Exercise 2.6 The first part of the exercise asks you to:
Choose your own prior for the parameters of the beta distribution. You can do this by sketching it here: https://jhubiostatistics.shinyapps.io/drawyourprior.
After sketching a plot, I chose the parameters to set up a prior: \(\alpha\) = 2.47 and \(\beta\) = 8.5.
Using this prior Next, the exercise asks you:
Once you have set up a prior, re-analyse the data from Section 2.
The vocabulary quiz will be live here during the start of the course.
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As always, load libraries first.
library(ggplot2) library(tidyverse) library(dplyr) Exercise 2.3 from Modern Statistics for Modern Biologists A sequence of three nucleotides codes for one amino acid. There are 4 nucleotides, thus \(4^3\) would allow for 64 different amino acids, however there are only 20 amino acids requiring only 20 combinations + 1 for an “end” signal. (The “start” signal is the codon, ATG, which also codes for the amino acid methionine, so the start signal does not have a separate codon.
The vocabulary quiz will be live here during the start of the course.
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These sections introduced Markov chains and the Bayesian paradigm. Markov chain transitions were used to model dependencies along DNA sequences. The vocabulary terms are:
Markov chain a sequence where given the current state, the next state is conditionally independent of all previous states Bayesian paradigm approaching statistics from the perspective that probability can be viewed as a degree of belief in an event Beta distribution a probability distribution defined on the interval [0, 1] often used to model probabilities in Bayesian statistics Exponential distribution a probability distribution defined on the positive real numbers that can be used to model the time between events in a Poisson point process Prior a probability distribution describing our knowledge of a hypothesis/parameter before incorporating new data Posterior a probability distribution describing our knowledge of a hypothesis/parameter after incorporating new data Haplotype a collection of DNA sequence variants (e.
Vocabulary for the first part of Chapter 2