![]() The algorithm starts with a large interval, known to contain \(x_0\), and then successively reduces the size of the interval until it brackets the root. The goal is to find a root \(x_0\in\) such that \(f(x_0)=0\). The bisection algorithm is a simple method for finding the roots of one-dimensional functions. 7.3.6 Example: Bernoulli Random Effects Model.7.3.3 Gibbs Sampling and Metropolis Hastings.7.3.1 Example: Bivariate Normal Distribution.7.2.5 Single Component Metropolis-Hastings.7.2.2 Independence Metropolis Algorithm.6.4.2 Properties of the Importance Sampling Estimator.6.4.1 Example: Bayesian Sensitivity Analysis.6.3.3 Empirical Supremum Rejection Sampling.4.3.2 Constrained Minimization With and Adaptive Barrier.4.3.1 Example: Minorization in a Two-Part Mixture Model.4.1 EM Algorithm for Exponential Families.2.4.3 Newton’s Method for Maximum Likelihood Estimation. ![]() 2.4.2 Convergence Rate of Newton’s Method.2.3.2 Convergence Rates for Shrinking Maps.
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