection among total marks “degree of inexactness” with sensibility of measurement scale. A lot of different situation which are connected with distribution of the function accessory significance and orientation of the concrete take to task decision making are analyses here.

On some Mixture Distributions

The aim of this paper is to establish some mixture distributions that arise in stochastic processes. Some basic functions associated with the probability mass function of the mixture distributions, such as k-th moments, characteristic function and factorial moments are computed. Further we obtain a three-term recurrence relation for each established mixture distribution.

Hermite Polynomials and the Zero-Distribution of Riemann's Zeta Function

AMS Subject Classification 2010: 11M26, 33C45, 42A38.

Some Properties of Mittag-Leffler Functions and Matrix-Variate Analogues: A Statistical Perspective

Mathematical Subject Classification 2010:26A33, 33E99, 15A52, 62E15.

Special Functions and Pathways for Problems in Astrophysics: An Essay in Honor of A.M. Mathai

The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions related to reaction, diffusion, and reaction-diffusion models. The essay also highlights Mathai's recent work on entropic, distributional, and differential pathways to basic concepts in statistical mechanics, making use of his earlier research results in information and statistical distribution theory. The results presented in the essay cover a period of time in Mathai's research from 1982 to 2008 and are all related to the thematic area of the gravitationally stabilized solar fusion reactor and fractional reaction-diffusion, taking into account concepts of non-extensive statistical mechanics. The time period referred to above coincides also with Mathai's exceptional contributions to the establishment and operation of the Centre for Mathematical Sciences, India, as well as the holding of the United Nations (UN)/European Space Agency (ESA)/National Aeronautics and Space Administration (NASA) of the United States/ Japanese Aerospace Exploration Agency (JAXA) Workshops on basic space science and the International Heliophysical Year 2007, around the world. Professor Mathai's contributions to the latter, since 1991, are a testimony for his social con-science applied to international scientific activity.

Conditional Confidence Interval for the Scale Parameter of a Weibull Distribution

2000 Mathematics Subject Classification: 62F25, 62F03.

Mixed Negative Binomial Distribution by Weighted Gamma Mixing Distribution

Павел Т. Стойнов - В тази работа се разглежда отрицателно биномното разпределение, известно още като разпределение на Пойа. Предполагаме, че смесващото разпределение е претеглено гама разпределение. Изведени са вероятностите в някои частни случаи. Дадени са рекурентните формули на Панжер.

An Estimate of the Probability Pr(X

2000 Mathematics Subject Classification: 33C90, 62E99

Bayesian Prediction of Weibull Distribution Based on Fixed and Random Sample Size

2000 Mathematics Subject Classification: 62E16, 65C05, 65C20.

A bizonyosságfüggvények elméletének alkalmazása a pénzügyi kimutatások ellenőrzésében (The application of the theory of belief functions in the audit of financial statements)

A könyvvizsgálati kockázat a téves auditjelentés kiadásának kockázata olyan esetekben, amikor a beszámoló lényeges hibás állítást tartalmaz. Ez a kockázat indirekt módon a hitelintézetek és pénzügyi vállalkozások működésében is megjelenik azokban az esetekben, amikor a lényeges hibás állítást a finanszírozott vállalkozás auditált beszámolója tartalmazza, amelynek az alapján finanszírozási döntést hoznak, vagy a finanszírozás folytatásáról a beszámolóban szereplő, hibás információkból számított hitelkovenánsok alapján döntenek. A könyvvizsgálat kockázatában a vizsgált gazdálkodó üzleti kockázatai tükröződnek vissza, ezért a kockázat felmérése és az ellenőrzés ennek alapján való megtervezése, majd végrehajtása kulcsfontosságú. Jelen tanulmány – kapcsolódva a Hitelintézeti Szemle 2011. évi 4. számához – szintén a kockázat és bizonytalanság témakörét tárgyalja, pontosabban ennek egy gyakorlati vetületét: a bizonyosságfüggvények (belief functions) alkalmazását a könyvvizsgálatban; mindezt a teljesség és a tankönyvszerű rendszerfelépítés igénye nélkül. A módszer ugyanis hazánkban szinte ismeretlen, nemzetközi viszonylatban viszont empirikus kutatásban is rámutattak már az alkalmazás lehetséges előnyeire a hagyományos valószínűségelméleten alapuló számszerű kockázatbecslésekkel szemben. Eszerint a bizonyosságfüggvények jobban reprezentálják a könyvvizsgálóknak a kockázatról alkotott képét, mint a valószínűségek, mert – szemben a hagyományos modellel – nem két, hanem három állapotot kezelnek: a pozitív bizonyíték létezését, a negatív bizonyíték létezését és a bizonyíték hiányának esetét. _______ Audit risk is the risk that the auditor expresses an inappropriate audit opinion when the fi nancial statements are materially misstated. This kind of risk indirectly appears in the fi nancial statements of fi nancial institutions, when the material misstatement is in the fi nanced entity’s statements that serve as a basis for lending decisions or when the decision is made based upon credit covenants calculated from misstated information. The risks of the audit process refl ect the business risks of the auditee, so the assessment of risks, and further the planning and performance of the audit based on it is of key importance. The current study – connecting to No 4 2011 of Hitelintézeti Szemle – also discusses the topic of risk and uncertainty, or to be more precise a practical implementation of the aforementioned: the application of belief functions in the fi eld of external audit. All this without the aim of achieving completeness or textbook-like scrutiny in building up the theory. While the formalism is virtually unknown in Hungary, on the international scene empirical studies pointed out the possible advantages of the application of the method in contrast to risk assessments based on the traditional theory of probability. Accordingly, belief functions provide a better representation of auditors’ perception of risk, as in contrast to the traditional model, belief functions deal with three rather than two states: the existence of supportive evidence, that of negative evidence and the lack of evidence.

Indication strength of coenological similarity patterns based on genus-level taxon lists and prevalence distribution

Several methods and indicators can be used to evaluate the coenological state of a given habitat, the ones which can be created simply, quickly, standardizably and reliably and which can be used to exactly quantify the state of a given habitat in point of numbers can be of outstanding practical importance in ecology. One possible method is the examination of the genera which can be found in a given habitat in great abundance and have little number of species and various ecological characteristics. For this purpose one of the most appropriate groups is that of ground-dwelling oribatid mites (Acari: Oribatida). In our research, joining the bioindication methodological project of the “Adaptation to Climate Change” Research Group of the Hungarian Academy of Sciences, the indication strength of genus-level taxon lists and the effects of the main pattern-generating factors creating similarity patterns were analysed with the help of data series on oribatid mites collected by us and originating from literature. Our aim was to develop a method with the help of which the difference expressed with distance functions between two oribatid mite genus lists originating from any sources can correspond to spatial and temporal scales. Our results prove that these genus lists are able to express the spatial distance of the habitats. With the help of this base of comparison changes in disturbed or transformed habitats can be expressed by means of oribatid mite communities, with spatial and temporal distances.

Phylogenetic and ontogenetic influences on the distribution of anthocyanins and betacyanins in leaves of tropical plants

We examined the anatomy of expanding, mature, and senescing leaves of tropical plants for the presence of red pigments: anthocyanins and betacyanins. We studied 463 species in total, 370 genera, belonging to 94 families. This included 21 species from five families in the Caryophyllales, where betacyanins are the basis for red color. We also included 14 species of ferns and gymnosperms in seven families and 29 species with undersurface coloration at maturity. We analyzed 399 angiosperm species (74 families) for factors (especially developmental and evolutionary) influencing anthocyanin production during expansion and senescence. During expansion, 44.9% produced anthocyanins and only 13.5% during senescence. At both stages, relatively few patterns of tissue distributions developed, primarily in the mesophyll, and very few taxa produced anthocyanins in dermal and ground tissue simultaneously. Of the 35 species producing anthocyanins both in development and senescence, most had similar cellular distributions. Anthocyanin distributions were identical in different developing leaves of three heteroblastic taxa. Phylogeny has influenced the distribution of anthocyanins in the epidermis and mesophyll of expanding leaves and the palisade parenchyma during senescence, although these influences are not strong. Betacyanins appear to have similar distributions in leaves of taxa within the Caryophyllales and, perhaps, similar functions. The presence of anthocyanins in the mesophyll of so many species is inconsistent with the hypothesis of protection against UV damage or fungal pathogens, and the differing tissue distributions indicate that the pigments may function in different ways, as in photoprotection and freeradical scavenging.

Development of safety performance functions for empirical Bayes estimation of crash reduction factors

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.

Hydrological drivers of wetland vegetation community distribution within Everglades National Park, Florida

The influence of hydrological dynamics on vegetation distribution and the structuring of wetland environments is of growing interest as wetlands are modified by human action and the increasing threat from climate change. Hydrological properties have long been considered a driving force in structuring wetland communities. We link hydrological dynamics with vegetation distribution across Everglades National Park (ENP) using two publicly available datasets to study the probability structure of the frequency, duration, and depth of inundation events along with their relationship to vegetation distribution. This study is among the first to show hydrologic structuring of vegetation communities at wide spatial and temporal scales, as results indicate that the percentage of time a location is inundated and its mean depth are the principal structuring variables to which individual communities respond. For example, sawgrass, the most abundant vegetation type within the ENP, is found across a wide range of time inundated percentages and mean depths. Meanwhile, other communities like pine savanna or red mangrove scrub are more restricted in their distribution and found disproportionately at particular depths and inundations. These results, along with the probabilistic structure of hydropatterns, potentially allow for the evaluation of climate change impacts on wetland vegetation community structure and distribution.