This chapter is from the book
This chapter is from the book
This chapter is from the book
Continuing the Code
The R statement that I was about to discuss before introducing the topic of R’s distributional function syntax is
Tax ~ dnorm( mu , sigma ) ,
That statement establishes that Tax comprises the parameters mu and sigma, but we don’t yet know how they are involved. For all we know, Tax could be the sum of mu and sigma, or their difference, or their ratio—it’s just too soon to know. But we do know that you can specify the normal, Gaussian distribution with only two parameters:
The mean of the distribution, usually termed mu. The mu parameter locates the distribution along the horizontal axis. So, the mean of a population’s IQ scores might be 100; the mean of a population’s HDL cholesterol score might be 65 mg/dl. It is the normal curve’s central tendency.
The standard deviation of the distribution, usually termed sigma. In a Gaussian distribution, about 34% of the cases fall between the mean and one sigma above the mean, and another below it; another 13.6% falls between one and two sigmas above (and another below) the mean; and 2.1% falls three sigmas above and below the mean. It’s a measure of the distribution’s spread: the width of the distribution, relative to its height.
Software that actually performs Bayesian statistical analysis needs some way of knowing what the underlying distributions look like, and the arguments to the quap function in R provide that capability. Because the Gaussian distribution requires so little information to structure—that is, the mean and the standard deviation—it’s straightforward to code.
Furthermore, many topics of interest to all life forms follow the template of a standard normal distribution, and they do so intrinsically. Consequently it’s not usually necessary to provide code that takes into account anomalous distributions, such as bimodal curves, highly skewed shapes, and fits that require some grappling.