pblas

My implementations for pair-based likelihood approximations as seen in Stockdale, et al. (2019). This software adds to the original reference code at jessicastockdale/PBLA. Namely, I have:

• implemented all PBLAs in the R scripting language;
• optimized an O(m^2 n^2) task for computational efficiency;
• provided wrappers pbla_gsem and pbla_multi for optimizing general and multitype stochastic epidemic models;
• made the option of a fixed exposed period for SEIR models;
• made the option of numerous patient zeros;
• and supplemented code for simulation studies, MCMC samplers, and real data analyses.

See this video for my oral exam. Some functions exist to reproduct the results of Stockdale, et al. (2019). Practitioners should use:

• pbla_std for complex SEMs;
• pbla_prod for general SEMs;
• rgsem to simulate epidemics;
• pbla_gsem, pbla_multi as wrappers for MLE.

For large epidemics, some efficient memory use may be important; I demonstrate such with global variable assignments <<- in pbla-ebola.R. To simulate a general stochastic epidemic, use rgsem. (See multitypes.R with pbla_multi.R for mulitype SEM. A case study is pbla-mcmc-tristan.R.)

Some key files in this repository are:

• pbla-report-sdtemple.pdf documents the model, theoretical developments, and experimental results;
• pbla-slides-sdtemple.pdf summarizes the model, theoretical developments, and experimental results;
• pbla-ebola.R, pbla-ebola-contours.R examine the Ebola virus epidemic in West Africa (see data/ebola/);
• pbla-nN.R studies PBLA independence assumptions under increasing n / N infected proportion;
• pbla-under.R considers adjustments in the case of underreporting;
• pbla-time.R, pbla-parallel.R benchmark computational performance;
• pbla-rabies investigates the dog rabies epidemic in Bangui, Central African Republic;
• pbla-mcmc-tristan.R examines the common cold outbreak in Tristan da Cunha;
• pbla-mcmc-example.R offers a sampler with random walk proposals and Hastings ratios based on PBLAs;
• ncda-mcmc-example.R offers a sampler for non-centered data augmentation;
• pbla-bakeoff.R compares 5 PBLAs in a simulation study;
• pbla-exp.R is the basis for simulation studies with exponential infectious periods;
• pbla-erl.R is the basis for simulation studies with Erlang infectious periods;
• pbla-figure.R is a sample script for figures in simulation studies.

This package has been tested on R 3.6.2 and R 4.0.5. Besides pbla_prod_parallel, source code is exclusively base R, so the package should operate for older versions of R. pbla_prod_parallel utilizes parallel, foreach, and doParallel to offer parallel computing for the O(n^2) loop. Parallel computing will only speed up calculations for n > 10,000.

Correction! Please note that there is a mistake in the slides and in the report. On slide 8/31, the MLE for the removal rate gamma should be the MLE for an exponential rate. This impacts the figure on slide 22/31. R[0] estimates for the completely observed SEM do increase with increasing infected proportion. Thus, any commentary in the report and in the YouTube talk related to this figure are invalid. Other commentary remains valid.