How does monster health scaling work?

I can't remember where exactly it was said (I follow a lot of gaming news sites...) but in an interview with the Director, The Multiplayer works like this:

Single Player Monsters have less health (as it always has been)

Firing off an SOS does not increase monster health until someone joins, same with regular session joining. Once someone joins your quest, you will see a notification saying something along the lines of "increasing difficulty due to player joining"

The Monster Health difference between 2 players and 4 players isn't much, so full parties are far more optimal than duo teams.

Again... I'll try and find the interview where this was all said.

With update 10.11 (the update for Iceborne, although the change does not require Iceborne), the dynamic difficulty settings had undergone a major revamp. See the section "Monster Adjustments" for more information.

• Now the difficulty is scaled according to the current number of players. This means that, when the number of hunters reduce from two to one, the difficulty will shift back to the singleplayer difficulty, shrinking the hit points and flinch points back to singleplayer ones as such.
• A new difficulty for two players is introduced. This has less hit points and flinch points than in the full-fledged multiplayer difficulty, but more than in the singleplayer one. From multiple expeciences, I suspect it to be the average of the singleplayer stats and the full multiplayer stats. Note that there is no exclusive difficulty for three players, and a party of three players will experience the same difficulty as in a full party.

Also, some High Rank-exclusive quests (namely Behemoth and Ancient Leshen) have their difficulty locked at the full party multiplayer difficulty.

As soon as there are two hunters out on a quest at the same time, the quest is locked to multiplayer difficulty, even if the extra hunters leave after departing on the quest. Multiplayer difficulty also does not change based on the number of hunters. Hunting with 2 people or a full party of 4 will result in the same changes to the monsters.

This has been confirmed several times by the developers, but the most explicit mention of this was in the latest Developer Diary.

While in multiplayer difficulty, the monster's values are multiplied in various ways, depending on the monster's tier, the quest's rank, and possibly other factors.
For a full list of singleplayer and multiplayer stats for every quest in the game, see this document.
For a quick look at the multipliers for the hardest quests in the game, see hexhexhex's data mining.