1. An image processing apparatus comprising: a next observation estimator that estimates a position selected from among a plurality of position candidates using (i) operation history information including first information based on observed positions in an image under previous observations and (ii) information including estimation results for the plurality of position candidates, the estimated results being obtained on the basis of a probability value obtained from a predetermined probability distribution; and a displayed image generator that generates an image to be displayed so that at least the estimated position is visually recognizable, wherein the previous observations respectively correspond to the observed positions in the image, wherein a total number of the previous observations is n, where n is a natural number greater than or equal to two, wherein the observed positions in the image are respectively denoted as (a k , b k ), where k is a natural number from 1 to n, and wherein the first information includes (i) a value of (a 1 +. .. +a k +. .. +a n )/n and (ii) a value of (b 1 +. .. +b k +. .. +b n )/n.