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.

Consider an SEIR model.  For adding $x \geq 0$ S->E event times we have:
\begin{equation}
S(t+1) &=& S(0) - (N_{se}(t) + x) \geq 0 \\
E(t+1) &=& E(0) + (N_{se}(t) + x) \geq 0
\end{equation}
such that $x$ is bounded by
$$
x \leq S(0) - N_{se}(t).
$$

Similarly for adding $x \geq 0$ E->I event times we have:
$$
x \leq E(0) + N_{se}(t) - N_{ei}(t).
$$

For deleting $x \geq 0$ S->E event times we have:
$$
x \leq E(0) + N_{se}(t) - N_{ei}(t)
$$
and for E->I event times we have;
$$
x \leq I(0) + N_{ei}(t) - N_{ir}(t).
$$

Changes:

1. Previously, we initialised from the first imputed event at T-s, where s was random due
to the initialisation process;

2. We now calculate the state at time T given s (and the event imputation).

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.

Introduced counting process respecting AddOccultsProposal.  This now check to make sure
we don't invalidate the epidemic by adding too many events.  To achieve this, we combine
occults and POEs into 1 structure.  This has the advantage of requiring less storage, but
is less easy to monitor occults separately from POEs.

Changes:

1. Bounded convergence parameter mis-specified in samplers (was 0.0, now 1.0)
2. Added 'name' property to GibbsStep

Changes:

1. Implemented GibbsStep and GibbsKernel classes
2. Modified mcmc.sample function to use Gibbs sampler
3. Amended bugs in event_time_mh.py and occult_proposal.py (edge cases where tf.gathers
were overshooting the bounds of the data stuctures, not apparent on a GPU but raised on
CPU).

Changes:

1. Brought UncalibratedLogRandomWalk up to speed with latest tfp changes (stateless seed)
2. Added thin to example_config.yaml
3. Added parameter 'xi' to model to allow time-varying infec rate
4. Added parameter 'xi' to overall MCMC scheme.

Changes:

1. Beta2 introduced to measure the effect of inter-ltla commute
2. Introduced chain thinning to reduce size of posterior output

Changes:

1. Replaced 149 UTLAs with 315 LTLAs mixing matrix;
2. Wrote geometric initialisation for censored event times;
3. Modified data ingester to take PHE Anonymised Line Listing data.

Changes:

1. Added occult Metropolis Hastings update.
2. Factored out Categorical2 distribution for use by both event time move and occults.
3. Refactored mcmc.py script for HDF5 output purposes
4. Apply compression to HDF5 output file.

This has a considerable impact on the run speed of the algorithm, but gains in producing a
97% compression ratio for the posterior output.

The 'known' and 'occult' event tensors are added before feeding to the log_prob function.

This class was a thin wrapper around tfp.mcmc.MetropolisHastings, and was therefore just
extra code cruft.

Changes:

1. Fixed bug in inner tf.while_loop in sample()
2. Made number of event time updates per sweep a config file
parameter.

Also add a script to tune MH for event times

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

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.

1. Formatting -- black style!
2. After profiling, implemented a better workaround for the
tfd.Categorical bug.  Replaced with an inherited Categorical2 class,
with overloaded log_prob function.
3. Fixed a  bug in EventTimeProposal where tfd.FiniteDiscrete was
being used on a non-strictly-increasing outcomes vector.
4. Increased number of meta-populations to 149 to mirror UK UTLA regions.