Stefan Eng
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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…
Sep 17, 2023
Stefan Eng
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
Sep 16, 2023
Stefan Eng
Sum of uniform random variables until sum is greater than one
math
I saw this problem on r/probabilitytheory
Nov 10, 2022
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…
May 17, 2020
Stefan Eng
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
\[ G(z) = E[z^X] = \sum_{j = 0}^\infty z^j P(X = j) \]
May 15, 2020
Stefan Eng
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…
Sep 1, 2019
Stefan Eng
Dynamic R Markdown Reports with Shiny
R
development
TL;DR here is an example application. See the explaination below.
Aug 31, 2019
Stefan Eng
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…
Jul 6, 2019
Stefan Eng
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…
Feb 8, 2019
Stefan Eng
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…
Nov 5, 2018
Stefan Eng
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