Single Page Category Filter Dropdown or Box Selection

I am trying to add a filter to our blog posts that appears at the top of the page. Where a visitor can check, 1, 2 or all post types and filter the results with out leaving that main page.

For example, post page is on http://www.blog.com/my-posts/
Categories include: dog, cat, chipmuncks, pigs.
When first arriving at the site you would see all the posts. But if I checked pigs and cat, only those to categories would show, without being directed to a different page. I want to stay on /my-posts/

Also, right now my posts are not on my index page. The homepage is pointed to a static page, while the posts are on a different page.

Suggestions?