BASIC PROBABILISTIC METHODS IN GEOLOGICAL SEARCH

Geophysics ◽  
1964 ◽  
Vol 29 (1) ◽  
pp. 105-108 ◽  
Author(s):  
A. Kyrala
Keyword(s):  
Poisson Distribution ◽  
Conditional Probability ◽  
Optimal Allocation ◽  
Probabilistic Methods ◽  
A Posteriori ◽  
Mathematical Methods ◽  
Geological Structures ◽  
Restrictive Assumption ◽  
Specific Distribution ◽  
Successful Search

An exposition of the basic mathematical methods used in calculating the probability of successful search for geological structures in a discrete set of regions is given. The argument is framed without the restrictive assumption of a specific distribution for the conditional probability of discovery but is subsequently illustrated by the specific case of a Poisson distribution. The optimal allocation of search effort to the various regions is determined. The important question of how the probabilities of occurrence of deposits should be adjusted after unsuccessful search is specifically answered by calculation of the a posteriori probabilities.

scholarly journals INVESTIGATION OF THE EFFICIENCY OF LABOUR SAFETY MEANS BY STATISTICAL GAMES

2002 ◽  
Vol 8 (3) ◽  
pp. 192-196
Author(s):  
Petras Čyras ◽  
Sigutė Vakrinienė
Keyword(s):  
Optimal Strategy ◽  
Optimal Allocation ◽  
Statistical Data ◽  
Preventive Measures ◽  
Matrix Game ◽  
Mathematical Methods ◽  
The Real ◽  
Safe Control ◽  
Definite Period ◽  
Statistical Game

Statistical data regarding causes and number of accidents in enterprises and organisations allow to foresee the average number of traumas for a definite period when no additional means for trauma prevention have been provided. The trauma prevention means differ because they require different financing and decreasing the number of traumas. The suggested mathematical methods give the possibility to appraise the means of trauma prevention according to the definite sum invested. Some accidents are related to individual miss-steps/mistakes at work. Trying to find out the ways for optimal trauma prevention we can take the latter causes as statistical game of “nature” state and certain possible situations of existing in determination. They are impossible to be changed, though some preventive means applied by employees may decrease the trauma cases caused by individual safe control violation. As soon as the optimal strategy of the aforementioned matrix game is found, the most important preventive means could be determined. They could guarantee the real decrease of the trauma cases in spite of any violations by employees. A certain modification of the straightforward programme making task allows us to get an optimal allocation of means necessary for trauma prevention, thus evaluating the effectiveness of preventive measures when the optimal financing is found as the means are increasing.

scholarly journals Determination of risk planning a route with the use of a probability model

2018 ◽  
Vol 19 (6) ◽  
pp. 266-270
Author(s):  
Katarzyna Topolska
Keyword(s):  
Reduction Method ◽  
Probability Model ◽  
Probabilistic Methods ◽  
Bayes Classifier ◽  
Optimal Parameters ◽  
Mathematical Methods ◽  
Varimax Rotation ◽  
Related Risk ◽  
Variable Reduction

This paper aims to familiarize readers with notions related to probabilistic methods used for planning routes in telematics systems. The classification task made use of the model based on probabilistic Bayes’ classifier and the probability density function. The first part of the paper describes problems with planning routing in contemporary telematics systems. The second part covers a theoretical basis of classifiers based on hard mathematical methods. If such a model is to make sense, it should account for smaller kinds of risk related to a transport process. This paper presents a method of selecting the most optimal parameters in transport planning. Its author draws attention to the variable reduction method necessary for planning supported by a factor analysis of principal components together with Varimax rotation normalized with Kaiser’s method for quantitative features. The third part is devoted to the process of planning routes and the related risk

The Water-Land-Energy-Food-Climate Nexus In Sardinia

2020 ◽  
Author(s):  
Antonio Trabucco ◽  
Sara Masia ◽  
Janez Sušnik ◽  
Donatella Spano ◽  
Simone Mereu
Keyword(s):  
Climate Change ◽  
Water Management ◽  
Land Use ◽  
Natural Resources ◽  
Optimal Allocation ◽  
Freshwater Ecosystems ◽  
Irrigated Agriculture ◽  
Trade Offs ◽  
Specific Distribution ◽  
The Mediterranean

<p>Water use in the Mediterranean has been often pushed beyond sustainability, leading to water degradation and deterioration of ecosystem services. Different factors are interlinked with water management within a dynamically complex system (i.e. the Nexus) characterized by many feedbacks, trade-offs and high complexity of socioeconomic and environmental agents inducing non-linear responses hard to predict. Understanding such nexus systems requires innovative methodologies able to integrate different domains (e.g. hydrology, economics, planning, environmental and social sciences) and potential feedbacks, to support effective and targeted adaptation measures, taking into consideration uncertainty of climate change forecasts and associated impacts. Within the H2020 SIM4NEXUS project, water-land-energy-food-climate nexus links for Sardinia Island were represented with system dynamics modelling, together with relevant policy objectives, goals and measures. Sardinia, as many other Mediterranean regions, must implement a sustainable approach to water management, taking into account an equitable distribution of water resources between different sectors, economic needs, social priorities and ecology of freshwater ecosystems.</p><p>For the Sardinia case study, the main focus was the representation of the reservoir water balance for the island, accounting predominantly for water supply and for water demand related to agricultural, hydro-power production, domestic/tourist consumption and environmental flows. With irrigated agriculture being the largest water consumer, this sector was modelled in more detail with crop specific distribution and projections. While water is the central focus, links with other nexus sectors including energy, climate, food and land use are included. Energy generation and consumption were also important along with the mode of generation and sector of consumption, as was modelling the change in crop types (i.e. land use and food production changes) and the crop water requirements associated with potential crop and cropped area changes, and in response to change in the local climate. Energy production is modelled from sources including oil, coal and methane, solar, wind and hydropower, while energy demand comes from the agricultural, domestic, industrial and service sectors (including transportation). The use of energy from the different sectors and using different energy sources, either renewable and not renewable, have different implication on GHG and climate change.</p><p>While driven by strong interests to secure food provisions, an increase in irrigation in the Mediterranean may not be totally sustainable. Irrigation requirements of crops are projected to increase between 4 and 18% for 2050 compared to present conditions, limiting expansion of irrigated agriculture in Sardinia. Over the same period the inflow in the reservoirs can decrease between 5 and 20% and evaporation losses from reservoir surface bodies increase by 10%. Policy rules are tested and highlight how optimal allocation should be enforced in order to safeguard sustainability of natural resources over time, especially when considering climate variability. Natural resources are better preserved avoiding conflicts with strong seasonal peaks (i.e. summer). To meet these criticalities, new infrastructures and investments should increase use efficiency, All this would require changes in institutional and market conditions with a more cautious water management that includes prices and recycling policies.</p>

Probabilistic Pressurized Thermal Shocks Analysis for a Reactor Pressure Vessel by Considering Plume Effect

2015 ◽  
Author(s):  
Guian Qian ◽  
V. F. González-Albuixech ◽  
Markus Niffenegger ◽  
Medhat Sharabi
Keyword(s):  
Crack Initiation ◽  
Conditional Probability ◽  
Pressure Vessel ◽  
Cooling Water ◽  
Reactor Pressure Vessel ◽  
Probabilistic Methods ◽  
Integrity Assessment ◽  
Inner Surface ◽  
Reactor Pressure ◽  
Thermal Shocks

The inner surface of a reactor pressure vessel (RPV) is assumed to be subjected to pressurized thermal shocks (PTSs) caused by the downstream of emergency cooling water. The downstream is not homogeneous but typically in a plume shape coming from the inlet nozzles. In this paper, both deterministic and probabilistic methods are used to assess the integrity of a model RPV subjected to PTS. The FAVOR code is used to calculate the probabilities for crack initiation and failure of the RPV considering crack distributions based on cracks observed in the Shoreham and PVRUF RPVs. The study shows that peak KI of the cracks inside the plume increases about 33% compared with that outside. The conditional probability inside the plume is more than eight orders of magnitude higher than outside the plume. In order to be conservative, it is necessary to consider the plume effect in the integrity assessment.

scholarly journals Calculation of Interspike Intervals for Integrate-and-Fire Neurons with Poisson Distribution of Synaptic Inputs

2000 ◽  
Vol 12 (8) ◽  
pp. 1789-1820 ◽  
Author(s):  
A. N. Burkitt ◽  
G. M. Clark
Keyword(s):  
Membrane Potential ◽  
Probability Density ◽  
Poisson Distribution ◽  
Conditional Probability ◽  
Conditional Probability Density ◽  
Interspike Intervals ◽  
Translational Invariance ◽  
Postsynaptic Response ◽  
Arrival Times ◽  
Integrate And Fire

We present a new technique for calculating the interspike intervals of integrate-and-fire neurons. There are two new components to this technique. First, the probability density of the summed potential is calculated by integrating over the distribution of arrival times of the afferent post-synaptic potentials (PSPs), rather than using conventional stochastic differential equation techniques. A general formulation of this technique is given in terms of the probability distribution of the inputs and the time course of the postsynaptic response. The expressions are evaluated in the gaussian approximation, which gives results that become more accurate for large numbers of small-amplitude PSPs. Second, the probability density of output spikes, which are generated when the potential reaches threshold, is given in terms of an integral involving a conditional probability density. This expression is a generalization of the renewal equation, but it holds for both leaky neurons and situations in which there is no time-translational invariance. The conditional probability density of the potential is calculated using the same technique of integrating over the distribution of arrival times of the afferent PSPs. For inputs with a Poisson distribution, the known analytic solutions for both the perfect integrator model and the Stein model (which incorporates membrane potential leakage) in the diffusion limit are obtained. The interspike interval distribution may also be calculated numerically for models that incorporate both membrane potential leakage and a finite rise time of the postsynaptic response. Plots of the relationship between input and output firing rates, as well as the coefficient of variation, are given, and inputs with varying rates and amplitudes, including inhibitory inputs, are analyzed. The results indicate that neurons functioning near their critical threshold, where the inputs are just sufficient to cause firing, display a large variability in their spike timings.

scholarly journals A Stochastic Graphs Semantics for Conditionals

Erkenntnis ◽  
2019 ◽  
Author(s):  
Krzysztof Wójtowicz ◽  
Anna Wójtowicz
Keyword(s):  
Conditional Probability ◽  
General Problem ◽  
Powerful Method ◽  
Mathematical Methods ◽  
Simple Method ◽  
Stochastic Graphs ◽  
Standard Notion ◽  
Stochastic Graph ◽  
Satisfactory Answer

AbstractWe define a semantics for conditionals in terms of stochastic graphs which gives a straightforward and simple method of evaluating the probabilities of conditionals. It seems to be a good and useful method in the cases already discussed in the literature, and it can easily be extended to cover more complex situations. In particular, it allows us to describe several possible interpretations of the conditional (the global and the local interpretation, and generalizations of them) and to formalize some intuitively valid but formally incorrect considerations concerning the probabilities of conditionals under these two interpretations. It also yields a powerful method of handling more complex issues (such as nested conditionals). The stochastic graph semantics provides a satisfactory answer to Lewis’s arguments against the PC = CP principle, and defends important intuitions which connect the notion of probability of a conditional with the (standard) notion of conditional probability. It also illustrates the general problem of finding formal explications of philosophically important notions and applying mathematical methods in analyzing philosophical issues.

scholarly journals Methods of Learning the Structure of the Bayesian Network

2021 ◽  
Vol 4 ◽  
pp. 56-59
Author(s):  
Anna Salii
Keyword(s):  
Genetic Algorithm ◽  
Bayesian Network ◽  
Conditional Probability ◽  
Real World ◽  
Intelligent Systems ◽  
Probabilistic Reasoning ◽  
Probabilistic Methods ◽  
Independent Basis ◽  
Common Framework ◽  
Methods Of Learning

Sometimes in practice it is necessary to calculate the probability of an uncertain cause, taking into account some observed evidence. For example, we would like to know the probability of a particular disease when we observe the patient’s symptoms. Such problems are often complex with many interrelated variables. There may be many symptoms and even more potential causes. In practice, it is usually possible to obtain only the inverse conditional probability, the probability of evidence giving the cause, the probability of observing the symptoms if the patient has the disease.Intelligent systems must think about their environment. For example, a robot needs to know about the possible outcomes of its actions, and the system of medical experts needs to know what causes what consequences. Intelligent systems began to use probabilistic methods to deal with the uncertainty of the real world. Instead of building a special system of probabilistic reasoning for each new program, we would like a common framework that would allow probabilistic reasoning in any new program without restoring everything from scratch. This justifies the relevance of the developed genetic algorithm. Bayesian networks, which first appeared in the work of Judas Pearl and his colleagues in the late 1980s, offer just such an independent basis for plausible reasoning.This article presents the genetic algorithm for learning the structure of the Bayesian network that searches the space of the graph, uses mutation and crossover operators. The algorithm can be used as a quick way to learn the structure of a Bayesian network with as few constraints as possible.learn the structure of a Bayesian network with as few constraints as possible.

scholarly journals Application of a Priori and a Posteriori Estimate on Risk Assessment 

2018 ◽  
Vol 20 (2) ◽  
pp. 56-61
Author(s):  
Lenka Sivakova ◽  
Anna Zubkova ◽  
Witalis Pellowski
Keyword(s):  
Risk Assessment ◽  
Crisis Management ◽  
A Priori ◽  
Main Idea ◽  
A Posteriori ◽  
Mathematical Methods ◽  
A Posteriori Estimate ◽  
Safety Protection ◽  
Expected Values ◽  
Potential Use

The problem of setting the values and interconnections between elements of the models in the safety, protection and security field, appears as the biggest obstacle in taking crisis management decisions. The article attempts to represent a mathematical approach to modify the expected values and interconnections that can occur in the models describing the protected system in order to minimize errors caused by subjectivity. Here presented procedures are described in the examples of their potential use. The main idea is to focus on improving estimates for better response to reality, then to find new estimates, since those would still be weighed down by the subjectivity caused errors. Based on this premise this article attempts to characterize application of mathematical methods on minimizing the subjectivity caused errors in the models in risk assessment.

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