PHP Santizing/Validating Array of Integers

foreach( $array as $key => $value) {
    $array[$key] = (int) $value;

    if( $array[$key] != $value ) {
        // error
    }
}

An alternative would be using phps filter functions:

$array = array(
  13, 12, '1', 'a'
);

$result = filter_var($array, FILTER_VALIDATE_INT, array(
  'flags'   => FILTER_REQUIRE_ARRAY,
  'options' => array('min_range' => 1)
));

var_dump($result);

/*
array(4) {
  [0]=>
  int(13)
  [1]=>
  int(12)
  [2]=>
  int(1)
  [3]=>
  bool(false)
}
*/

Since it's $_POST data, you'll want to check for ctype_digit (i.e. a string containing only digits):

$sanitizedValues = array_filter($_POST['taxonomy'], 'ctype_digit');

Note that this simply discards non-numeric values.

if(is_array($_POST['taxonomy'])) {
    $term_ids = array_map('intval', $_POST['taxonomy']);
}

Should do the trick. NOTE: this is sanitation. More: http://php.net/manual/en/function.intval.php