- Global Partial Likelihood for Nonparametric Proportional Hazards Models
- Would-be Midterm Exam of Math 341 10:30-11:50am, March 32, Spring 2009
- 4.3. Likelihood and maximum likelihood estimation. Suppose X1, ..., Xn are iid random p-vectors MN(, ). Their joint density is
- Chapter 5. Poisson Processes Patience Pays.
- Would-be Midterm Exam of Math 341 10:30-11:50am, March 32, Spring 2009
- Remarks about conditional expectation. For a given event A with P(A) > 0 and a random variable X, the conditional expectation,
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- Markov Chain: Introduction Whatever happened in the past, be it glory or misery, be Markov!
- 3.6. Branching Processes Branching process, as a typical discrete time Markov chain, is a very useful tool in epidemiologic
- Chapter 4. The Long Run Behavior of Markov Chains In the long run, we are all equal. ---with apology to John Maynard Keynes
- Review of Discrete time Markov Chains (Chapters 3 and 4) 1. A diagram.
- Chapter 6. Continuous Time Markov Chains (Birth & Death Processes) Birth is the inception of death, and death that of resurrection; Right is the inception of wrong, and
- Solutions to DIY Exercises of Chapters 5 Exercise 5.1. Use the moment generating function to derive the mean and variance of a Poisson
- Solutions to All Select-One Problems/Exercises of HW #1 and # 2. Chapter 3. Markov Chains: Introduction
- Solutions to Selected Problems/Exercises of Chapter 5 of the Textbook. Chapter 5. Poisson Processes
- Review of Chapters 5 and 6 Chapter 5. Poisson Processes
- Chapter 7. Renewal Phenomena Renewal is life reborn.
- 7.3. The asymptotic behavior of renewal process. X1, X2, ... are iid positive inter-occurrence times with mean , variance 2
- The Epilogue: Brownian Motion and Beyond. 1. Central limit theorem and the universality of Gaussian distribution.
- Analysis of least absolute deviation By KANI CHEN
- 6.2. Pure death processes 6.2.1. Postulates of pure death processes.
- STOCHASTIC MODELING Spring 2011, HKUST
- Appendix: a forensic analysis of an exercise problem. The aim of this lecture is actually not for review, but rather for a somewhat bigger purpose--to
- Solutions to DIY Exercises of Chapter 7 Exercise 7.1 Please Verify that N(t) + k for any k 1 is a stopping time, but N(t) is not.
- Solutions to Problems/Exercises of Chapter 4 (Homework # 4). Chapter 4. The Long Run Behavior of Markov Chains.
- Advanced Probability Theory Fall 2010, HKUST
- Multivariate Statistical Analysis Fall 2010, HKUST
- Solutions to DIY Exercises of Chapters 3 and 4. Exercise 3.1 Bunny rabbit has three dens A, B and C. It likes A better than B and C. If it's
- Advanced Probability Theory (Math541) Instructor: Kani Chen
- 4.3. More sophisticated examples. Markov Chains require conditional independence of future (tomorrow and after) and past (yesterday
- Solutions to DIY Exercises of Chapter 6 Exercise 6.1 Does Postulate 1 for Poisson Process imply independent increment?
- The Multivariate Normal Distribution. 4.1. Some properties about univariate normal distributiona review.
- 1.2. Distribution, expectation and inequalities. Expectation, also called mean, of a random variable is often referred to as the location or center of
- Advanced Probability Fall 2011, HKUST
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- 1.8. Large deviation and some exponential inequalities. Theory of large deviation (Varadhan, 1984), concerning chance of rare events that are usually of
- 1.7. Strong law of large numbers. Strong law of large numbers (SLLN) is a central result in classical probability theory. The conver-
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- Chapter 8. Principal Components. Principal component, abbreviated as P.C., analysis, was invented by Carl Pearson in 1901. The
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- 1.3. Convergence modes. Unlike convergence of a sequence of numbers, the convergence of a sequence of r.v.s at least has
- Chapter 2. Central Limit Theorem. Central limit theorem, or DeMoivre-Laplace Theorem, which also implies the weak law of large
- Chapter 6. Comparison of Several Multivariate Means. This chapter addresses comparison of several multivariate means. We begin with paired comparison
- Chapter 10. Canonical Analysis Canonical analysis aims at finding the relation between two sets of variables, by singling out pairs
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- Biometrika (2011), xx, x, pp. 111 C 2008 Biometrika Trust
- 1.5. Weak law of large numbers. For a sequence of independent r.v.s X1, X2, ..., classical law of large numbers is typically about the
- 2.2. Central limit theorem. The most ideal case of the CLT is that the random variables are iid with finite variance. Although
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- Chapter 11. Discrimination and Classification. Suppose we have a number of multivariate observations coming from two populations, just as in the
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- Chapter 5. Inferences About The Mean Vector This chapter addresses the most basic and most standard statistical problem about the mean
- Stochastic Modeling Spring 2012, HKUST
- Solutions to DIY Exercises of Chapters 3 and 4. Exercise 3.1 Bunny rabbit has three dens A, B and C. It likes A better than B and C. If it's
- Remarks about conditional expectation. For a given event A with P(A) > 0 and a random variable X, the conditional expectation,
- Beat dealers in blackjack using first step analysis. We use this example to explore the techniques of first step analysis. The rules of blackjack in our
- STOCHASTIC MODELING Spring 2012, HKUST
- 3.5. First step analysis A journey of a thousand miles begins with the first step. Lao Tse
- 3.6. Branching Processes Branching process, as a typical discrete time Markov chain, is a very useful tool in epidemiologic
- Chapter 4. The Long Run Behavior of Markov Chains In the long run, we are all equal. ---with apology to John Maynard Keynes
- Markov Chain: Introduction Whatever happened in the past, be it glory or misery, be Markov!
- 4.3. More sophisticated examples. Markov Chains require conditional independence of future (tomorrow and after) and past (yesterday
