probability distributions
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2022 ◽  
Vol 31 (2) ◽  
pp. 1-39
Olawole Oni ◽  
Emmanuel Letier

Release planning—deciding what features to implement in upcoming releases of a software system—is a critical activity in iterative software development. Many release planning methods exist, but most ignore the inevitable uncertainty in estimating software development effort and business value. The article’s objective is to study whether analyzing uncertainty during release planning generates better release plans than if uncertainty is ignored. To study this question, we have developed a novel release planning method under uncertainty, called BEARS, that models uncertainty using Bayesian probability distributions and recommends release plans that maximize expected net present value and expected punctuality. We then compare release plans recommended by BEARS to those recommended by methods that ignore uncertainty on 32 release planning problems. The experiment shows that BEARS recommends release plans with higher expected net present value and expected punctuality than methods that ignore uncertainty, thereby indicating the harmful effects of ignoring uncertainty during release planning. These results highlight the importance of eliciting and analyzing uncertainty in software effort and value estimations and call for increased research in these areas.

2022 ◽  
Vol 73 (1) ◽  
pp. 59-70

Estimation of rainfall for a given return period is of utmost importance for planning and design of minor and major hydraulic structures. This can be achieved through Extreme Value Analysis (EVA) of rainfall by fitting Extreme Value family of Distributions (EVD) such as Generalized Extreme Value, Extreme Value Type-1, Extreme Value Type-2 and Generalized Pareto to the series of observed Annual 1-Day Maximum Rainfall (AMR) data. Based on the intended applications and the variate under consideration, Method of Moments (MoM), Maximum Likelihood Method (MLM) and L-Moments (LMO) are used for determination of parameters of probability distributions. The adequacy of fitting EVD to the AMR series was evaluated by quantitative assessment using Goodness-of-Fit (viz., Chi-square and Kolmogorov-Smirnov) and diagnostic test (viz., D-index) tests and qualitative assessment by the fitted curves of the estimated rainfall. The paper presents a study on intercomparison of EVD (using MoM, MLM and LMO) adopted in EVA of rainfall with illustrative example and the results obtained thereof. 

2022 ◽  
pp. 1-24
Kohei Ichikawa ◽  
Asaki Kataoka

Abstract Animals make efficient probabilistic inferences based on uncertain and noisy information from the outside environment. It is known that probabilistic population codes, which have been proposed as a neural basis for encoding probability distributions, allow general neural networks (NNs) to perform near-optimal point estimation. However, the mechanism of sampling-based probabilistic inference has not been clarified. In this study, we trained two types of artificial NNs, feedforward NN (FFNN) and recurrent NN (RNN), to perform sampling-based probabilistic inference. Then we analyzed and compared their mechanisms of sampling. We found that sampling in RNN was performed by a mechanism that efficiently uses the properties of dynamical systems, unlike FFNN. In addition, we found that sampling in RNNs acted as an inductive bias, enabling a more accurate estimation than in maximum a posteriori estimation. These results provide important arguments for discussing the relationship between dynamical systems and information processing in NNs.

2022 ◽  
Vol 5 (4) ◽  
Muhammad Ilyas ◽  
Shaheen Abbas ◽  
Afzal Ali

In this study, we present a univariate probability distribution through application of the three Sub and Super Exponential heavier-longer and lighter-shorter tails fitting. This univariate family includes the Lognormal, Gamma and Weibull distribution, the adequacy of the distribution tails is obtained by adequate Fitting Tests and descriptive Criterion. It emphasizes on tail values and is independent of the number of intervals. In this regards the time series analysis for the last three centuries of the logarithm population data sets over to Karachi region (from1729 to1946 and from 1951 to 2018) is used, which contains irregular and regular length and peaks, That peaks /tails fitting is attained by methods for validation and normality tests and defined by stochastic depiction. In other hand, Weibull and Lognormal distribution tails are found as heavier distribution by two validation tests (Maximum Likelihood Estimation and probability of correct selection), In the final section, the univariate probability distributions are used to Monte Carlo simulation for generating the actual population data, it indicates that the heavy-tailed Lognormal and Weibull distributions are also fitted contract than the more commonly seen lighter tailed Gamma distribution. So, the Monte Carlo Simulation performs the appropriate Lognormal and Weibull distributions for irregular and regular data and generate data values (298 and 69) from duration of 1729 to 2020 and 1951 to 2020. Copyright(c) The Author

Wolfgang Hornfeck

Abstract We present an illustrative analysis of the complexity of a crystal structure based on the application of Shannon’s entropy formula in the form of Krivovichev’s complexity measures and extended according to the contributions of distinct discrete probability distributions derived from the atomic numbers and the Wyckoff multiplicities and arities of the atoms and sites constituting the crystal structure, respectively. The results of a full crystallographic complexity partition analysis for the intermetallic phase Mo3Al2C, a compound of intermediate structural complexity, are presented, with all calculations performed in detail. In addition, a partial analysis is discussed for the crystal structures of α- and β-quartz.

2022 ◽  
Vol 12 (1) ◽  
Joelma Alexandra Ruberti Medeiros ◽  
Mellina Yamamura ◽  
Zilda Pereira da Silva ◽  
Carmen Silvia Bruniera Domingues ◽  
Eliseu Alves Waldman ◽  

AbstractWe aimed to estimate the occurrence of syphilis in pregnant women (SPW) and congenital syphilis (CS) in the municipalities of the state of São Paulo (SP) and evaluate their relationship with socioeconomic, demographic, and health care variables. We developed an ecological study based on secondary data of SPW and CS with spatiotemporal components from 645 municipalities in SP including data from 2007 to 2018. We modeled the data in a Bayesian context, considered spatial and temporal random effects, and used binomial negative probability distributions. We found a continuous increase in the relative temporal risk of SPW, from 2007 to 2018, and CS, from 2007 to 2017, when their incidences increased by 8.6 and 6.6 times, respectively. This increase occurred en bloc in practically all municipalities of SP. The increase in SPW was associated with teenage pregnancy, municipalities with a large number of inhabitants, and acquired immunodeficiency syndrome (AIDS) incidence. The increase in CS was associated with municipalities with a large number of inhabitants, incomplete antenatal care, and AIDS incidence. Although actions to control these diseases are required in all municipalities of SP, the identification of high-risk areas points to priority regions for development.

Min Dai ◽  
Xiaodian Chen ◽  
Kun WANG ◽  
Yangping Luo ◽  
Shu Wang ◽  

Abstract The development of large-scale time-domain surveys provides an opportunity to study the physical properties as well as the evolutionary scenario of B-type subdwarfs (sdB) and M-type dwarfs (dM). Here, we obtained 33 sdB+dM eclipsing binaries based on the Zwicky Transient Facility (ZTF) light curves and {\sl Gaia} early data release 3 (EDR3) parallaxes. By using the PHOEBE code for light curve analysis, we obtain probability distributions for parameters of 29 sdB+dM. $R_1$, $R_2$, and $i$ are well determined, and the average uncertainty of mass ratio $q$ is 0.08. Our parameters are in good agreement with previous works if a typical mass of sdB is assumed. Based on parameters of 29 sdB+dM, we find that both the mass ratio $q$ and the companion's radius $R_2$ decrease with the shortening of the orbital period. For the three sdB+dMs with orbital periods less than 0.075 days, their companions are all brown dwarfs. The masses and radii of the companions satisfy the mass--radius relation for low-mass stars and brown dwarfs. Companions with radii between $0.12R_\odot$ and $0.15R_\odot$ seem to be missing in the observations. As more short-period sdB+dM eclipsing binaries are discovered and classified in the future with ZTF and {\sl Gaia}, we will have more information to constrain the evolutionary ending of sdB+dM.

2022 ◽  
Vol Volume 18, Issue 1 ◽  
Batya Kenig ◽  
Dan Suciu

Integrity constraints such as functional dependencies (FD) and multi-valued dependencies (MVD) are fundamental in database schema design. Likewise, probabilistic conditional independences (CI) are crucial for reasoning about multivariate probability distributions. The implication problem studies whether a set of constraints (antecedents) implies another constraint (consequent), and has been investigated in both the database and the AI literature, under the assumption that all constraints hold exactly. However, many applications today consider constraints that hold only approximately. In this paper we define an approximate implication as a linear inequality between the degree of satisfaction of the antecedents and consequent, and we study the relaxation problem: when does an exact implication relax to an approximate implication? We use information theory to define the degree of satisfaction, and prove several results. First, we show that any implication from a set of data dependencies (MVDs+FDs) can be relaxed to a simple linear inequality with a factor at most quadratic in the number of variables; when the consequent is an FD, the factor can be reduced to 1. Second, we prove that there exists an implication between CIs that does not admit any relaxation; however, we prove that every implication between CIs relaxes "in the limit". Then, we show that the implication problem for differential constraints in market basket analysis also admits a relaxation with a factor equal to 1. Finally, we show how some of the results in the paper can be derived using the I-measure theory, which relates between information theoretic measures and set theory. Our results recover, and sometimes extend, previously known results about the implication problem: the implication of MVDs and FDs can be checked by considering only 2-tuple relations.

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