I am reading about this algorithm called "ABC" (Approximate Bayesian Computation).
Over here, it makes mention of "summary statistics".
For example, in the Bayesian Setting where we want to estimate some parameter "thetha": A randomly chosen value of the "thetha_i" is selected by randomly sampling the priors. This value of "thetha_i" is used to generate a series of realizations "y1, y2, y3...yn", collectively denoted as "y_i".
A "summary statistic" for each "Yi" generated through simulation is denoted as : S(Yi). A "distance" (e.g. euclidean distance) is evaluated between the "summary statistics" of the original data and the simulated data, e.g. D[ S(Yi), S(Y0) ] ... where Y0 is the original data. IF D[ S(Yi), S(Y0) ] > "some threshold" , THEN the choice of "thetha_i" is accepted.
We repeat this procedure many times, and keep track of all accepted values of "thetha_i". These (many) values of "thetha_i" can be used to make the posterior distribution of "thetha_i", and a final value of "thehta_i" can be selected.
Throughout this whole procedure, I am still confused about what exactly is a "summary statistic". Does anyone know what is the functional form of the "summary statistic"?