CHANGES:

1. Implemented log-linear model for weekday effect in I->R hazard;
2. Updated summary.py and within_between.py to match;
3. Implemented linear random walk for new gamma0 parameter.
4. Implemented per-parameter data structure in output HDF5 file.

CHANGES:

1. Re-implemented trace_fn
2. Implemented new Posterior class in `gemlib`

MCMC update kernels in `interface.py` changed to reflect new
AdaptiveRandomWalkMetropolis interface.

==============================

enqueue_pipeline.sh --> covid_pipeline.sge --> prepare_config.py --> inference.py --> summary.py

enqueue_pipeline.sh identifies the dataset and analysis period, launching 4 SGE jobs [P1, P1+2]\times[specimen_date, report_date]

Each SGE job runs the inference and summary scripts, using information contained in a config.yaml file.

The config.yaml file, together with results outputs, are stored in a results directory specified the config file
and over-ridden in the top-level enqueue_pipeline.sh script.

CHANGES:

1. Added `data/example_cases.py`, `data/uk_clip.py`, `covid/summary.py`, `summary.py`
2. `summary.py` computes summary values required by reports to SAGE
3. Small changes to `inference.py` and `simulate.py` to reflect baked-in `nu` parameter in `model_spec.py`.

Removed redundant code from `inference.py` (duplicated in `model_spec.py`). Small change to `xi_freq` parameter in `model_spec.py`.

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