Publications by Enrico Sebastiani
Day4 Assignment
Exercises Repeat the PCA after removing half of the features with lowest variance. Does it look any different? library(GSE5859) library(tissuesGeneExpression) data(tissuesGeneExpression) e.standardize.fast <- t(scale(t(e), scale = FALSE)) p <- prcomp(t(e.standardize.fast)) plot( p$x[, 1:2], xlab = "PC1", ylab = "PC2", main = "...
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Exercise n.1 We will use the following dataset to demonstrate the use of permutations: library(dplyr) url <- "https://raw.githubusercontent.com/genomicsclass/dagdata/master/inst/extdata/babies.txt" babies <- read.table(url, header=TRUE) summary(babies) ## bwt gestation parity age ## Min. : 55.0 Min. ...
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Bernoulli distribution The Bernoulli probability function is: \[ P(x) = \begin{cases} p & x= 1 \\ 1-p & x = 0 \\ \end{cases} \] The Bernoulli distribution function is: \[ F(x) = \begin{cases} 0 & x< 0 \\ 1-p & 0\leq x< 1 \\ 1 & x \geq 1 \end{cases} \] The probability that \(X\) takes the value 1.5 is 0 since the probability is ...
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Bernoulli distribution The Bernoulli probability function is: \[ P(x) = \begin{cases} p & x= 1 \\ 1-p & x = 0 \\ \end{cases} \] The Bernoulli distribution function is: \[ F(x) = \begin{cases} 0 & x< 0 \\ 1-p & 0\leq x< 1 \\ 1 & x \geq 1 \end{cases} \] The probability that \(X\) takes the value 1.5 is 0 since the probability is ...
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MLE for Exponential distribution Let’s start by computing the Likelihood function given \(y_{1},...,y_{n}\) i.i.d random variables that follow an exponential distribution with an expected value equals to 1/\(\lambda\): \[\begin{align} L(\lambda; x_{1},...,x_{n}) & = \prod_{i = 1}^{n} f_{i}(x) \\ & = \prod_{i = 1}^{n} \lambda^{i}exp[-\lambda x_{...
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Assignment 3 Biostatistics
MLE of the exponential distribution Let’s start by computing the Likelihood function given \(y_{1},...,y_{n}\) i.i.d random variables that follow an exponential distribution with an expected value equals to 1/\(\lambda\): \[ \begin{align} L(\lambda; \underline{x}) & = \prod_{i = 1}^{n} f_{i}(x) \\ & = \prod_{i = 1}^{n} \lambda exp[-\lambda x_{i...
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