Programatically trigger a click on an AJAX enabled form field (button, select, etc)
In order to select radio buttons using jQuery I came up with the following solution:

base = 'edit-my-radio-button';
id = '#'+base;
$(id).click();
Drupal.ajax[base].eventResponse($(id), 'click');


After some digging around in misc/ajax.js, I found that Drupal AJAX stores the result of new Drupal.ajax(base, element, element_settings) in the Drupal.ajax[] JavaScript Array. This led me to realize that I did not need to create a fake element or an element_settings object as the Use Drupal7 AJAX goodness programmatically answer suggested. While that simplified my code, and eventResponse() created a successful AJAX request, the AJAX commands being returned still did not execute.

On a hunch, I decided to use .click() followed by .eventResponse() because I noticed that false was being printed on the console.

After looking at the .eventResponse() code, I am not 100% sure where it is looking for the element to be currently selected. After stepping through the function calls, I believe jquery.form.js is checking to see if the item is selected, but since this file is minified by default, I have not gone through it yet. If anyone else can shed light on this or be willing to step through the function calls, that would be great!

FYI: If I run these commands manually in the console, .eventResponse() still returns false, so don't be alarmed when you see that.