A fair die is about to be tossed. The probability that it lands with ‘5’ showing up is 1/6; this is an unconditional probability. But the probability that it lands with ‘5’ showing up, given that it lands with an odd number showing up, is 1/3; this is a conditional probability. In general, conditional probability is probability given some body of evidence or information, probability relativised...

in this paper, we show that the chapman-kolmogorov formula could be used as a recursive formula for computing the m-step-ahead conditional density of a markov bilinear model. the stationary marginal probability density function of the model may be approximated by the m-step-ahead conditional density for sufficiently large m.

The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS’s) [Blume, Brandenburger, and Dekel 1991a; Blume, Brandenburger, and Dekel 1991b], and nonstandard probability spaces (NPS’s) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS’s are equivalent; without the as...

Conditional probability density functional theory (CP-DFT) determines the ground-state energy of a many-electron system by finding conditional from parallelizable series Kohn-Sham DFT calculations. By directly calculating densities, authors bypass need for an approximate exchange-correlation (XC) functional. CP-DFT is formally exact, but potentials are used in practice. We explore suitable appr...