Likelihood slices, profiles, Monte Carlo adjusted profiles, and diagnostic plots

[atpabuser]

What it adds

• Designs (src/design.jl): slice_design, profile_design,
  runif_design, sobol_design, as in R pomp. profile_design records
  which parameters are profiled, so that profile can refuse a
  perturbation of them.
• Likelihood estimation at a point (pfilter_loglik): nreps
  independent particle filters, combined by logmeanexp, with the
  jack-knife standard error and the effective sample size of the
  replicates. A replicate whose estimate is zero (log likelihood −∞) is
  kept, since dropping it biases the average upward.
• Slices (slice): the log likelihood along each row of a design,
  with the model and resampling settings (trigger, target) of the
  object passed, including a pfilter or mif result.
• Profiles (profile): for each design row, mif with the profiled
  parameters held fixed, then an evaluation by pfilter_loglik at
  exactly the reported point, with the model and resampling settings
  that mif used.
• Monte Carlo adjusted profile (mcap) as in R pomp::mcap. The local quadratic smoother is R's loess with
  surface = "direct", fitted in standardized units so that the result
  does not depend on the units of the parameter. When fewer than three
  distinct parameter values carry weight, the quadratic is not
  determined by the data: its coefficients, standard errors and interval
  are NaN (R's NA), with a warning, and a smoothing window that cannot
  determine its local quadratic is refused rather than resolved by a
  pseudoinverse.
• Monitoring mif (monitor): the log likelihood of the
  unperturbed model at the point estimates recorded in the traces,
  across one run or a sequence of continuations, using its own random
  numbers so the fit is unchanged. Also hyperbolic_cooling and
  resampled.
• Plots (sliceplot, mcapplot, traceplot, filterplot), as a
  package extension loaded only with AlgebraOfGraphics.

New dependencies: Sobol and LinearAlgebra; AlgebraOfGraphics as a
weak dependency.

How it was checked

• Against exact likelihoods. For the Gompertz model, whose
  likelihood is exact by the Kalman filter, the particle-filter
  estimates, the slices and the profile are compared with the exact
  values. Further tests use models whose likelihood is known in closed
  form, so that each estimate reveals the parameters it was computed
  at.
• Against R. loess and mcap agree with R (pomp::mcap on the
  direct surface) to about 1e-10. Over 600 profile layouts with
  irregular spacing and unequal numbers of starts, the cases Julia
  refuses or marks NaN are exactly those where R stops, falls back on its
  pseudoinverse, or returns NA.
• Each test was run against deliberately wrong
  versions of the code, e.g. a slice evaluated on the bare model, a
  profile evaluated at the swarm average, or mcap without centring.
  Every such version that changes a result is caught.

Notes

• profile with the default avfun = geomean fails for a parameter
  that takes negative values, or that the model needs as an integer. The
  docstring says to pass avfun = mean.
• test/mif.jl also carries the geometric_cooling value test that I
  sent separately.

[codecov]

Codecov Report

❌ Patch coverage is 96.84211% with 12 lines in your changes missing coverage. Please review.
✅ Project coverage is 99.04%. Comparing base (d592885) to head (54a1145).

Additional details and impacted files

@@             Coverage Diff             @@
##             devel      #25      +/-   ##
===========================================
- Coverage   100.00%   99.04%   -0.96%     
===========================================
  Files           28       33       +5     
  Lines          871     1251     +380     
===========================================
+ Hits           871     1239     +368     
- Misses           0       12      +12     

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.