Example For example, let X 2 1, ..., Xn be a random sample from distribution N(μ, σ ) with σ known and μ ∈ M. Suppose our hypothesis is that μ ∈ M1 for some M1 ⊂ M, i.e. M1 is some subset of M. It is called the null hypothesis. It is denoted as H0 : μ ∈ M1. Then the alternative hypothesis is that μ ∈/ M1, i.e. μ ∈ M\M1. It is denoted as Ha : μ ∈/ M\M1. For example, if M1 = μ0 and M = {μ : μ ≥ μ...

So far, we have been considering point estimation. In this lecture, we will study interval estimation. Let X denote our data. Let θ ∈ R be our parameter of interest. Our task is to construct a data-dependent interval [l(X), r(X)] so that it contains θ with large probability. One possibility is to set l(X) = −∞ and r(X) = +∞. Such an interval will contain θ with probabity 1. Of course, the probl...

This paper presents a method for automatic color and intensity normalization of digitized histology slides stained with two different agents. In comparison to previous approaches, prior information on the stain vectors is used in the estimation process, resulting in improved stability of the estimates. Due to the prevalence of hematoxylin and eosin staining for histology slides, the proposed me...

Preamble The course is aimed at people who already know how to do elementary rigid-body dynamics using 3D vectors. It follows the treatment of spatial vectors appearing in the book Rigid Body Dynamics Algorithms, which should be consulted for more details. Another source that may be useful is the Springer Handbook of Robotics, Chapter 2. Other materials relating to this course can be found on D...

on genomics, became aware of the potential commercial, technical, and social importance of the human genome project during the late 1990s. The human genome project was formally initiated in 19901 and was expected to last 15 years. It had the major goals of identifying all the genes in human DNA, determining the sequences of those genes, and storing the information in public databases. However, ...

Let X be our data. Let θ̂ = T (X) be an estimator where T is some function. We say that θ̂ is unbiased for θ if Eθ[T (X)] = θ for all possible values of θ where Eθ denotes the expectation when θ is the true parameter value. Thus, the concept of unbiasness means that we are on average right. The bias of θ̂ is de ned by Bias(θ̂) = Eθ[θ̂] − θ. Thus, θ̂ is unbiased if and only if its bias equals 0. For e...

Pathology digital lab is the modern, flexible and time effective research assistant. The process of creating pathology slides contains five creation steps from the tissue samples collection till clearing and staining stage. The reservation and sharing of such slides using classical models limit the ability of pathologists to benefit from important and rare slides. The virtual lab with its digit...