A method and system for probability distribution forecast evaluation are disclosed. The present disclosure is directed to embodiments of a system that evaluates probability distribution forecasts by acquiring one or more of a probability distribution forecast, a probability distribution realization, and a prior knowledge of the probability distribution forecast. The system disclosed herein may then compute an accuracy score and an information score based on the acquired forecast, realization, and prior knowledge. In evaluating the forecast, a performance score may also be computed based on the accuracy score and the information score.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A probability distribution forecast evaluation system comprising at least one processor; at least one memory device that stores a plurality of instructions which, when executed by the at least one processor, cause the at least one processor to operate with the at least one memory device to: acquire one or more of a probability distribution forecast, a probability distribution realization corresponding to the probability distribution forecast, and a prior knowledge of the probability distribution forecast; compute an accuracy score based on the one or more of a probability distribution forecast, a probability distribution realization corresponding to the probability distribution forecast, and a prior knowledge of the probability distribution forecast; compute an information score based on the one or more of a probability distribution forecast, a probability distribution realization corresponding to the probability distribution forecast, and a prior knowledge of the probability distribution forecast; and compute a performance score based on the accuracy score and the information score. 2. The probability distribution forecast evaluation system of claim 1, wherein the accuracy score is computed based on the probability distribution forecast and the probability distribution realization. 3. The probability distribution forecast evaluation system of claim 2, wherein the accuracy score is computed by calculating a dissimilarity score between the probability distribution forecast and the probability distribution realization. 4. The probability distribution forecast evaluation system of claim 3, wherein the dissimilarity score is either (1) the Kullback-Leibler (KL) divergence between the probability distribution forecast and the probability distribution realization, or (2) a quadratic approximation of the KL divergence between the probability distribution forecast and the probability distribution realization. 5. The probability distribution forecast evaluation system of claim 1, wherein the information score is computed based on the probability distribution realization and the prior knowledge of the probability distribution forecast. 6. The probability distribution forecast evaluation system of claim 5, wherein the information score is computed by calculating a dissimilarity score between the probability distribution realization and the prior knowledge of the probability distribution forecast. 7. The probability distribution forecast evaluation system of claim 6, wherein the dissimilarity score is either (1) the Kullback-Leibler (KL) divergence between the probability distribution realization and the prior knowledge of the probability distribution forecast, or (2) a quadratic approximation of the KL divergence between the probability distribution realization and the prior knowledge of the probability distribution forecast. 8. The probability distribution forecast evaluation system of claim 1, wherein the performance score is computed by subtracting the accuracy score from the information score. 9. The probability distribution forecast evaluation system of claim 1, wherein one or more of the probability distribution forecast, the probability distribution realization corresponding to the probability distribution forecast, and the prior knowledge of the probability distribution forecast are computed based on samples. 10. The probability distribution forecast evaluation system of claim 9, wherein one or more of the probability distribution forecast, the probability distribution realization corresponding to the probability distribution forecast, and the prior knowledge of the probability distribution forecast are partitioned into discrete probability bins. 11. The probability distribution forecast evaluation system of claim 9, wherein one or more of the probability distribution forecast, the probability distribution realization corresponding to the probability distribution forecast, and the prior knowledge of the probability distribution forecast contain sample errors and the performance score is normalized to account for the sample errors. 12. The probability distribution forecast evaluation system of claim 1, wherein a relative performance score is further computed based on the computed performance score and the entropy of the prior knowledge of the probability distribution forecast. 13. The probability distribution forecast evaluation system of claim 1, further comprising instructions that, when executed by the at least one processor, cause the at least one processor to operate with the at least one memory device to: calculate a probability distribution for the performance score based on one or more of the probability distribution of the accuracy score and the probability distribution of the information score; and calculate a confidence interval of the performance score based on the probability distribution of the performance score. 14. A method for evaluating a probability distribution forecast comprising: acquiring one or more of a probability distribution forecast, a probability distribution realization corresponding to the probability distribution forecast, and a prior knowledge of the probability distribution forecast; computing an accuracy score based on the one or more of a probability distribution forecast, a probability distribution realization corresponding to the probability distribution forecast, and a prior knowledge of the probability distribution forecast; computing an information score based on the one or more of a probability distribution forecast, a probability distribution realization corresponding to the probability distribution forecast, and a prior knowledge of the probability distribution forecast; and computing a performance score based on the accuracy score and the information score. 15. The method for evaluating a probability distribution forecast of claim 14, wherein the accuracy score is computed based on the probability distribution forecast and the probability distribution realization. 16. The method for evaluating a probability distribution forecast of claim 15, wherein the accuracy score is computed by calculating a dissimilarity score between the probability distribution forecast and the probability distribution realization. 17. The method for evaluating a probability distribution forecast of claim 16, wherein the dissimilarity score is either (1) the Kullback-Leibler (KL) divergence between the probability distribution forecast and the probability distribution realization, or (2) a quadratic approximation of the KL divergence between the probability distribution forecast and the probability distribution realization. 18. The method for evaluating a probability distribution forecast of claim 14, wherein the information score is computed based on the probability distribution realization and the prior knowledge of the probability distribution forecast. 19. The method for evaluating a probability distribution forecast of claim 18, wherein the information score is computed by calculating a dissimilarity score between the probability distribution realization and the prior knowledge of the probability distribution forecast. 20. The method for evaluating a probability distribution forecast of claim 19, wherein the dissimilarity score is either (1) the Kullback-Leibler (KL) divergence between the probability distribution realization and the prior knowledge of the probability distribution forecast, or (2) a quadratic approximation of the KL divergence between the probability distribution realization and the prior knowledge of the probability distribution forecast. 21. The method for evaluating a probability distribution forecast of claim 14, wherein the performance score is computed by subtracting the accuracy score from the information score. 22. The method for evaluating a probability distribution forecast of claim 14, wherein one or more of the probability distribution forecast, the probability distribution realization corresponding to the probability distribution forecast, and the prior knowledge of the probability distribution forecast are computed based on samples. 23. The method for evaluating a probability distribution forecast of claim 22, wherein one or more of the probability distribution forecast, the probability distribution realization corresponding to the probability distribution forecast, and the prior knowledge of the probability distribution forecast are partitioned into discrete probability bins. 24. The method for evaluating a probability distribution forecast of claim 22, wherein one or more of the probability distribution forecast, the probability distribution realization corresponding to the probability distribution forecast, and the prior knowledge of the probability distribution forecast contain sample errors and the performance score is normalized to account for the sample errors. 25. The method for evaluating a probability distribution forecast of claim 14, wherein a relative performance score is further computed based on the computed performance score and the entropy of the prior knowledge of the probability distribution forecast. 26. The method for evaluating a probability distribution forecast of claim 14, further comprising: calculating a probability distribution for the performance score based on one or more of the probability distribution of the accuracy score and the probability distribution of the information score; and calculating a confidence interval of the performance score based on the probability distribution of the performance score.