MC-QUANTITIES:  Quantities from log files relating to Monte Carlo simulation.

The quantities below relating to Markov chain Monte Carlo can be
obtained from log files (eg, for use in xxx-plt).  Note that the
generic quantities documented in quantities.doc will also be
available, as will quantities specific to the particular Markov chain
application being used.

    T   Temperature used (see xxx-mc.doc, NOT from the tempering schedule)
    E   Potential energy at end of iteration
    E0  Potential energy at end of iteration at inverse temperature of 0
    E1  Equal to E - E0
    K   Kinetic energy at end of iteration
    K0  Expected value of kinetic energy, equal to half the dimensionality 
    H   Total energy at end of iteration (sum of E and K)
    D[n] Change in total energy for last state proposed (up to max of n)
         (for Metropolis, hybrid, and multivariate slice sampling operations)
    h   Current value of the thermostat variable (only for use with  
        Metropolis importance sampling, xxx-mis.doc)

    i   Inverse temperature being used (from the tempering schedule)
    I   Index of current inverse temperature value in schedule
    j   Direction of change for inverse temperature
    J   Higher temperature for attempted transition (meaningful only if
        last operation in iteration was sim-temp)
    Q[n] Importance weight, or log of importance weight (see below)
    F[n] Factor for estimating ratio of normalizing constants using
         tempered transitions (see below).

    d   Heatbath decay factor used in this iteration
    f   Stepsize factor used in this iteration
    e   Average number of evaluations per slice sampling update this iteration
    k   Cumulative cpu usage in minutes.

    r   Rejection rate for this iteration
    C0  Number of consecutive acceptances of metropolis/hybrid updates, 
        zero if last update rejected
    C1  Number of consecutive acceptances previous to this rejection, zero 
        if last update was not rejected
    Cn  (for n>1) The value of n^2*f(C1/n), where f(c) = c*(1-exp(-0.6*c-c^2)).
        This provides an approximation to the value of the sequence of
        acceptances if movement is mostly systematic up to about n steps,
        and a random walk at larger scales.

    m   Point last moved to relative to starting point
    m0  Point moved to relative to lowest point for spiral and double-spiral
    m1  Starting point relative to lowest point for spiral and double-spiral
    m2  Switch point for double-spiral operations
    m3  Equal to m0-m2 (double-spiral only)
    m4  Equal to m1-m2 (double-spiral only)
    m5  Equal to |m3|-|m4|

    qn  Component n of position
    pn  Component n of momentum
    sn  Stepsize selected by application for component n

    s   Value used for the most recent accept/reject decision or setting
        of the slice level (in [-1,+1], with absolute value used).  Only
        available if an slevel operation was done at some time; if not, 
        has value zero.

None of these quantities can be used with a range; 'q' and 'p' must
have a modifier; 'D' and 'Q' may have a modifier; 'E' may only have a
modifier of '0' or '1'; 'K' may only have a modifier of '0'; the
meaning of 's' is different with and without a modifier; the others
may not have a modifier.

The 'Q' quantity is the importance weight, which will always be one
except during annealed importance sampling.  Note that these weights
might sometimes be so extreme that this value overflows or underflows.
If a modifier of 0 is given to 'Q', the value is the log of the
importance weight, which is much less likely to be out of bounds.  If
a modifier n greater than zero is given for 'Q', the value is the log
of the importance weight unless that is less than -n, in which case
the value is -n.

The 'F' quantities are factors obtained from the last tempered
transition in the iterations, which can be averaged to estimate the
ratio of normalizing constants for the distribution at temperature one
to that of the distribution at the highest temperature.  The 'F1'
quantity is based on only the first half of the tempered transition.
The 'F2' quantity is based on both halves if the tempered transition
is accepted, and is otherwise based on just the first half.

Momenta of zero are assumed if none exist.

            Copyright (c) 1995-2019 by Radford M. Neal