Course:CPSC532:StaRAI:2017:As1:Q1:dp

Here is what I got from running 10000 iterations....

Method	n=1	n=2	n=3	n=4	n=5	n=10	n=20	n=100	n=1000
Predict 0.5	25	25	25	25	25	25	25	25	25
empirical ave	33.359	24.986	22.261	20.830	20.0244	18.364	17.545	16.797	16.718
median	33.239	25.050	29.861	24.975	28.669	24.919	25.091	24.960	24.972
thresholded ave	33.329	25.022	22.249	20.762	20.072	18.334	17.438	16.871	16.629
Laplace (pseudo-count 1)	22.199	20.8249	19.957	19.463	19.0139	18.036	17.409	16.819	16.659
pseudo-count 2	22.679	21.308	20.413	19.765	19.291	18.163	17.453	16.835	16.680
pseudo-count 0.5	22.859	21.297	20.331	19.692	19.217	18.127	17.419	16.833	16.678

Method	n=1	n=2	n=3	n=4	n=5	n=10	n=20	n=100	n=1000
Predict 0.5	50	50	50	50	50	50	50	50	50
empirical ave	33.48	33.28	33.40	33.33	33.40	33.36	33.41	33.36	33.389
median	33.39	33.32	29.99	29.86	28.62	27.27	26.21	25.23	24.99
thresholded ave	33.45	33.41	33.37	33.39	33.34	33.38	33.26	33.30	33.30
Laplace (pseudo-count 1)	44.48	41.68	39.97	38.87	38.09	36.01	34.85	33.65	33.35
pseudo-count 2	46.66	44.46	42.88	41.65	40.76	38.14	36.13	33.90	33.43
pseudo-count 0.5	41.68	38.79	37.42	36.64	36.18	34.75	34.21	33.53	33.37

Method	n=1	n=2	n=3	n=4	n=5	n=10	n=20	n=100	n=1000
Predict 0.5	100	100	100	100	100	100	100	100	100
empirical ave	33376.10	17022.11	10061.59	6603.60	4888.64	1624.61	525.45	93.89	72.30
median	33387.90	16273.63	30082.50	20187.84	28589.00	22705.33	23753.52	24556.73	24588.09
thresholded ave	332.53	199.40	149.93	124.83	110.31	86.35	77.68	72.88	72.01
Laplace (pseudo-count 1)	91.76	88.03	84.55	82.28	81.14	77.51	74.79	72.68	72.38
pseudo-count 2	92.98	89.01	85.72	84.04	82.32	78.61	76.21	72.24	71.49
pseudo-count 0.5	94.48	90.97	86.04	84.02	82.83	77.85	75.69	72.68	72.47