Cosmic fmow reconstructjon from deepest distance surveys (and - PowerPoint PPT Presentation

Cosmic fmow reconstructjon from deepest distance surveys (and redshifu surveys) I n s t i t u t d ' A s t r o p h y s i q u e d e P a r i s ( C N R S ) C o l l a b o r a t i o n : J e n s J a s c h e ( T U M / E x C ) , M i c h a e l H u d s o n ( U o W) , B e n j a m i n D . Wa n d e l t ( U P M C / I A P ) , → F l o r e n t L e c l e r c q ( I A P P o r t s m o u t h )

O u t l i n e ● C o n t e x t a n d p r o b l e m s ● T h e s t a t i s t i c a l m o d e l s : B O R G ( s p e c t r o s c o p i c ) a n d V I R B I U S ( d i s t a n c e + s p e c t r o s c o p i c ) ● A p p l i c a t i o n t o C o s m i c F l o w s , C O M P O S I T E a n d 2 M + + ● R e s u l t s ● C o n c l u s i o n 2 July 5 th 2016

C o n t e x t ● C o s m i c d i s t a n c e s u r v e y s c o m i n g o u t o f i n f a n c y ● S u p e r b s p e c t r o s c o p i c s u r v e y s 6 d F v s u r v e y ( S p r i n g o b e t a l . 2 0 1 4 ) C o s m i c fm o w s 3 ( T u l l y e t a l . 2 0 1 6 ) S D S S 3 / B O S S ( S D S S w e b s i t e ) 3 July 5 th 2016

C o n t e x t ● C o s m i c d i s t a n c e s u r v e y s c o m i n g o u t o f i n f a n c y ● S u p e r b s p e c t r o s c o p i c s u r v e y s ● S t i l l n a i v e d a t a a n a l y s i s 4 July 5 th 2016

C o n t e x t ● C o s m i c d i s t a n c e s u r v e y s c o m i n g o u t o f i n f a n c y ● S u p e r b s p e c t r o s c o p i c s u r v e y s ● S t i l l n a i v e d a t a a n a l y s i s ● I s i t p o s s i b l e t o d o a f u l l a n d s t a t i s t i c a l l y a c c u r a t e a n a l y s i s o f s u r v e y s ? O b t a i n v e l o c i t y fj e l d s ? 5 July 5 th 2016

O u t l i n e ● C o n t e x t a n d p r o b l e m s ● T h e s t a t i s t i c a l m o d e l s : B O R G ( s p e c t r o s c o p i c ) a n d V I R B I U S ( d i s t a n c e + s p e c t r o s c o p i c ) ● A p p l i c a t i o n t o C o s m i c F l o w s , C O M P O S I T E a n d 2 M + + ● R e s u l t s ● C o n c l u s i o n 6 July 5 th 2016

B ayesian O rigins R econstruction from G alaxies (BORG)

B O R G 2 m o d e l C o s m o l o g i c a l p r i o r G a l a x y r e d s h i f t s s u r v e y F o r w a r d m o d e l : I n i t i a l c o n d i t i o n s ✔ P e r t u r b a t i o n T h e o r y → p a r t i c l e s ✔ P a r t i c l e M e s h M a t t e r D e n s i t y b u i l d i n g G a l a x y d e n s i t y : p a r t i c l e s → d e n s i t y g a l a x y p o s i t i o n → d e n s i t y B i a s m o d e l P o i s s o n s t a t i s t i c s L a v a u x & J a s c h e , 2 0 1 5 , M N R A S ~ O p e n M P p a r a l l e l J a s c h e & Wa n d e l t , 2 0 1 3 , M N R A S 8 July 5 th 2016

B O R G 3 m o d e l C o s m o l o g i c a l p r i o r G a l a x y r e d s h i f t s s u r v e y F o r w a r d m o d e l : I n i t i a l c o n d i t i o n s ✔ P e r t u r b a t i o n T h e o r y → p a r t i c l e s ✔ P a r t i c l e M e s h ✔ R e d s h i f t S p a c e D i s t o r t i o n M a t t e r D e n s i t y b u i l d i n g G a l a x y d e n s i t y : p a r t i c l e s → d e n s i t y g a l a x y p o s i t i o n → d e n s i t y B i a s m o d e l P o i s s o n s t a t i s t i c s L a v a u x & J a s c h e , 2 0 1 6 , i n p r e p . M P I + O p e n M P p a r a l l e l , e x a c t s u p e r s a m p l i n g , e n t i r e c o d e r e w r i t i n g J a s c h e & L a v a u x , 2 0 1 6 , i n p r e p . 9 July 5 th 2016

B O R G 3 m o d e l ( e fg e c t i v e l y ) Linear response operator (mask, radial selection) « Mean » density of tracers bias ∑ | ^ 2 δ k | − log P (δ , α , ~ n )= A + ∑ ~ α × ... ]− N i [α log ( 1 +δ NL ,i [δ])+ ... ]+ k n R i [( 1 +δ NL ,i [δ]) 2 P k i NGP binned data Gaussian prior Poisson probability LJ, JL, 2016 in prep. sampled using Hamiltonian Monte Carlo algorithm Jasche & Wandelt (2013) 10 July 5 th 2016

B O R G 3 s a m p l i n g t e c h n i q u e H a m i l t o n i a n S a m p l e r F o r w a r d F o r w a r d P o i s s o n L i k e l i h o o d I n i t i a l d e n s i t y fj e l d F i n a l d e n s i t y fj e l d B i a s m o d e l D a t a G r a d i e n t G r a d i e n t B i a s p a r a m e t e r N p a r a m e t e r m e a n S a v e M a r k o v C h a i n s t a t e S a v e M a r k o v C h a i n s t a t e 11 July 5 th 2016

Velocity Reconstruction using Bayesian Inference Scheme

V I R B I U S m o d e l D i s t a n c e m o d u l i / C o s m o l o g i c a l p r i o r G a l a x y s u r v e y I n d i c a t o r s R e d s h i f t s ( + e r r o r s ) B u l k fm o w : V e l o c i t y fj e l d p r i o r : P o t e n t i a l , G a u s s i a n u n i f o r m p r i o r D i s t a n c e p r i o r V e l o c i t y / d e n s i t y T r u e D i s t a n c e s fj e l d L a v a u x , 2 0 1 6 , M N R A S 13 July 5 th 2016

V I R B I U S m o d e l D i s t a n c e m o d u l i / C o s m o l o g i c a l p r i o r G a l a x y s u r v e y I n d i c a t o r s R e d s h i f t s ( + e r r o r s ) B u l k fm o w : V e l o c i t y fj e l d p r i o r : P o t e n t i a l , G a u s s i a n u n i f o r m p r i o r D i s t a n c e p r i o r V e l o c i t y / d e n s i t y L o g n o r m a l m o d e l T r u e D i s t a n c e s fj e l d P r e d i c t e d v e l o c i t i e s G a u s s i a n e r r o r m o d e l M e t a p a r a m e t e r s ( c a l i b r a t i o n , e r r o r s , c l a s s i fj c a t i o n ) O p e n M P p a r a l l e l L a v a u x , 2 0 1 6 , M N R A S 14 July 5 th 2016

V I R B I U S m o d e l D i s t a n c e m o d u l i / C o s m o l o g i c a l p r i o r G a l a x y s u r v e y I n d i c a t o r s R e d s h i f t s ( + e r r o r s ) B u l k fm o w : V e l o c i t y fj e l d p r i o r : P o t e n t i a l , G a u s s i a n u n i f o r m p r i o r N o L C D M a s s u m p t i o n s D i s t a n c e p r i o r V e l o c i t y / d e n s i t y fj e l d L C D M a s s u m p t i o n s O p e n M P p a r a l l e l 15 July 5 th 2016

V I R B I U S m o d e l ( e fg e c t i v e l y ) H a r d t o w r i t e c o m p l e t e l y h e r e . . . T h e f o l l o w i n g i s o n l y t h e c o r e p a r t : L i k e l i h o o d P o s t e r i o r d i s t r i b u t i o n 16 July 5 th 2016

V I R B I U S s a m p l i n g t e c h n i q u e G i b b s s a m p l i n g P a r t i a l l y c o l l a p s e d G i b b s s a m p l i n g Θ d e n s i t y fj e l d E x p e n s i v e D i s t a n c e s S e l e c t i o n f u n c t i o n B o x b u l k fm o w T y p e C l a s s i fj e r T y p e p r o b a b i l i t y C l a s s i fj e r S a v e M a r k o v C h a i n s t a t e S a v e M a r k o v C h a i n s t a t e 17 July 5 th 2016