Approximate Bayesian computation schemes for parameter inference of discrete stochastic models using simulated likelihood density

Table 2 Comparison of averaged error and mean count number for estimated rate constants of system 2 using algorithms 1 and 2.

Δt	*α\k*		1	2	3	4	5
Algorithm 1
2	0.05	MN	18.29	7.53	9.8	12.7	14.23
		AE	4.6211	4.4179	4.7138	4.2188	3.8119
	Same ∈_k	MN	2.69	2.07	2.16	1.93	1.93
		AE	4.7006	4.9603	4.8841	4.6833	4.7298
	Diff. ∈_k	MN	15.26	7.85	8.78	13.06	12.28
		AE	4.8295	4.5322	5.0418	4.7346	4.6069
5	0.05	MN	9.69	3.48	3.12	58.2	74.07
		AE	4.1076	4.3243	4.1868	3.5311	3.5194
	Same ∈_k	MN	2.34	2.31	2.42	16.9	11.38
		AE	4.9862	4.7669	4.6716	3.8873	4.0017
	Diff. ∈_k	MN	25.72	8.14	10.45	25.8	174.88
		AE	4.0461	3.9583	3.7474	3.5655	3.6951
Algorithm 2
2	0.05	MN	89.7	19.75	17.8	40.42	69.52
		AE	4.0540	4.1339	4.1376	3.9696	3.9009
	Same ∈_k	MN	2.52	3.85	3.55	3.82	3.84
		AE	5.0456	4.6069	4.3666	4.5876	3.8958
	Diff. ∈_k	MN	197.49	15.05	22.09	36.85	94.24
		AE	3.8712	3.7934	4.3158	3.6485	3.5989
5	0.05	MN	138.14	30.52	46.66	98.87	377.66
		AE	4.0258	3.7218	3.8258	3.8445	3.9205
	Same ∈_k	MN	21.67	11.34	11.17	26.65	59.64
		AE	4.0545	3.5715	4.1910	3.7252	3.8667
	Diff. ∈_k	MN	185.54	28.39	33.81	89.81	846.61
		AE	3.7810	3.6694	3.6939	3.9806	3.8515

Three strategies are used to choose the discrepancy tolerance α: a fixed value of α= 0.05; varying α values; and α= ∈_kdenoted as same ∈_k); varying α values that are smaller than ∈_k (denoted as diff. ∈_k).(AE:Averaged Error; MN: Mean count Number).

ISSN: 1471-2105