6. Joint Posteriors and Correlation Functions

RealTrace can calculate joint posterior distributions that can be used to calculate correlation functions. To run add the flag -j.

Running the calculation of the joint distributions also runs the prediction part and generates. Setting both flags is therefore redundant.

The number of joints $P(z_{n+m}, z_n)$ that are calculated for each $z_n$ is determined by the rel_tolerance_joints that is set.

Output:

• Will create a file named _joints.csv containing all calculated joints formatted as an upper triangle matrix. Rows correspond to the earlier time point in the joint, while columns correspond to the later time point named celllid_time, where cellid corresponds to whatever is defined as the cell id and time is time.

cell_id	parent_id	time	cell1_0	cell1_1	cell1_2	cell1_3	cell2_4	cell2_5
cell1		0		P(z_1, z_0)	P(z_2, z_0)	P(z_3, z_0)	P(z_4, z_0)	P(z_5, z_0)
cell1		1			P(z_2, z_1)	P(z_3, z_1)	P(z_4, z_1)	P(z_5, z_1)
cell1		2				P(z_3, z_2)	P(z_4, z_2)	P(z_5, z_2)
cell2	cell1	3					P(z_4, z_3)	P(z_5, z_3)
cell2	cell1	4						P(z_5, z_4)

Each joint probability consists of its means and the upper triangle of its covariance matrix and thus of 8+36=44 values in total.

To calculate correlation functions, the Python script correlation_from_joint.py can be used. The usage is explained here.