We present a new technique called “t-SNE” that visualizes high-dimensional data by giving each datapoint a location in a two or three-dimensional map. The technique is a variation of Stochastic Neighbor Embedding (Hinton and Roweis, 2002) that is much easier to optimize, and produces significantly better visualizations by reducing the tendency to crowd points together in the center of the map. t-SNE is better than existing techniques at creating a single map that reveals structure at many different scales. This is particularly important for high-dimensional data that lie on several different, but related, low-dimensional manifolds, such as images of objects from multiple classes seen from multiple viewpoints. For visualizing the structure of very large datasets, we show how t-SNE can use random walks on neighborhood graphs to allow the implicit structure of all of the data to influence the way in which a subset of the data is displayed. We illustrate the performance of t-SNE on a wide variety of datasets and compare it with many other non-parametric visualization techniques, including Sammon mapping, Isomap, and Locally Linear Embedding. The visualizations produced by t-SNE are significantly better than those produced by the other techniques on almost all of the datasets.

/pdf/visualizing-data-using-t-sne-2w1n304iq0.pdf

Visualizing Data using t-SNE

The analysis of censored failure times is considered. It is assumed that on each individual arc available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations are outlined.

https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.2517-6161.1972.tb00899.x

Regression Models and Life-Tables

Generalized Additive Models.

An essential textbook for any student or researcher in biology needing to design experiments, sample programs or analyse the resulting data The text begins with a revision of estimation and hypothesis testing methods, covering both classical and Bayesian philosophies, before advancing to the analysis of linear and generalized linear models Topics covered include linear and logistic regression, simple and complex ANOVA models (for factorial, nested, block, split-plot and repeated measures and covariance designs), and log-linear models Multivariate techniques, including classification and ordination, are then introduced Special emphasis is placed on checking assumptions, exploratory data analysis and presentation of results The main analyses are illustrated with many examples from published papers and there is an extensive reference list to both the statistical and biological literature The book is supported by a website that provides all data sets, questions for each chapter and links to software

/pdf/experimental-design-and-data-analysis-for-biologists-8ybva8d53x.pdf

Experimental Design and Data Analysis for Biologists

Wireless Communications

Publisher Summary This chapter discusses the efficient estimation of a parameter measurable by two instruments of unknown precisions. Let μ be the unknown value of a parameter for which an estimate is required. Suppose that this parameter may be measured by either of the two instruments whose precisions are not known in advance. It is desired to obtain an estimate of satisfactorily low variability with as little waste in sampling cost as possible. A rule for procedure is presented and evaluated in the context of normally distributed data. The rule used combines an approach used for stopping sampling in a one-sample problem and the solutions of a one-armed and two-armed bandit problem. It makes sense to use the nominal significance level in variations of the one-armed bandit problem where the data are not normally distributed and it is desired to maximize. Monte Carlo simulations have been carried out to measure the efficiency of the rule. The efficiency is measured by comparing the loss with the case where the precisions are known, in which case one can sample with the better instrument the appropriate number of times.

The efficient estimation of a parameter measurable by two instruments of unknown precisions

(2007). The Effect of Fasting during Ramadan on Traffic Accidents in Turkey. CHANCE: Vol. 20, Interview with a Centennial Chart, pp. 10-18.

The Effect of Fasting during Ramadan on Traffic Accidents in Turkey

: Let X(1), X(2),...,X(n) be the order statistics from a large sample of n independent identically distributed random variables with unknown scale and location parameters. Linear unbiased estimates of these parameters can be constructed using k order statistics, where the orders are approximately (lambda(1)n), (lambda(k)n) for specified lambda(1), lambda(2),...,lambda(k). As k approaches infinity let the number of lambda(i) in an interval be proportional to a density function f. Then one may select f to yield approximately optimal spacings (i.e., choice of lambda(i)). The study is carried out for estimating the mean of a normal distribution with known variance. (Author)

A Note on Optimal Spacings for Systematic Statistics.

: A numerical approach is described for calculating the optimal policy in the stochastic control problem of keeping a satellite close to a fixed point in space when it is subject to random forces The random forces are modelled by Brownian Motion A policy is evaluated in terms of its long run expected average cost The running costs consist of a charge for fuel used plus a charge of x sub 1 squared per unit of time when the satellite is x sub 1 units away from the target The space is one-dimensional The method used is to apply backward induction to a bounded discrete space, discrete time version of the problem Incidentally a solution is presented for the deterministic version of the problem where there are no random forces

Herman Chernoff

Papers

The efficient estimation of a parameter measurable by two instruments of unknown precisions

The Effect of Fasting during Ramadan on Traffic Accidents in Turkey

A Note on Optimal Spacings for Systematic Statistics.

A satellite control problem

Simple computer intensive methods for estimating parameters of complex models