2.1.1 Factor ~ KO Beta PIP

2.1.2 Factor ~ KO Posterior Association

2.1.3 Beta PIP vs P-Value

2.1.4 Local False Sign Rate (LFSR)

2.2.1 Association results for 2 randomly initialized GSFA runs

2.2.2 Chain mixing and convergence evaluation

To check the convergence of a certain scalar estimand, we adopt the potential scale reduction metric (\(\hat{R}\)) as described in Section 11.4 of Bayesian Data Analysis, 3rd ed.

The basic idea is to evaluate both the within-sequence variance and the between-sequence variance, and assess how close the two variances are.

If the potential scale reduction \(\hat{R}\) is close to 1, it means our inference has reached a good level of convergence;
if \(\hat{R}\) is high, then we have reason to believe that proceeding with further simulations may improve our inference on this estimand.

Since the order and sign of factors are intercahngeable, we focus on evaluating the estimation of all pairs of \(\beta_{m\cdot} \cdot W_{j\cdot}\) (a dot product that sums over all factors for each marker-gene pair).

We take the last 1000 stable samples from each of the 3 runs (1 SVD initialized, 2 randomly initialized). Each chain was further split into 2 halves, resulting in 6 chains with 500 iterations of samples each to assess convergence on.

The table below shows the summary of \(\hat{R}\) of \(\beta_{m\cdot} \cdot W_{j\cdot}\) across genes for a given KO condition \(m\):

2.2.3 Difference btw methods in factor estimation

For a pair of \(Z\) estimations from 2 inference methods, \(Z_1, Z_2\), we quantify the pairwise estimation difference as \(||Z_1Z_1^T - Z_2Z_2^T||_1/N^2\), where \(N\) is the number of rows (samples) in \(Z\).

Guided SVD vs Rand_01: 0.546

Guided SVD vs Rand_02: 0.441

Rand_01 vs Rand_02: 0.533