Changes:

1. Created a TFP JointDistribution to represent full probability model;
2. Renamed CovidUKStochastic --> DiscreteTimeStateTransitionModel;
3. DiscreteTimeStateTransitionModel now inherits from tfp.Distribution.

Changes:

1. Dates are pulled out of CovidUKStochastic
2. CovidUKStochastic now behaves more like a tfd.Distribution
    * CovidUKStochastic is now instantiated with an initial time, number of time steps and
time step size
    * CovidUKStochastic is now instantiated with the initial state.

Changes:

1. We adopt the convention [start, end) for *all* date ranges.
2. Modified PHE case ingestor to reflect this
3. Modified CovidUK to reflect this
4. Corrected a bug in the use of time in simulation.

Bug in discrete_markov.propagate found, introduced after changes for vectorised
likelihood.

Cast data structures to float32 for tfd.Multinomial.log_prob
computation saves time on lgamma calculation.  Approx x1.8 speedup as
lgamma is approx linear in digits of precision required.

Results in over a x2 speedup.

Moved construction of Markov transition matrix format from
model.make_hazard.h into discrete_markov_log_prob.  Achieved a 33%
increase in run speed.

Re-wrote discrete_markov_log_prob to batch the call to
tfd.Multinomial.log_prob to avoid lgamma time.

1. Replaced TensorArray buffer with simple reduction in
discrete_markov_log_prob.
2. tf.lgamma is slow with lots of events, so cast to tf.float32 gives
a  a bit over x2 speedup.

Previously, the Events matrix expected by model.log_prob was ordered
[T, M, X] where T is the number of timpoints, M is the number of
meta-populations and X is the number of transitions.  However, it was
found more convenient to work with [M, T, X] for the purposes of data
augmentation.  This meant extra tf.transpose calls.

model.log_prob now expects [M, T, X], with any further batch
dimensions added as outer dimensions.

First pass implementation of data augmentation MCMC.  This is slow, buggy, and possibly not correct yet!  Use with caution!

Working event time update.  Not compatible with XLA due to tf.boolean_mask which depends on tf.where.

Got stochastic model fitting with new bounded convergence respecting adaptive proposal.  However, XLA appears now very slow.

Performance approximation replacing matrix exponential with row-wise independent draws, a la chain binomial.

1. chainbinom* file and methods renamed to discrete_markov* files and methods.

2. Implemented batched hazard rate calculation, adding functions to automatically broadcast rates to the Markov transition rate matrix.

3. Implemented test simulation and MCMC algorithm.

Updated ODE model with overall number of starting individuals parameter, and daily confirmed cases up to 27th March (PHE, whole of England).

Big changes:
 1. replace python for loop with tf.while_loop
 2. work with a transposed state tensor shape
   - instead of [4, nlads * nages], use [nlads * nages, 4]
   - this made it pretty easy to eliminate some transposes in
     propagate_fn (there were comments there seemingly contemplating
     this shape arrangement)
   - this feels a little more natural to me, too; in TFP we'd call the 4
     SEIR states components of the "event shape" of the system, and the
     nlads * nages part a "batch shape" (although one could reasonably
     also combine these together into one big matrix "event shape")
   - anyway, this allowed elimination of 3 transpose ops which makes for
     simpler code and avoids some memcpys
   - I also made an effort to update surrounding code to use the same data
     layout, but it seems like mcmc.py and covid_ode.py are broken right
     now anyway, due to other changes made in support of stochastic mode,
     so I couldn't confirm that my changes were sufficient.
 3. switch off XLA (which didn't yield any clear improvement, although
    it also didn't really hurt), and disable autograph (which tries to
    do things like rewrite python for loops into TF graph code but tends
    to produce less performant than manually optimized code like what
    I've done here)

Wrote chainbinom_simulate.py function.  Halfway through re-writing the ODE class (which should now not be an ODE!).