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Lecture 6
Lecture 6

(10) Frequentist Properties of Bayesian Methods
(10) Frequentist Properties of Bayesian Methods

... For any prior that does not depend on the sample size, as n increases the prior is overwhelmed by the likelihood and the posterior approaches the MLE’s sampling distribution ST495/590: Applied Bayesian Statistics ...
A detail-preserving and flexible adaptive filter for speckle
A detail-preserving and flexible adaptive filter for speckle

Further Properties and a Fast Realization of the Iterative
Further Properties and a Fast Realization of the Iterative

Dynamics of spherical particles on a surface: Collision
Dynamics of spherical particles on a surface: Collision

... and the interaction with the substrate introduce an additional set of parameters ~e.g., the coefficients of rolling and sliding friction!, which have not been included in the theoretical descriptions of the system. Our goal is to bridge this gap between experiment and theory, and formulate a model t ...
Introduction to Bayesian Analysis Procedures
Introduction to Bayesian Analysis Procedures

Introduction to Bayesian Analysis Procedures
Introduction to Bayesian Analysis Procedures

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circular motion

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Contents Syllabus

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Chapter 3 Kinetics of Particles

... Observing that θ̇ ≠ 0 as a function of time, the differential equation of motion is obtained as p mgα mR 2 (1 + α2 )θ̈ + √ ...
lectur~4-1 - Dr. Khairul Salleh Basaruddin
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Conditional Probability Estimation
Conditional Probability Estimation

... 2. Bayesian Approach Let pθ (x) denote the probability function (or density function, in the continuous case) of a random variable X, where “random variable” is not interpreted as implying that X is necessarily real-valued (X could also be categorical, vector-valued, set-valued, and so on). The para ...
a guidebook to particle size analysis
a guidebook to particle size analysis

... A spherical particle can be described using a single number—the diameter— because every dimension is identical. As seen in Figure 1, non-spherical particles can be described using multiple length and width measures (horizontal and vertical projections are shown here). These descriptions provide grea ...
Swarm Intelligence based Soft Computing Techniques for the
Swarm Intelligence based Soft Computing Techniques for the

... Fieldsend [29] defined multi objective problems as being typically complex, with both a large number of parameters to be adjusted and several objectives to be optimized. Multi objective evolutionary algorithms (MOEAs) are a popular approach to confronting multi objective optimization problems by usi ...
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Statistical uncertainty in calculation and measurement of radiation 1

... absorption peak after calculation was finished for incident particle of n. Let’s write a probability that some incident particle participates in full energy absorption peak as p. As shown in Fig. 6, the probability that x particle from 1st to x-th particle participate is px . As the probability of N ...
canim-11 - The University of Texas at Dallas
canim-11 - The University of Texas at Dallas

MAE 241 –Statics Fall 2006 Jacky C. Prucz
MAE 241 –Statics Fall 2006 Jacky C. Prucz

... The motion of a particle is governed by Newton’s three laws of motion.  First Law: A particle originally at rest, or moving in a straight line at constant velocity, will remain in this state if the resultant force acting on the particle is zero.  Second Law: If the resultant force on the particle ...
A Comparative Study on Particle Swarm Optimization for Optimal
A Comparative Study on Particle Swarm Optimization for Optimal

... minimization, and interior point algorithms, have failed in handling nonconvexities and nonsmoothness in engineering optimization problems. The main advantage of EA is that they do not require the objective functions and the constraints to be differentiable and continuous [6]. However, their main pr ...
Major 1 - KFUPM Faculty List
Major 1 - KFUPM Faculty List

Mechanics 3 Revision Notes
Mechanics 3 Revision Notes

... Example: When a golf ball is hit, the ball is in contact with the club for 0.0008 seconds, and over that time the force is modelled by the equation F = kt(0.0008 – t) newtons, where k = 4.3 × 1010. Taking the mass of the golf ball to be 45 grams, and modelling the ball as a particle, find the speed ...
Quantum Mechanics in One Dimension
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... Therefore, although it is not possible to specify with certainty the location of a particle, it is possible to assign probabilities for observing it at any given position. The quantity 兩⌿兩2, the square of the absolute value of ⌿, represents the intensity of the matter wave and is computed as the pro ...
Relational Dynamic Bayesian Networks
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... them, including greater simplicity and expressivity. Furthermore, they may be more easily learned using ILP techniques. We develop a series of efficient inference procedures for RDBNs (which are also applicable to DPRMs or any other relational stochastic process model). The Rao-Blackwellised particl ...
Connected Particles
Connected Particles

... Many of the examples involving moving objects have involved a resistive force. This is often due to friction. Friction depends on the roughness of the bodies touching and on the normal contact force. The roughness is characterised by the coefficient of friction, μ, and the frictional force is then F ...
A Review of Population-based Meta-Heuristic
A Review of Population-based Meta-Heuristic

... described in Section 2 and Section 3 respectively. A brief review of related works is presented in Section 4. In Section 5, several population-based meta-heuristic algorithms in real and binary search spaces are provided in details. Finally, a discussion and summary of this paper will be demonstrate ...
Monte Carlo Simulations
Monte Carlo Simulations

... may have a large number of model parameters, and an inspection of the marginal probability densities of interest may be impractical, or even useless. But it is possible to pseudorandomly generate a large collection of models according to the posterior probability distribution and to analyze and disp ...
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Particle filter

Particle filters or Sequential Monte Carlo (SMC) methods are a set of genetic-type particle Monte Carlo methodologies to solve the filtering problem. The term ""particle filters"" was first coined in 1996 by Del Moral in reference to mean field interacting particle methods used in fluid mechanics since the beginning of the 1960s. The terminology ""sequential Monte Carlo"" was proposed by Liu and Chen in 1998.From the statistical and probabilistic point of view, particle filters can be interpreted as mean field particle interpretations of Feynman-Kac probability measures. These particle integration techniques were developed in molecular chemistry and computational physics by Theodore E. Harris and Herman Kahn in 1951, Marshall. N. Rosenbluth and Arianna. W. Rosenbluth in 1955 and more recently by Jack H. Hetherington in 1984. In computational physics, these Feynman-Kac type path particle integration methods are also used in Quantum Monte Carlo, and more specifically Diffusion Monte Carlo methods. Feynman-Kac interacting particle methods are also strongly related to mutation-selection genetic algorithms currently used in evolutionary computing to solve complex optimization problems.The particle filter methodology is used to solve Hidden Markov Chain (HMM) and nonlinear filtering problems arising in signal processing and Bayesian statistical inference. The filtering problem consists in estimating the internal states in dynamical systems when partial observations are made, and random perturbations are present in the sensors as well as in the dynamical system. The objective is to compute the conditional probability (a.k.a. posterior distributions) of the states of some Markov process, given some noisy and partial observations. With the notable exception of linear-Gaussian signal-observation models (Kalman filter) or wider classes of models (Benes filter) Mireille Chaleyat-Maurel and Dominique Michel proved in 1984 that the sequence of posterior distributions of the random states of the signal given the observations (a.k.a. optimal filter) have no finitely recursive recursion. Various numerical methods based on fixed grid approximations, Markov Chain Monte Carlo techniques (MCMC), conventional linearization, extended Kalman filters, or determining the best linear system (in expect cost-error sense) have never really coped with large scale systems, unstable processes or when the nonlinearities are not sufficiently smooth.Particle filtering methodology uses a genetic type mutation-selection sampling approach, with a set of particles (also called individuals, or samples) to represent the posterior distribution of some stochastic process given some noisy and/or partial observations. The state-space model can be nonlinear and the initial state and noise distributions can take any form required. Particle filter techniques provide a well-established methodology for generating samples from the required distribution without requiring assumptions about the state-space model or the state distributions. However, these methods do not perform well when applied to very high-dimensional systems.Particle filters implement the prediction-updating transitions of the filtering equation directly by using a genetic type mutation-selection particle algorithm. The samples from the distribution are represented by a set of particles; each particle has a likelihood weight assigned to it that represents the probability of that particle being sampled from the probability density function. Weight disparity leading to weight collapse is a common issue encountered in these filtering algorithms; however it can be mitigated by including a resampling step before the weights become too uneven. Several adaptive resampling criteria can be used, including the variance of the weights and the relative entropy w.r.t. the uniform distribution. In the resampling step, the particles with negligible weights are replaced by new particles in the proximity of the particles with higher weights.Particle filters and Feynman-Kac particle methodologies find application in signal and image processing, Bayesian inference, machine learning, risk analysis and rare event sampling, engineering and robotics, artificial intelligence, bioinformatics, phylogenetics, computational science, Economics and mathematical finance, molecular chemistry, computational physics, pharmacokinetic and other fields.
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