An apparatus for estimating a characteristic of a posterior distribution includes a sampling section configured to generate a plurality of samples from a prior distribution, an obtaining section configured to obtain, for each sample among the plurality of samples, a likelihood of observation given the sample, a calculation section configured to calculate a parameter relating to a density at each sample in the prior distribution, and an estimation section configured to estimate, for the plurality of samples, a characteristic of the posterior distribution based on the parameter relating to the density at each sample and the likelihood of observation for each sample.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. An apparatus, comprising: a sampling section to generate a plurality of samples from a prior distribution; an obtaining section to obtain, for each sample among the plurality of samples, a likelihood of observation given the sample; a calculation section to calculate a parameter relating to a density at each sample in the prior distribution; and an estimation section to estimate, for the plurality of samples, a characteristic of a posterior distribution based on the parameter relating to the density at each sample and the likelihood of observation for each sample. 2. The apparatus of claim 1, wherein the estimation section is further configured to estimate a differential entropy of the posterior distribution as the characteristic of the posterior distribution. 3. The apparatus of claim 2, wherein the calculation section is further configured to calculate a distance from each sample to at least one neighboring sample as the parameter relating to the density. 4. The apparatus of claim 2, wherein the calculation section further is configured to calculate a distance from each sample to a kth-nearest neighbor as the parameter relating to the density, k being a natural number. 5. The apparatus of claim 4, wherein the estimation section is further configured to estimate the characteristic of the posterior distribution by approximating a probability density function of the prior distribution at each sample using a volume of a sphere having a radius equal to the distance. 6. The apparatus of claim 4, wherein the estimation section is further configured to estimate the characteristic of the posterior distribution having Euler's constant as a constant term. 7. The apparatus of claim 1, wherein the estimation section is further configured to estimate the characteristic of each of a plurality of posterior distributions based on the parameter relating to the density at each sample in the prior distribution and a likelihood of transition for each sample from the prior distribution to each posterior distribution. 8. The apparatus of claim 1, further comprising a reduction section to reduce an amount of samples calculated by the calculation section by eliminating each sample having a likelihood of transition that is less than a threshold likelihood. 9. The apparatus of claim 1, further comprising a selecting section to select an action from a plurality of candidate actions based on the characteristic of the posterior distribution corresponding to each observation caused by each of the candidate actions. 10. The apparatus of claim 9, further comprising an observation section to obtain the observation from a model having an internal state estimated by the prior distribution. 11. The apparatus of claim 10, wherein the model is a behavioral model of a person. 12. The apparatus of claim 11, further comprising: an interaction section to generate an interaction with the person based on the selected action; wherein the estimation section is further configured to estimate a differential entropy of each of a plurality of posterior distributions as the characteristic of each of the plurality of posterior distributions. 13. A computer-implemented method, comprising: generating a plurality of samples from a prior distribution; obtaining, for each sample among the plurality of samples, a likelihood of observation given the sample; calculating a parameter relating to a density at each sample in the prior distribution; and estimating, for the plurality of samples, a characteristic of a posterior distribution based on the parameter relating to the density at each sample and the likelihood of observation for each sample. 14. A computer program product comprising a non-transitory computer readable storage medium having program instructions embodied therewith, the program instructions executable by a computer to cause the computer to perform operations comprising: generating a plurality of samples from a prior distribution; obtaining, for each sample among the plurality of samples, a likelihood of observation given the sample; calculating a parameter relating to a density at each sample in the prior distribution; and estimating, for the plurality of samples, a characteristic of a posterior distribution based on the parameter relating to the density at each sample and the likelihood of observation for each sample.