LFI problems/packages/methods

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W
1	Name of problem	Motivating system	Commonly benchmark?	External code dependency	Dim of parameters	Continuous/discrete params?	Dim of raw output	Dim of summary stats	Known sufficient stats	Continous/discrete data?	Properties of likelihood / posterior	Algorithm getting stuck on local modes	Dim of latents	Nature of latent process	Tractable likelihood (posterior?)	dx / dtheta tractable?	p(x,z) etc ("gold") tractable?	Execution time	Code available?	Authors that already used it (for comparison)	Additional comments	Publically available canonical observational data?	Implementation in benchmark repo
2	GMM (Gaussian Mixture Models)	None	Yes	No	Flexible	Continuous	n			Continuous	Multimodal	No			Yes	Yes				https://www.pnas.org/content/pnas/104/6/1760.full.pdf, https://arxiv.org/pdf/0805.2256.pdf, https://arxiv.org/pdf/1210.1388.pdf, https://arxiv.org/pdf/1503.07791.pdf			@jan-matthis
3	GLM	None	No	No	Flexible (e.g., 10)	Continuous or discrete	Flexible	Same as raw output		Continuous or discrete		Unknown			Yes	We could				https://arxiv.org/abs/1711.01861
4	GLM: Probabilistic linear regression	None	No	No	3	Continuous	3					Yes				We could			http://dfm.io/emcee/current/user/line/
5	Stable distributions	None	No	No	4	Continuous	1	1		Continuous	Heavy-tailed and skewed likelihood	Unknown			Only in special cases				https://github.com/elfi-dev/zoo/blob/master/notebooks/stable_distribution.ipynb
6	ARCH	Econometrics, applied elsewhere to timeseries	No	No		Continuous									No (but accurate approximation available)
7	g-and-k	None	Yes	No	Flexible	Continuous									No				https://github.com/elfi-dev/elfi/blob/dev/elfi/examples/gnk.py	https://arxiv.org/pdf/1507.00874.pdf
8	MA2	Standard timeseries model	Yes	No	2	Continuous	n	2		Continuous		No			No (but accurate approximation available)				https://github.com/elfi-dev/elfi/blob/dev/elfi/examples/ma2.py
9	Ricker	Ecology	Yes	No	3	Continuous	n			Discrete									https://github.com/cran/synlik
10	blowfly	Ecology (similar to Ricker; less commonly used)	No	No		Continuous	n												https://github.com/cran/synlik
11	Silk	None	No	No	1	Continuous	n	1		Continuous	Posterior is Dirac delta	Yes!			Yes					https://arxiv.org/pdf/1210.3296.pdf
12	INFERNO synthetic toy model	Loosely motivated by particle physics (very simplified)	No	No	4 (3 of which nuisance)	Continuous	3	3		Continous		No	2	One categorical latent	Yes	Yes	Yes	Very fast	https://github.com/pablodecm/paper-inferno	https://arxiv.org/abs/1806.04743	Similar to Gaussian Mixture Models
13	Lotka-Volterra	Predator-prey dynamics	Yes!	No	4	Continuous	2n	George: 9		Discrete (but effectively continous)		Unknown	Large and variable: ~ number of events	Stochastic markov jump process	No	No	Yes		https://github.com/gpapamak/epsilon_free_inference	Toni et al., 2009; https://arxiv.org/abs/1605.06376, https://arxiv.org/pdf/1507.00874.pdf
14	M/G/1 queue model	Server queue	Yes	No	3	Continuous		George: 5		Continous		Unknown	Fixed: ~ number of jobs						https://github.com/gpapamak/epsilon_free_inference	https://arxiv.org/abs/1605.06376
15	Hodgkin-Huxley model	Neuroscience	No	No	12	Continuous	n	Lueckmann: 20		Continuous		Unknown			No	Nasty		Cython version around 10ms (depends on sim length)	https://github.com/gpapamak/snl/blob/master/simulators/hodgkin_huxley.py	https://arxiv.org/abs/1711.01861; https://arxiv.org/abs/1805.07226
16	Weinberg	Historic particle physics	No	No	2	Continuous	1				Highly multi-modal likelihood/posteriors	Yes			No	No			https://github.com/montefiore-ai/hypothesis/blob/master/hypothesis/benchmark/weinberg.py
17	Pythia detector alignment	Particle physics	No	Yes	1	Continuous	n x n					No			No	No			https://github.com/maxim-borisyak/pythia-mill
18	Type Ia Supernova	Cosmology	No	Yes	4 (2 nuisance)	Continuous	2 (or 3)				"banana shape"	No			No				https://github.com/EliseJ/astroABC	https://arxiv.org/pdf/1608.07606.pdf	Python 2.5 code; SMC-ABC avail	Yes
19	Daycare Center	Transmission of disease	(Yes) within ELFI work		3	Continuous	29x53x33 n_{bact. strains}*sum_i=1^{n_dcc} n_{ind_i}	116		Discrete				Markov process	No	No	No		https://github.com/elfi-dev/elfi/blob/dev/elfi/examples/daycare.py	Numminen et al. (2013) [https://doi.org/10.1111/biom.12040], Gutmann et al. (2017) [https://doi.org/10.1007/s11222-017-9738-6], Jebthava & Dubhashi [https://arxiv.org/abs/1711.11139]	Matlab/Python code	Yes
20	Birth-death-mutation	Transmission of disease	No	Yes (C within ELFI)		Continuous	n	3		Discrete									https://github.com/elfi-dev/elfi/blob/dev/elfi/examples/bdm.py	https://www.biorxiv.org/content/biorxiv/early/2015/12/11/021972.full.pdf	Output grows with runs or diminish	Yes
21	Ebola Outbreak in West Africa	Transmission of disease	No	Yes (R)	4+2*T	Continuous		4		Discrete				Markov process	No	No	No		https://github.com/MingweiWilliamTang/LNAphyloDyn	https://arxiv.org/abs/1902.08877		Yes
22	Tumor spheroid growth	Cell-growth	No	Yes	8	Continuous	3			Continuous	Unknown	Unknown							https://github.com/ICB-DCM/tumor2d
23	Primordial power spectrum	Cosmology	No	C code?	100	Continuous				Continuous									https://bitbucket.org/florent-leclercq/simbelmyne	https://arxiv.org/abs/1902.10149
24	Landscape evolution model	Geophysics	No	Yes	5	Continuous	n x n			Discrete (image)		Unknown							https://xarray-simlab.readthedocs.io/en/latest/examples/landscape-evolution-model.html		Inference could also depend on the initial state of the grid (nxn)
25	Lorenz '96 System	Weather	Yes		40	Continuous	time series, e.g. 160 steps	6											https://github.com/gboeing/lorenz-system	[https://doi.org/10.1256/qj.04.03]; [https://arxiv.org/abs/1810.09899]
26	FLASK: Full-sky Lognormal Astro-fields Simulation Kit	Cosmology	No	Yes	8	Continuous	millions	power spectra		Continuous	Multivariate Gaussian				Yes			few secs to few mins	http://www.astro.iag.usp.br/~flask/	https://arxiv.org/abs/1602.08503	There are many different sims like this in this
27	Camelus	Cosmology	No	Yes	8	Continuous	m x n	variable	No	Continuous	Unknown				No	No	No	~10s	https://github.com/Linc-tw/camelus	http://arxiv.org/abs/1410.6955
28	Gaussian Cox Process	Spatial Point Process (to model locations)	Yes		Flexible	Continuous	Flexible			Continuous									https://github.com/cmjt/lgcpSPDE	[https://arxiv.org/abs/1701.00857], [https://arxiv.org/abs/1808.00831]	Doubly stochastic process making it hard to fit
29	Cell Biology model	Cell modelling	No	No	2	Continuous	time series + cell size	150		Discrete	skewed but otherwise regular	no			No
30	Pints: github.com/pints-team/pints	Different time series problems (e.g. from biology)	No (not yet within LFI)	Yes		Continuous				Continuous									https://github.com/pints-team/pints	https://arxiv.org/abs/1812.07388
31	OpenAI gym: gym.openai.com	Reinforcement learning	No (not yet within LFI)	Yes	Flexible (depends on env)	Continuous or discrete													https://gym.openai.com
32	Galton-board
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