Table 2.

Simulation results showing mean, bias, root mean squared error (RMSE) and the 2.5 and 97.5 empirical percentiles of the estimates of θ = (λ₀₁ λ₁₀ μ₁)^⊺ under model $M_{\{1\}}^0$ for both the PSHMM and exponential fitting (Exp) methods across 100 repeat experiments. $\Delta =\frac{1}{30}s$, δ, ω > 0 (unknown), the number of emitters N_E = 100. N_F indicates the number of frames simulated. For both methods, log − log scatterplots of λ₀₁ and λ₁₀ are shown in Figure 7

Study	NF	θ	PSHMM Mean	PSHMM Bias	PSHMM RMSE (× 10−2)	PSHMM (2.5%, 97.5%) percentiles	Exp Mean	Exp Bias	Exp RMSE (× 10−2)	Exp (2.5%, 97.5%) percentiles
1	16,800	0.32	0.32	0.00	0.97	(0.30, 0.34)	0.29	−0.029	3.29	(0.26, 0.32)
		0.32	0.32	−0.001	0.76	(0.30, 0.33)	0.31	−0.007	0.89	(0.30, 0.32)
		0.01	0.01	0.001	0.21	(0.01, 0.02)	0.01	0.001	0.11	(0.01, 0.01)
2	11,151	0.32	0.32	−0.001	0.66	(0.30, 0.33)	0.30	−0.012	1.47	(0.29, 0.32)
		1	1.00	0.003	1.91	(0.96, 1.04)	0.95	−0.053	5.95	(0.89, 0.99)
		0.03	0.03	0.001	0.35	(0.03, 0.04)	0.03	0.001	0.33	(0.03, 0.04)
3	9364	0.32	0.31	−0.004	0.68	(0.30, 0.32)	0.30	−0.017	1.90	(0.28, 0.32)
		3.16	3.16	0.002	6.56	(3.05, 3.28)	2.45	−0.712	77.85	(1.78, 3.92)
		0.11	0.11	0.001	1.02	(0.09, 0.13)	0.09	−0.017	2.12	(0.06, 0.12)
4	8799	0.32	0.30	−0.013	1.40	(0.29, 0.31)	0.28	−0.032	3.35	(0.27, 0.30)
		10	9.96	−0.042	23.03	(9.52, 10.42)	3.19	−6.809	690.87	(1.52, 5.91)
		0.33	0.35	0.014	3.79	(0.29, 0.42)	0.12	−0.210	21.49	(0.06, 0.25)
5	10,962	1	1.00	−0.002	1.86	(0.96, 1.04)	0.90	−0.104	12.43	(0.74, 1.01)
		0.32	0.32	0.000	0.72	(0.30, 0.33)	0.30	−0.013	1.47	(0.29, 0.32)
		0.01	0.01	0.000	0.10	(0.01, 0.01)	0.01	0.001	0.11	(0.01, 0.01)
6	5312	1	1.00	−0.004	1.81	(0.96, 1.03)	0.95	−0.054	6.44	(0.87, 1.01)
		1	1.00	0.001	1.76	(0.96, 1.04)	0.93	−0.066	6.88	(0.89, 0.97)
		0.03	0.03	0.001	0.29	(0.03, 0.04)	0.03	0.001	0.28	(0.03, 0.04)
7	3526	1	0.99	−0.015	2.32	(0.95, 1.02)	0.95	−0.053	5.78	(0.91, 0.99)
		3.16	3.17	0.003	7.33	(3.01, 3.30)	2.71	−0.451	46.16	(2.50, 3.89)
		0.11	0.11	0.001	1.06	(0.08, 0.13)	0.10	−0.004	0.99	(0.08, 0.12)
8	2961	1	0.97	−0.033	3.91	(0.93, 1.00)	0.91	−0.095	9.75	(0.85, 0.95)
		10	9.94	0.003	27.21	(9.46, 10.47)	5.02	0.003	504.34	(3.66, 6.52)
		0.33	0.35	0.017	3.94	(0.28, 0.42)	0.20	−0.133	13.77	(0.14, 0.27)
9	9116	3.16	3.15	−0.008	6.88	(3.04, 3.29)	2.31	−0.855	95.19	(1.64, 3.04)
		0.32	0.31	−0.002	1.53	(0.28, 0.34)	0.28	−0.037	3.74	(0.27, 0.29)
		0.01	0.01	0.000	0.11	(0.01, 0.01)	0.01	0.001	0.13	(0.01, 0.01)
10	3466	3.16	3.13	−0.035	7.47	(3.01, 3.28)	2.83	−0.335	37.76	(2.49, 3.06)
		1	1.00	0.004	4.04	(0.90, 1.07)	0.87	−0.129	13.00	(0.84, 0.90)
		0.03	0.03	0.001	0.37	(0.03, 0.04)	0.04	0.002	0.36	(0.03, 0.04)
11	1680	3.16	3.11	−0.052	9.49	(2.98, 3.31)	2.92	−0.245	25.63	(2.75, 3.08)
		3.16	3.18	0.015	9.12	(2.99, 3.37)	2.60	−0.567	56.96	(2.48, 3.70)
		0.11	0.11	0.002	1.21	(0.09, 0.13)	0.11	−0.000	0.98	(0.09, 0.13)
12	1115	3.16	3.03	−0.135	14.73	(2.92, 3.15)	2.79	−0.377	38.19	(2.66, 3.92)
		10	9.99	−0.008	24.86	(9.54, 10.48)	6.35	−3.648	365.97	(5.72, 6.93)
		0.33	0.35	0.015	3.92	(0.29, 0.44)	0.27	−0.061	6.79	(0.22, 0.33)
13	8532	10	9.93	−0.069	25.64	(9.47, 10.47)	5.33	−4.666	506.70	(1.98, 8.60)
		0.32	0.32	0.000	4.42	(0.24, 0.37)	0.22	−0.099	9.95	(0.21, 0.23)
		0.01	0.01	0.000	0.09	(0.01, 0.01)	0.01	0.001	0.10	(0.01, 0.01)
14	2882	10	9.86	−0.142	29.52	(9.44, 10.39)	7.75	−2.246	241.85	(5.53, 8.71)
		1	1.03	0.026	10.53	(0.78, 1.16)	0.68	−0.323	32.37	(0.64, 0.71)
		0.03	0.03	0.001	0.36	(0.03, 0.04)	0.04	0.001	0.37	(0.03, 0.04)
15	1096	10	9.73	−0.266	38.40	(9.22, 10.34)	8.19	−1.814	184.84	(7.38, 8.66)
		3.16	3.21	0.049	20.73	(2.45, 3.47)	2.05	−1.108	110.97	(1.97, 3.16)
		0.11	0.11	0.004	1.22	(0.09, 0.13)	0.11	0.004	1.04	(0.09, 0.13)
16	531	10	9.50	−0.501	55.72	(9.10, 9.96)	7.93	−2.072	207.90	(7.55, 8.22)
		10	9.91	−0.095	54.47	(9.02, 10.88)	5.63	−4.368	436.96	(5.40, 5.89)
		0.33	0.34	0.007	4.51	(0.26, 0.43)	0.30	−0.029	4.06	(0.26, 0.36)