How do I efficiently select the previous non-null value?

I found this answer for SQL Server that also works in Postgres. Having never done it before, I thought the technique was quite clever. Basically, he creates a custom partition for the windowing function by using a case statement inside of a nested query that increments a sum when the value is not null and leaves it alone otherwise. This allows one to delineate every null section with the same number as the previous non-null value. Here's the query:

SELECT
  id, value, value_partition, first_value(value) over (partition by value_partition order by id)
FROM (
  SELECT
    id,
    value,
    sum(case when value is null then 0 else 1 end) over (order by id) as value_partition

  FROM p
  ORDER BY id ASC
) as q

And the results:

 id | value | value_partition | first_value
----+-------+-----------------+-------------
  1 |   100 |               1 |         100
  2 |       |               1 |         100
  3 |       |               1 |         100
  4 |       |               1 |         100
  5 |       |               1 |         100
  6 |       |               1 |         100
  7 |       |               1 |         100
  8 |   200 |               2 |         200
  9 |       |               2 |         200
(9 rows)

You can create a custom aggregate function in Postgres. Here's an example for the int type:

CREATE FUNCTION coalesce_agg_sfunc(state int, value int) RETURNS int AS
$$
    SELECT coalesce(value, state);
$$ LANGUAGE SQL;

CREATE AGGREGATE coalesce_agg(int) (
    SFUNC = coalesce_agg_sfunc,
    STYPE  = int);

Then query as usual.

SELECT *, coalesce_agg(b) over w, sum(b) over w FROM y
  WINDOW w AS (ORDER BY a);

a b coalesce_agg sum 
- - ------------ ---
a 0            0   0
b ∅            0   0
c 2            2   2
d 3            3   5
e ∅            3   5
f 5            5  10
(6 rows)