Sorry for the delayed reply. You can modify the page template template-blog.php file at line number 23 to filter by category –
$query = array('posts_per_page' => intval(get_option('posts_per_page')), 'ignore_sticky_posts' => 0, 'category__in' => array( 2, 6 ), 'paged' => $paged);
where you supply the category ids as explained here – http://codex.wordpress.org/Class_Reference/WP_Query#Category_Parameters.
You can have this template file in your child theme if you do not want to modify the parent theme template file and you can even rename this as another page template and use it.