## Tuesday, February 17, 2015

### Plotting as a useful debugging tool

While writing the code for bayesian modeling, you will have to test the distribution (prior, likelihood or posterior). Here are two common scenarios that you might encounter:
1. You want to test the function that generates random deviates. For example: you have derived a conjugate formula for a parameter of your model and want to test whether it is correct or not.
2. You want to test a probability density function. For example: likelihood or posterior function that you might want to run rejection sampler on.
In both these cases, you will start by making sure the property of the distribution (for example: range, mean, variance) are correct. For example: if the parameter you are sampling is variance, then you will have “assert(returnedVariance > 0)” in your code. Then, the next obvious test should be visual inspection (trust me, it has helped me catch more bugs than I would by traditional programming debugging techniques/tools). This means you will plot the distribution and see if the output of your code makes sense.
We will start by simplifying the above two cases by assuming standard normal distribution. So, in the first case, we have access to “rnorm” function and in second case, we have access to “dnorm” function of R.
Case 1: In this case, we first collect random deviates (in “vals”) and then use ggplot to plot them:
```library(ggplot2)
vals = rnorm(10000, mean=0, sd=1)
df = data.frame(xVals=vals)
ggplot(df, aes(x=xVals)) + geom_density()
```

The output of above R script will look something like this:
Case 2: In this case, we have to assume a bounding box and sample inside that to get “x_vals” and “y_vals” (just like rejection sampling):
```library(ggplot2)
x_vals=runif(10000,min=-4,max=4)
y_vals=dnorm(x_vals, mean=0, sd=1)
df = data.frame(xVals=x_vals, yVals=y_vals)
ggplot(df, aes(x=xVals, y=yVals)) + geom_line()
```

The output of above R script will look something like this:
Just as a teaser to a post that I will post later, we can use the script somewhat similar to that of case 1 to study the characteristics of a distribution: