Applied probability /
"This textbook on applied probability is intended for graduate students in applied mathematics, biostatistics, computational biology, computer science, physics, and statistics. It presupposes knowledge of multivariate calculus, linear algebra, ordinary differential equations, and elementary pro...
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| Format: | Book |
| Language: | English |
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New York :
Springer,
©2003.
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| Series: | Springer texts in statistics.
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| Subjects: |
Table of Contents:
- Basic Notions of Probability Theory
- Probability and Expectation
- Conditional Probability
- Independence
- Distributions, Densities, and Moments
- Convolution
- Random Vectors
- Multivariate Normal Random Vectors
- Convergence
- Calculation of Expectations
- Indicator Random Variables and Symmetry
- Conditioning
- Moment Transforms
- Tail Probability Methods
- Moments of Reciprocals and Ratios
- Reduction of Degree
- Spherical Surface Measure
- Dirichlet Distribution
- Convexity, Optimization, and Inequalities
- Convex Functions
- Minimization of Convex Functions
- The MM Algorithm
- Moment Inequalities
- Combinatorics
- Inclusion-Exclusion
- Applications to Order Statistics
- Stirling Numbers
- Application to an Urn Model
- Pigeonhole Principle
- Combinatorial Optimization
- Quick Sort
- Data Compression and Huffman Coding
- Graph Coloring
- Point Sets with Only Acute Angles
- Sperner's Theorem
- Subadditivity and Expectations
- Poisson Processes
- The Poisson Distribution
- Characterization and Construction
- One-Dimensional Processes
- Transmission Tomography
- Mathematical Applications
- Transformations
- Marking and Coloring
- Campbell's Moment Formulas
- Discrete-Time Markov Chains
- Definitions and Elementary Theory
- Coupling
- Hitting Probabilities and Hitting Times
- Markov Chain Monte Carlo
- The Hastings-Metropolis Algorithm
- Gibbs Sampling
- Convergence of the Independence Sampler
- Simulated Annealing
- Continuous-Time Markov Chains.