kjytay’s blog summarizes some properties of equicorrelation matix, which has the following form,
This note is based on Ma, J., Du, K., & Gu, G. (2019). An efficient exponential twisting importance sampling technique for pricing financial derivatives. Communications in Statistics - Theory and Methods, 48(2), 203–219.
This post is based on the talk given by Dr. Yue Wang at the Department of Statistics and Data Science, Southern University of Science and Technology on Jan. 04, 2020.
Prof. Inchi HU will give a talk on Large Scale Inference for Chi-squared Data tomorrow, which proposes the Tweedie’s formula in the Bayesian hierarchical model for chi-squared data, and he mentioned a thought-provoking paper, Efron, B. (2011). Tweedie’s Formula and Selection Bias. Journal of the American Statistical Association, 106(496), 1602–1614., which is the focus of this note.
This post is based on the talk, Gradient-based Sparse Principal Component Analysis, given by Dr. Yixuan Qiu at the Department of Statistics and Data Science, Southern University of Science and Technology on Jan. 05, 2020.
This post is based on the seminar, Data Acquisition, Registration and Modelling for Multi-dimensional Functional Data, given by Prof. Shi.
This post is based on the material of the second lecture of STAT 6050 instructed by Prof. Wicker, and mainly refer some more formally description from the book, Mehryar Mohri, Afshin Rostamizadeh, Ameet Talwalkar - Foundations of Machine Learning-The MIT Press (2012).
Prof. Jon A. WELLNER introduced the application of a new multiplier inequality on lasso in the distinguish lecture, which reminds me that it is necessary to read more theoretical results of lasso, and so this is the post, which is based on Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical Learning with Sparsity. 362.
This post is based on the talk, Next-Generation Statistical Methods for Association Analysis of Now-Generation Sequencing Studies, given by Dr. Xiang Zhan at the Department of Statistics and Data Science, Southern University of Science and Technology on Jan. 05, 2020.
This note is based on
This post is based on the slides for the talk given by Zijian Guo at The International Statistical Conference In Memory of Professor Sik-Yum Lee
This post is the notes for Mithani et al. (2009).
The post is based on the BIOS Consortium, van Iterson, M., van Zwet, E. W., & Heijmans, B. T. (2017). Controlling bias and inflation in epigenome- and transcriptome-wide association studies using the empirical null distribution. Genome Biology, 18(1), 19.
This post is based on section 8.3 of Casella and Berger (2001).
This post is based on Li, Y., Wang, N., & Carroll, R. J. (2010). Generalized Functional Linear Models With Semiparametric Single-Index Interactions. Journal of the American Statistical Association, 105(490), 621–633.
This post is based on Li, H., & Zhou, Q. (2019). Gaussian DAGs on network data. ArXiv:1905.10848 [Cs, Stat].
This note is based on Zhou, T., Sengupta, S., Müller, P., & Ji, Y. (2019). TreeClone: Reconstruction of tumor subclone phylogeny based on mutation pairs using next generation sequencing data. The Annals of Applied Statistics, 13(2), 874–899.
This note is based on Chapter 15 of Wainwright, M. (2019). High-Dimensional Statistics: A Non-Asymptotic Viewpoint (Cambridge Series in Statistical and Probabilistic Mathematics). Cambridge: Cambridge University Press.
This note is for Doucet, A., & Johansen, A. M. (2009). A tutorial on particle filtering and smoothing: Fifteen years later. Handbook of Nonlinear Filtering, 12(656–704), 3. For the sake of clarity, I split the general SMC methods (section 3) into my next post.
I read the topic in kiytay’s blog: Proximal operators and generalized gradient descent, and then read its reference, Hastie et al. (2015), and write some program to get a better understanding.
Gibbs sampler is an iterative algorithm that constructs a dependent sequence of parameter values whose distribution converges to the target joint posterior distribution.
Prof. YUAN Ming will give a distinguish lecture on Low Rank Tensor Methods in High Dimensional Data Analysis. To get familiar with his work on tensor, I read his paper, Yuan, M., & Zhang, C.-H. (2016). On Tensor Completion via Nuclear Norm Minimization. Foundations of Computational Mathematics, 16(4), 1031–1068., which is the topic of this post.
This note is based on Wong, S. W. K., Liu, J. S., & Kou, S. C. (2018). Exploring the conformational space for protein folding with sequential Monte Carlo. The Annals of Applied Statistics, 12(3), 1628–1654.
Larry wrote that “Noninformative priors are a lost cause” in his post, LOST CAUSES IN STATISTICS II: Noninformative Priors, and he mentioned his review paper Kass and Wasserman (1996) on noninformative priors. This note is for this paper.
This report shows how to use importance sampling to estimate the expectation.
The first peep to SMC as an abecedarian, a more comprehensive note can be found here.
There is an important probability distribution used in many applications, the chain-structured model.
This report implements the simulation of growing a polymer under the self-avoid walk model, and summary the sequential importance sampling techniques for this problem.
There are my notes when I read the paper called Genetic network inference.
There are my notes when I read the paper called System Genetic Approach.
There are my notes when I read the paper called Maximal information component analysis.
There are my notes when I read the paper called Detecting Novel Associations in Large Data Sets.
This is the implement in R of MINE.
Use the e1071 library in R to demonstrate the support vector classifier and the SVM.
Any time series without a constant mean over time is nonstationary.
For a given time series, how to choose appropriate values for $p, d, q$
Monte Carlo plays a key role in evaluating integrals and simulating stochastic systems, and the most critical step of Monte Carlo algorithm is sampling from an appropriate probability distribution $\pi (\mathbf x)$. There are two ways to solve this problem, one is to do importance sampling, another is to produce statistically dependent samples based on the idea of Markov chain Monte Carlo sampling.
“The p value was never meant to be used the way it’s used today.” –Goodman
The conjugate gradient method is an iterative method for solving a linear system of equations, so we can use conjugate method to estimate the parameters in (linear/ridge) regression.
Survival analysis examines and models the time it takes for events to occur. It focuses on the distribution of survival times. There are many well known methods for estimating unconditional survival distribution, and they examines the relationship between survival and one or more predictors, usually terms covariates in the survival-analysis literature. And Cox Proportional-Hazards regression model is one of the most widely used method of survival analysis.
This post is the notes of this paper.
This post is for The Human Microbiome Project Consortium, Huttenhower, C., Gevers, D., Knight, R., Abubucker, S., Badger, J. H., … White, O. (2012). Structure, function and diversity of the healthy human microbiome. Nature, 486(7402), 207–214.
Sebastian Schreiber gave a talk titled Persistence of species in the face of environmental stochasticity.
Repeated Linear Regression means that repeat the fitting of linear regression for many times, and there are some common parts among these regressions.
Repeated Linear Regressions refer to a set of linear regressions in which there are several same variables.
Discuss three different methods for formulating stochastic epidemic models.
This post aims to clarify the relationship between rates and probabilities.
The note is for Chapter 1 of Soyer, Orkun S., ed. 2012 Evolutionary Systems Biology. Advances in Experimental Medicine and Biology, 751. New York: Springer.
The note is for Chapter 2 of Soyer, Orkun S., ed. 2012 Evolutionary Systems Biology. Advances in Experimental Medicine and Biology, 751. New York: Springer.
This note is for Section 3 of Doucet, A., & Johansen, A. M. (2009). A tutorial on particle filtering and smoothing: Fifteen years later. Handbook of Nonlinear Filtering, 12(656–704), 3., and it is the complement of my previous post.
This is the note for Neal, R. M. (1998). Annealed Importance Sampling. ArXiv:Physics/9803008.
This post caught a glimpse of the pseudolikelihood.
The note is for Nelder, J. A., & Lee, Y. (1992). Likelihood, Quasi-Likelihood and Pseudolikelihood: Some Comparisons. Journal of the Royal Statistical Society. Series B (Methodological), 54(1), 273–284.
This note is based on Fan, X., Pyne, S., & Liu, J. S. (2010). Bayesian meta-analysis for identifying periodically expressed genes in fission yeast cell cycle. The Annals of Applied Statistics, 4(2), 988–1013.
This note is based on Chapter 7 of Hoff PD. A first course in Bayesian statistical methods. Springer Science & Business Media; 2009 Jun 2.
This note is based on Varin, C., Reid, N., & Firth, D. (2011). AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS. Statistica Sinica, 21(1), 5–42., a survey of recent developments in the theory and application of composite likelihood.
This note is based on LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature, 521(7553), 436–444.
I encounter the term RIP in Larry Wasserman’s post, RIP RIP (Restricted Isometry Property, Rest In Peace), and also find some material in Hastie et al.’s book: Statistical Learning with Sparsity about RIP.
This report is motivated by comments under Larry’s post, Modern Two-Sample Tests.
This post reviewed the topic of path sampling in the lecture slides of STAT 5020, and noted a general path sampling described by Gelman and Meng (1998), then used a toy example to illustrate it with Stan programming language.
A brief summary of the post, Eid ma clack shaw zupoven del ba.
I noticed that the papers of matrix/tensor completion always talk about the Bernstein inequality, then I picked the Bernstein Bounds discussed in Wainwright (2019).
I happened to read Yixuan’s blog about a question related to the course Statistical Inference, whether two marginal distributions can determine the joint distribution. The question is adopted from Exercise 4.47 of Casella and Berger (2002).
This note is for Efron’s slide: Frequentist Accuracy of Bayesian Estimates, which is recommended by Larry’s post: Shaking the Bayesian Machine.
This post is based on Chapter 7 of Statistical Learning with Sparsity: The Lasso and Generalizations, and I wrote R program to reproduce the simulations to get a better understanding.
This note is based on Larry’s post, Mixture Models: The Twilight Zone of Statistics.
This note is for Khan, Z., Balch, T., & Dellaert, F. (2004). An MCMC-Based Particle Filter for Tracking Multiple Interacting Targets. In T. Pajdla & J. Matas (Eds.), Computer Vision - ECCV 2004 (pp. 279–290). Springer Berlin Heidelberg.
Larry discussed the normalizing constant paradox in his blog.
This note is for Smal, I., Meijering, E., Draegestein, K., Galjart, N., Grigoriev, I., Akhmanova, A., … Niessen, W. (2008). Multiple object tracking in molecular bioimaging by Rao-Blackwellized marginal particle filtering. Medical Image Analysis, 12(6), 764–777.
This note is based on the Chapter 6 of Hastie, T., Tibshirani, R., & Wainwright, M. (2015). Statistical Learning with Sparsity. 362..
In the last lecture of STAT 5030, Prof. Lin shared one of the results in the paper, Neykov, M., Liu, J. S., & Cai, T. (2016). L1-Regularized Least Squares for Support Recovery of High Dimensional Single Index Models with Gaussian Designs. Journal of Machine Learning Research, 17(87), 1–37., or say the start point for the paper—the following Lemma. Because it seems that the condition and the conclusion is completely same with Sliced Inverse Regression, except for a direct interpretation—the least square regression.
Materials from STAT 5030.
This note is based on Chapter 1 of Lehmann EL, Romano JP. Testing statistical hypotheses. Springer Science & Business Media; 2006 Mar 30.
Last two days, I attended the conference Medicine Meets AI 2019: East Meets West, which help me know more AI from the industrial and medical perspective.
This note is based on Li Zhang, Yuan Li, & Nevatia, R. (2008). Global data association for multi-object tracking using network flows. 2008 IEEE Conference on Computer Vision and Pattern Recognition, 1–8.
This note is for Cai, T. T., & Zhang, L. (n.d.). High dimensional linear discriminant analysis: Optimality, adaptive algorithm and missing data. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 0(0).
This note is based on Campbell, N. A. (1979). CANONICAL VARIATE ANALYSIS: SOME PRACTICAL ASPECTS. 243.
This note is based on Chapter 13 of Nocedal, J., & Wright, S. (2006). Numerical optimization. Springer Science & Business Media.
Nocedal and Wright (2006) and Boyd and Vandenberghe (2004) present slightly different introduction on Interior-point method. More specifically, the former one only considers equality constraints, while the latter incorporates the inequality constraints.
This post is based on Section 6.4 of Hastie, Trevor, Robert Tibshirani, and Martin Wainwright. “Statistical Learning with Sparsity,” 2016, 362.
This note is for Thomas, O., Dutta, R., Corander, J., Kaski, S., & Gutmann, M. U. (2016). Likelihood-free inference by ratio estimation. ArXiv:1611.10242 [Stat]., and I got this paper from Xi’an’s blog.
This note is based on de Boor, C. (1978). A Practical Guide to Splines, Springer, New York.
This note is based on the survey paper Camplani, M., Paiement, A., Mirmehdi, M., Damen, D., Hannuna, S., Burghardt, T., & Tao, L. (2016). Multiple human tracking in RGB-depth data: A survey. IET Computer Vision, 11(4), 265–285.
This post is based on Wainwright (2019).
I came across isotropic and anisotropic covariance functions in kjytay’s blog, and then I found more materials, chapter 4 from the book Gaussian Processes for Machine Learning, via the reference in StackExchange: What is an isotropic (spherical) covariance matrix?.
This post is based on Lin Z†, Zamanighomi M, Daley T, Ma S and Wong WH†: Model-based approach to the joint analysis of single-cell data on chromatin accessibility and gene expression. Statistical Science
This post is based on Guo, Z., Wang, W., Cai, T. T., & Li, H. (2019). Optimal Estimation of Genetic Relatedness in High-Dimensional Linear Models. Journal of the American Statistical Association, 114(525), 358–369.
I came across the term meta-analysis in the previous post, and I had another question about nominal size while reading the paper of the previous post, which reminds me Keith’s notes. By coincidence, I also find the topic about meta-analysis in the same notes. Hence, this post is mainly based on Keith’s notes, and reproduce the power curves by myself.
The post is based on Jiang, Y., Neyshabur, B., Mobahi, H., Krishnan, D., & Bengio, S. (2019). Fantastic Generalization Measures and Where to Find Them. ArXiv:1912.02178 [Cs, Stat].which was shared by one of my friend in the WeChat Moment, and then I took a quick look.
This post is based on Meinshausen, N. (2006). Quantile Regression Forests. 17. since a coming seminar is related to such topic.
This note is based on the slides of the seminar, Dr. ZHU, Huichen. Conditional Quantile Random Forest.
This post is based on Peter BENTLER’s talk, S.-Y. Lee’s Lagrange Multiplier Test in Structural Modeling: Still Useful? in the International Statistical Conference in Memory of Professor Sik-Yum Lee.
This post is based on the material of the first lecture of STAT6050 instructed by Prof. Wicker.
This post is based on the talk, given by Timothy I. Cannings at the 11th ICSA International Conference on Dec. 22th, 2019, the corresponding paper is Cannings, T. I., Fan, Y., & Samworth, R. J. (2019). Classification with imperfect training labels. ArXiv:1805.11505 [Math, Stat]
The first two sections are based on a good tutorial on the isotonic regression, and the third section consists of the slides for the talk given by Prof. Cun-Hui Zhang at the 11th ICSA International Conference on Dec. 21st, 2019.
I came across the Bernstein-von Mises theorem in Yuling Yao’s blog, and I also found a quick definition in the blog hosted by Prof. Andrew Gelman, although this one is not by Gelman. By coincidence, the former is the PhD student of the latter!
This post is based on Flury (1984).