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1 c 1. SNS Social Networking Service [3,5,12] 3 1 CM eiji.motohashi@gmail.com Yahoo Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

2 [1,2,16,18] CTR : 100 CVR : CTR CVR CTR CVR CTR CTR 2.2 t y t(t =1,...,T) IMPS t π t y t binomial(imps t,π t) (1) Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited

3 IMPS t π t t 4 IMPS t π t µ t w t h t v t π t = exp(µt + wt + ht + vt) 1+exp(µ t + w t + h t + v t) (2) µ t 2 [9, 10] µ t =2µ t 1 µ t 2 + δ t, δ t N(0,σ 2 δ) (3) (3) (µ t µ t 1) (µ t 1 µ t 2) N(0,σδ) 2 t 1 t t 2 t 1 0 σ 2 δ σ 2 δ 0 w t 7 [9, 10] w t = 6 w t j + ɛ t, ɛ t N(0,σ 2 ɛ ) (4) j=1 (4) 6 j=0 wt j N(0,σ2 ɛ ) 1 0 σ 2 ɛ σ 2 ɛ 0 h t h t =I t (w t,sun w t) (5) I t {0, 1} t w t,sun t (2) µ t + w t,sun + v t v t 0 4 CTR CTR σ 2 v x t =[µ t,µ t 1,w t,w t 1,...,w t 5] (6) [9, 10, 17] x t = F tx t 1 + G te t (7) y t binomial(imps t,π t) (8) x t t y t F t [ ] Fµ O F t = (9) O F w F µ F w [ ] O 0 F µ =, F w = (10).. O 1 0 G t e t G t = [ Gµ G w ], e t = [ δt ɛ t ] (11) G µ G w [ ] G µ =, G w = (12) n y 1:n {y 1,...,y n} x t Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

4 [4, 8] 5 p(x t y 1:n) n t 3 n<t : n = t : n>t : = [σ v,σ δ,σ ɛ] n ( ) IMPS n p(y n ) = π yn n (1 π n) IMPSn yn (13) y n 1 N y 1:N {y 1,...,y N} Q( ) N p(y n y 1:ñ, ) (14) n=1 ñ = n 1 Q( ) L( ) ˆ MLE 1 [9, 11] ñ n Q( ) RTA CPM AREA 3 1, 4 2 Imps Click CTR 1 1 CTR 2 1 CTR (14) ñ n RTA 2 CPM 3 AREA Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited

5 Imps 4, 347, 030 2, 588, , 171, , 605 Click 5, 709 2, , 931 1, 165 CTR Imps 1, 895, 268 6, 077, , 781, , 401 Click 15, , , 209 2, 992 CTR Imps 11, 762, , 124, , 759, , 266 Click 28, , , 496 3, 310 CTR ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0.05 σ v log(σ δ), log(σ ɛ) ˆπ 6 [6] p(x t y 1:T ) L =28 p(x t y 1:t+L) t + L>T p(x t y 1:T ) CTR 3 CTR 3 e t = y t/imp S t ˆπ t CTR Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

6 4 ˆ MLE σ v σ δ exp( 5) exp( 5) exp( 4) exp( 7) σ ɛ exp( 10) exp( 10) exp( 8) exp( 7) σ v σ δ exp( 8) exp( 3) exp( 6) exp( 8) σ ɛ exp( 9) exp( 6) exp( 8) exp( 8) σ v σ δ exp( 5) exp( 4) exp( 5) exp( 8) σ ɛ exp( 6) exp( 8) exp( 6) exp( 8) 1 CTR CTR =[σ v,σ δ,σ ɛ] σ v v t σ δ σ ɛ δ t ɛ t 2 CTR µ t 95% σ δ 3 w t Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited

7 2 CTR 95% CTR Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

8 3 CTR CTR [14] [13, 15, 19] [7] Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited

9 A. t 1 t t t t p(x t y 1:t 1) t 1 p(x t 1 y 1:t 1) p(x t y 1:t 1) = p(x t x t 1)p(x t 1 y 1:t 1)dx t 1(15) p(x t x t 1) p(x t 1 y 1:t 1) M {x t 1 t 1} (i) M i=1 δ p(x t 1 y 1:t 1) 1 M M i=1 δ ( x t 1 x (i) t 1 t 1) (16) x (i) t t 1 = F (i) tx t 1 t 1 + G (i) te t {x (i) t t 1} M i=1 p(x t y 1:t 1) p(x t y 1:t 1) 1 M M i=1 δ ( ) x t x (i) t t 1 (17) t p(x t y 1:t) t p(x t y 1:t 1) p(x t y 1:t) = p(y t x t)p(x t y 1:t 1) p(yt x t)p(x t y 1:t 1)dx t (18) p(y t x t) p(x t y 1:t 1) (17) (18) p(x t y 1:t) M i=1 w (i) t δ ( ) x t x (i) t t 1 w (i) p(y t x t t 1) (i) t = M j=1 p(yt x(j) t t 1) (19) (20) {x (i) t t 1} M i=1 w (i) t M {x (i) t t} M i=1 p(x t y 1:t) p(x t y 1:t) 1 M M i=1 δ ( ) x t x (i) t t (21) t s t <s p(x s y 1:t) s = t +1 s p(x s y 1:t) p(x s y 1:t)= p(x s x s 1) p(x t+1 x t) p(x t y 1:t)dx s 1 dx t (22) s t s t L p(x t y 1:t+L) [6] [1] F. M. Bass, N. Bruce, S. Majumdar and B. P. S. Murthi, Wearout Effects of Different Advertising Themes: A Dynamic Bayesian Model of the Advertising-sales Relationship, Marketing Science, 26 (2007), [2] N. Bruce, Pooling and Dynamic Forgetting Effects in Multitheme Advertising: Tracking the Advertising Sales Relationship with Particle Filters, Marketing Science, 27 (2008), [3] P. Chatterjee, D. L. Hoffman and T. P. Novak, Modeling the Clickstream: Implications for Web- Based Advertising Efforts, Marketing Science, 22 (2003), [4] A. Doucet, N. D. Freitas and N. Gordon (eds.), Sequential Monte Carlo Methods in Practice, Springer, [5] A. Goldfarb and C. Tucker, Online Display Advertising: Targeting and Obtrusiveness, Marketing Science, 30 (2011), [6] [7] MapReduce 2009 [8] G. Kitagawa, Monte Carlo Filter and Smoother for Non-gaussian Nonlinear State Space Models, Journal of Computational and Graphical Statistics, 5 (1996), [9] Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited.

10 [10] G. Kitagawa, Introduction to Time Series Modeling, Chapman & Hall/CRC, [11] 2004 [12] P. Manchanda, J-P. Dubé, K. Y. Goh and P. K. Chintagunta, The Effect of Banner Advertising on Internet Purchasing, Journal of Marketing Research, 43 (2006), [13] M. Nagasaki, R. Yamaguchi, R. Yoshida, S. Imoto, A. Doi, Y. Tamada, H. Matsuno, S. Miyano and T. Higuchi, Genomic Data Assimilation for Estimating Hybrid Functional Petri Net from Time-Course Gene Expression Data, Genome Informatics, 17 (2006), [14] K. Nakamura, N. Hirose, B. H. Choi and T. Higuchi, Particle Filtering in Data Assimilation and its Application to Estimation of Boundary Condition of Tsunami Simulation Model, S. K. Park and L. Xu, (eds.), In Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications, Springer, 2009, [15] K. Nakamura, R. Yoshida, M. Nagasaki, S. Miyano and T. Higuchi, Parameter Estimation of in silico Biological Pathways with Particle Filtering Towards a Petascale Computing, The Proceedings of 14th Pacific Symposium on Biocomputing, 2009, [16] H. J. Van Heerde, C. F. Mela and P. Manchanda, The Dynamic Effect of Innovation on Market Structure, Journal of Marketing Research, 41 (2004), [17] M. West and J. Harrison, Bayesian Forecasting and Dynamic Models, Springer, [18] 49 (2004), [19] R. Yoshida, M. Nagasaki, R. Yamaguchi, S. Imoto, S. Miyano and T. Higuchi, Bayesian Learning of Biological Pathways on Genomic Data Assimilation, Bioinformatics, 24 (2008), Copyright c by ORSJ. Unauthorized reproduction of this article is prohibited

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