Stefan Eng - stefanengineering.com

Likelihood ratio test for 2x2 independence

statistics

Assume that \(n_1\) and \(n_2\) are fixed and we sample from binomial distributions with success probability \(p_1\) and \(p_2\). Then…

Jefferys prior for binomial proportion

math

One of the first ways that we learn to construct confidence intervals is for binomial proportion. The setup for a problem is usually something like

Sum of uniform random variables until sum is greater than one

math

I saw this problem on r/probabilitytheory

R package build

Joint distribution of sums of exponential random variables

math

This is a problem from Ross’s Stochastic Processes [1]. Let \[ \begin{aligned} S_1 &= X_1\\ S_2 &= X_1 + X_2\\ S_3 &= X_1 + X_2 + X_3 \end{aligned} \] where \(X_1, X_2, X_3\) are i.i.d exponential random variables with…

Probability of even/odd using probability generating functions

math

A probability generating function for a discrete random variable \(X\) taking values \(\{0,1,\ldots\}\) is defined as \[ G(z) = E[z^X] = \sum_{j = 0}^\infty z^j P(X = j) \]

Inside a Basel Novartis Internship

job

personal

This summer I had the privilege of doing a 3 month summer (2019) internship at Novartis’ head office in Basel, Switzerland. I worked in the Scientific Computing and…

Dynamic R Markdown Reports with Shiny

R

development

TL;DR here is an example application. See the explaination below.

Introduction to Time Series

statistics

\[ X_t = m_t + s_t + y_y \] where - \(m : \mathbb{Z} \rightarrow \mathbb{R}\) is a slowly changing function, the trend component. - \(s : \mathbb Z \rightarrow \mathbb R\) is a function with a known…

1990 to 1992 Census Crime Rate Prediction.

R

school

project

We are considering a dataset that provides some demographic information for 440 of the most populous counties in the United States in years 1990-92. Each line of the dataset…

Cloze Deletion Prediction with LSTM Neural Networks

machine-learning

project

A cloze deletion test is a form of language test where a sentence (or paragraph) is given to the test taker with blanks for missing words [7]. The student is expected to…