Statistical Modeling of Ad Campaigns in Online Advertising Systems

In this paper, statistical modeling of online advertising systems is addressed. The proposed model relies on the highest bidding price estimation in an auction network and the click-through rate estimation of the ad campaign. The estimation problem is faced with serious challenges due to the extremely time-varying and nonlinear behavior of users, the competitive behavior of the ad campaigns, and the variety of strategies incorporated by the demand-side platforms. Accordingly, estimation algorithms based on Kalman filtering may fail to provide reliable solutions in a real-time setting. In this paper, particle filtering is utilized to estimate the probability distribution of the highest bidding price. Advertisers observe the highest bidding price only if they win the auction. Otherwise, they do not have access to the highest bidding price. Thus, a biconditional update rule is proposed for the particles. The weighting scheme modifies the posterior distribution in case of winning or losing the auction. Next, the click-through rate of the ad campaign is introduced based on the Bayesian estimation. Since the user response is extremely variable over time, an adaptation rule is proposed to update the forgetting factor and the level of emphasis on the recent observations. Finally, by estimation of the highest bidding price and the click-through rate distributions, the input-output model of the ad campaign is developed. The input is the bidding signal or the control signal and the output is the total number of winning impressions for the campaign. The results are reported for a campaign with four individual segments and confirm that the proposed statistical approach can provide a reliable model for ad campaigns.