Academic literature on the topic 'Aposterior distribution'

The statistical rating of the image of a fuel jet allows to allocate the zones with homogeneous brightness, to define the distribution of masses and the concentration in a fuel jet and to look after their dynamics. In the research the coding with the usage of Byeses's definition of the aposteriory probability of the presence of the given brightness in the image is described. The bright zones of a fuel jet in a diesel engine will give to the conclusion how the fuel is distributed in the engine combustion camera.

Purpose This paper aims to present development and application of the Bayesian inverse approach for retrieving parameters of non-linear diffusion coefficient based on the integral information. Design/methodology/approach The Bayes formula was used to construct posterior distribution of the unknown parameters of non-linear diffusion coefficient. The resulting aposteriori distribution of sought parameters was integrated using Markov Chain Monte Carlo method to obtain expected values of estimated diffusivity parameters as well as their confidence intervals. Unsteady non-linear diffusion equation was discretised with the Global Radial Basis Function Collocation method and solved in time using Crank–Nicholson technique. Findings A number of manufactured analytical solutions of the non-linear diffusion problem was used to verify accuracy of the developed inverse approach. Reasonably good agreement, even for highly correlated parameters, was obtained. Therefore, the technique was used to compute concentration dependent diffusion coefficient of water in paper. Originality/value An original inverse technique, which couples efficiently meshless solution of the diffusion problem with the Bayesian inverse methodology, is presented in the paper. This methodology was extensively verified and applied to the real-life problem.

This work focuses on the multi-objective optimization of a compliant-mechanism accelerometer. The design objective is to maximize the sensitivity of the accelerometer in its sensing direction, while minimizing its sensitivity in all other directions. In addition, this work proposes a novel compliant hinge intended to reduce the stress concentration in compliant mechanisms. The paper starts with a brief description of the new compliant hinge, the Lamé-shaped hinge, followed by the formulation of the aposteriori multi-objective optimization of the compliant accelerometer. By using the normalized constrained method, an even distribution of the Pareto frontier is found. The paper also provides several optimum solutions on a Pareto plot, as well as the CAD model of the selected solution.

Дипломна робота: 169 с., 21 табл., 48 рис., 2 дод., 29 джерел. Об’єкт дослідження – актуарні ризики, які досліджуються за допомогою байєсівської методології, як потужного інструментарію врахування апріорної та вибіркової інформації з метою уточнення закону розподілу випадкової величини, а також задача прогнозування величини страхових виплат як складна задача актуарної математики, що може бути розв’язана засобами байєсівської методології. Мета роботи – дослідження можливості застосування байєсівської методології для підвищення якості оцінок прогнозів можливих втрат в актуарних задачах; розгляд задач, розв’язок яких може бути покращено шляхом використання байєсівських методів, аналіз задачі прогнозування розподілу величини страхових виплат як такої, що може бути успішно розв’язана за допомогою байєсівських методів аналізу. Моделі - досліджувались байєсівські методи аналізу як інструмент врахування вибіркової та апріорної інформації і модифікації на її основі запропонованих моделей, актуарні ризики як перспективна область застосування байєсівських методів дослідження невизначеності, уточнення структури та покращення адекватності прогностичних якостей моделей. Отримані результати – побудована модель аналізу та прогнозування виплат страхової та модель кількості звернень до страхової. Прогнозні припущення щодо розвитку об’єкту дослідження – узагальнення запропонованого методу аналізу різних типів розподілів випадкових величин, що зустрічаються у страхуванні, проведення дослідження точності моделі залежно від вибору нормуючого коефіцієнта, модифікація відомих методів аналізу та управління страховими ризиками з використанням байєсівської методики.
Bachelor thesis: 169 p., 21 tabl., 48 fig., 2 append., 29 sources. Object of study - actuarial risks, which are studied using Bayesian methodology as a powerful tool for a priori and sample information to clarify the law of distribution of random variables, as well as the problem of predicting the amount of insurance benefits as a complex problem of actuarial mathematics that can be solved by means of Bayesian methodology. Purpose - to study the possibility of applying the Bayesian methodology to improve the quality of estimates of forecasts of possible losses in actuarial problems; consideration of problems, the solution of which can be improved by using Bayesian methods, analysis of the problem of forecasting the distribution of the amount of insurance benefits as such, which can be successfully solved using Bayesian methods of analysis. Used models - Bayesian methods of analysis were studied as a tool to take into account sample and a priori information and modify the proposed models based on it, actuarial risks as a promising area of application of Bayesian methods of uncertainty research, refinement of structure and improvement of adequacy of prognostic qualities of models. Results - a model of analysis and forecasting of insurance payments and a model of the number of appeals to the insurance company. Predictive assumptions about the development of the object of study - generalization of the proposed method of analysis of different types of distributions of random variables found in insurance, study the accuracy of the model depending on the choice of standardization, modification of known methods of analysis and management of insurance risks using Bayesian methodology.

This thesis is concerned with several issues of a posteriori error estimates for linear problems. In its first part error estimates for the heat conduction equation discretized by the backward Euler method in time and discontinuous Galerkin method in space are derived. In the second part guaranteed and locally efficient error estimates involving algebraic error for Poisson equation discretized by the discontinuous Galerkin method are derived. The technique is based on the flux reconstruction where meshes with hanging nodes and variable polynomial degree are allowed. An adaptive strategy combining both adaptive mesh refinement and stopping criteria for iterative algebraic solvers is proposed. In the last part a numerical method for computing guaranteed lower and upper bounds of principal eigenvalues of symmetric linear elliptic differential operators is presented. 1