There is good news for Ulster however with Kiwi full-back Jared Payne coming back into the side for the first time since January as well as a return to action for captain Johan Muller.
Ulster have failed to win three of their last four RaboDirect PRO12 matches and slipped off top spot following their draw with Treviso last time out.
They face an Edinburgh side in freefall however with the Gunners losing their last 11 matches in all competitions while they have beaten Ulster just once in their last eight attempts.
Anscombe is refusing allow complacency to set into his side however but he does hope for further good news from the treatment room as his side prepare for the RaboDirect PRO12 run-in and a Heineken Cup quarter-final with Saracens.
"They've been missing for a while so they'll all get some game time this weekend," he told the Belfast Telegraph.
"We're starting to get some players back. They're not all 100 per cent yet, but we've talked about what we want to achieve.
"We're still up there at the top of the table and we're still in the running for everything we play in.
"So I don't think it's all gloom. Our season is 18 wins, four defeats, one draw as opposed to 23 games at this stage last year when it was 14 wins, nine defeats, so we're in a better state.
"This time last year we were chasing to make the Rabo play-offs, so we're better placed now than we were back then."
Anscombe makes seven changes in all with Lewis Stevenson joining Muller in the second row while Dan Tuohy comes into the back row.
John Afoa has switched back to his regular tight head prop position, with Tom Court at loose head and Rob Herring at hooker.
Paul Marshall is another returning player and he will be partnered at half back by fellow Irish cap Paddy Jackson.
Stuart Olding, who has scored twice in his last two games for the province, will again combine with Darren Cave in midfield.
Edinburgh meanwhile are beginning a new era under Stevie Scott and Duncan Hodge who make three changes to the pack for the Ulster clash, with international back-row Ross Rennie making a welcome return from a shoulder injury.
Netani Talei replaces the injured David Denton (knee) at number 8 and lock Grant Gilchrist comes back into the squad after his international debut against France.
Scrum-half Sean Kennedy is set for his RaboDirect PRO12 debut with Piers Francis playing at fly-half and Ben Atiga returns to inside centre, Dougie Fife has been moved infield to accommodate Tom Brown on the wing.
Scott said: "The players' reaction in training this week has been excellent.
"It's been a tough season but their commitment to improving and getting results for the club and its fans has been superb.
"A lot of hard work has gone in this week but, importantly, the work done has also been of a very high standard.
"There's a real will to do whatever it takes to get our results back on track."
At Murrayfield, 7.30pm. Live on BBC Sport NI website and via the BBC red button
Referee: Leighton Hodges (WRU, 26th competition game)
Assistant Referees: David Changleng, Graeme Marshall (both SRU)
Citing Commissioner: Paul Minto (SRU).