Chapter 5 Normal Model Flashcards
Why is the normal model probably one of the most useful for statistical analysis
Central limit theorem and the properties of the normal distribution are simple and are the population mean and variance - two quantities that
are often of primary interest.
What are the properties of the normal distribution
A symmetric, bell-shaped distribution.
It has two parameters: mean ◊ and variance
The median=mean=mode which is its first parameter
How is the normal distribution parameterised
Normal (theta,sigma) - SD is second parameter
What determines the shape of the normal curve
The mean and variance - mean is in the centre of the bell
What R commands will I use to find density, probability, quantiles and random numbers from normal distribution
dnorm pnorm qnorm rnorm with SD as argument
How far does 95% of population lie from the mean
about 95% of the population lies within two standard deviations of the
mean (more precisely, 1.96 standard deviations);
What happens summing normal distributions
The linear sum of any normal distributions will produce a normal distribution if the distributions are independent
What is the conjugate prior distribution for the normal model - normal likelihood
Normal
What is the precision
The inverse of the variance is often called the precision.. 1/variance
How can the posterior precision be written in terms of the prior and data and what is the effect of a large n value
the posterior precision is a combination of our prior
belief in the precision of the true population mean of the data, plus the
precision of the data,.
Larger n is more the precision is based on data and large precision gets.
What happens is precision increases for the variance
Increase in precision means decrease in variance
How can we write the posterior mean of the normal model as a weighted average
the posterior mean is a weighted average of
the prior expectation of the mean μ0 weighted by the precision of that
mean and the observed sample mean ybar weighted by the sampling precision
of the sample mean.
How does using variance of the mean of the prior observations as sigma squared/ K zero influence the posterior mean
K zero provides a way to control how influenctial the prior is in calculating the posterior mean
How do you approximate any expectation
sample average
As n gets bigger what happens to the posterior predictive distribution’s variance
More data means the posterior is more precise and its variance goes to zero. In the posterior predictive we also have sigma squared as part of the variance which is uncertainty in Y_tilde that cnanot be got rid of. Uncertainty about Y _tilde will enver go below sigma^”
