PPLR
It is the probability of first condition being up-regulated.
PPLR is acronym for Probability of Positive Log Ratio. In BitSeq, we consider the log of ratio of expression in condition 2 over expression in condition 1 or log(Exp_2 / Exp_1). When the ratio is positive, it simply means that the expression in condition 2 is higher than the expression in condition 1.
The PPLR expresses the probability or likelihood of the ratio being positive i.e. second condition being up-regulated in respect to the first. PPLR close to 1 means there is very high probability of a given transcript being up-regulated in the second condition.
When PPLR is very low, close to 0, this implies very low probability of up-regulation, and consequently the probability of down-regulation being high.
Usually we want to select significant transcripts in terms of differential expression. This means taking into account both up-regulated and down-regulated transcript. For this purpose, we can choose a significance threshold i.e. 0.05 and then select all transcripts with PPLR above 0.95 and below 0.05 as being significant.
There is no direct relation between PPLR and p-value as they come from a different perspective of looking at the problem. For selecting significant results just use the method described above.