Import libraries
using JSON
using Soss, Distributions, NamedTupleTools
using Random
using ArviZ
Check ArviZ python version is up to date, if necessary, update to latest python ArviZ
ArviZ.arviz_version()
v"0.10.0"
# ArviZ.update_arviz()
radon_data = JSON.parsefile("radon.json")
radon_data["county"] = convert(Vector{Int64}, radon_data["county"]) .+ 1
radon_data["county_name"] = convert(Vector{String}, radon_data["county_name"])
radon_data["x"] = convert(Vector{Int64}, radon_data["x"])
radon_data["u"] = convert(Vector{Float64}, radon_data["u"])
radon_data["y"] = convert(Vector{Float64}, radon_data["y"]);
nchains = 4
ndraws = 500;
# Bayesian linear regression.
mod = @model (
floor_idx,
county_idx,
uranium,
J,
) begin
# Hyperpriors:
g ~ Normal(0, 10) |> iid(2)
sigma_a ~ Exponential(1)
# Varying intercepts uranium model:
a = g[1] .+ g[2] .* uranium
za_county ~ Normal(0, 1) |> iid(J)
a_county = a .+ za_county .* sigma_a
# Common slope:
b ~ Normal(0, 1)
# Expected value per county:
theta = a_county[county_idx] .+ b .* floor_idx
# Model error:
sigma ~ Exponential(1)
y ~ For(eachindex(floor_idx)) do i
Normal(theta[i], sigma)
end
end
@model (floor_idx, county_idx, uranium, J) begin sigma_a ~ Exponential(1) sigma ~ Exponential(1) g ~ Normal(0, 10) |> iid(2) b ~ Normal(0, 1) a = g[1] .+ g[2] .* uranium za_county ~ Normal(0, 1) |> iid(J) a_county = a .+ za_county .* sigma_a theta = a_county[county_idx] .+ b .* floor_idx y ~ For(eachindex(floor_idx)) do i Normal(theta[i], sigma) end end
constant_data = (
floor_idx = radon_data["x"],
county_idx = radon_data["county"],
uranium = radon_data["u"],
J = radon_data["J"],
)
param_mod = mod(; constant_data...);
prior_priorpred = [rand(param_mod, nchains*ndraws)];
post = map(1:nchains) do _
dynamicHMC(param_mod, (y = radon_data["y"],), ndraws)
end;
pred = predictive(mod, :sigma_a, :sigma, :b, :g, :za_county)
post_postpred = map(post) do post_draws
map(post_draws) do post_draw
return merge(post_draw, rand(pred(; constant_data..., post_draw...)))
end
end;
coords = Dict(
"level" => ["basement", "floor"],
"obs_id" => 1:radon_data["N"],
"county" => radon_data["county_name"],
"g_coef" => ["intercept", "slope"],
)
dims = Dict(
"g" => ["g_coef"],
"za_county" => ["county"],
"y" => ["obs_id"],
"floor_idx" => ["obs_id"],
"county_idx" => ["obs_id"],
"theta" => ["obs_id"],
"uranium" => ["county"],
"a" => ["county"],
"a_county" => ["county"],
)
idata = from_namedtuple(
post_postpred;
posterior_predictive = [:y],
prior = prior_priorpred,
prior_predictive = [:y],
coords = coords,
dims = dims,
library = Soss,
);
post_data = idata.posterior
theta = post_data.theta.values
sigma = reshape(post_data.sigma.values,size(post_data.sigma.values)...,1)
y = reshape(radon_data["y"],1,1,radon_data["N"])
log_likelihood = logpdf.(Normal.(theta, sigma), y);
idata_aux = from_namedtuple(
log_likelihood=(y = log_likelihood,),
constant_data=constant_data,
observed_data=(y = radon_data["y"],),
coords=coords,
dims=dims
)
idata = concat(idata, idata_aux)
Dataset (xarray.Dataset) Dimensions: (chain: 4, county: 85, draw: 500, g_coef: 2, obs_id: 919) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 ... 492 493 494 495 496 497 498 499 * county (county) <U17 'AITKIN' 'ANOKA' ... 'WRIGHT' 'YELLOW MEDICINE' * g_coef (g_coef) <U9 'intercept' 'slope' * obs_id (obs_id) int64 1 2 3 4 5 6 7 8 ... 913 914 915 916 917 918 919 Data variables: a (chain, draw, county) float64 0.8079 0.6593 1.348 ... 1.47 1.817 b (chain, draw) float64 -0.5442 -0.5916 -0.5339 ... -0.8111 -0.6871 a_county (chain, draw, county) float64 0.8841 0.7961 1.398 ... 1.655 1.641 za_county (chain, draw, county) float64 0.4143 0.7434 ... 0.9959 -0.9463 sigma (chain, draw) float64 0.7353 0.7282 0.7287 ... 0.7818 0.7964 g (chain, draw, g_coef) float64 1.455 0.9388 1.485 ... 1.54 0.7789 theta (chain, draw, obs_id) float64 0.3399 0.8841 ... 1.641 1.641 sigma_a (chain, draw) float64 0.184 0.1848 0.08017 ... 0.1612 0.1856 Attributes: created_at: 2020-10-22T21:54:07.398248 arviz_version: 0.10.0 inference_library: Soss
array([0, 1, 2, 3])
array([ 0, 1, 2, ..., 497, 498, 499])
array(['AITKIN', 'ANOKA', 'BECKER', 'BELTRAMI', 'BENTON', 'BIG STONE', 'BLUE EARTH', 'BROWN', 'CARLTON', 'CARVER', 'CASS', 'CHIPPEWA', 'CHISAGO', 'CLAY', 'CLEARWATER', 'COOK', 'COTTONWOOD', 'CROW WING', 'DAKOTA', 'DODGE', 'DOUGLAS', 'FARIBAULT', 'FILLMORE', 'FREEBORN', 'GOODHUE', 'HENNEPIN', 'HOUSTON', 'HUBBARD', 'ISANTI', 'ITASCA', 'JACKSON', 'KANABEC', 'KANDIYOHI', 'KITTSON', 'KOOCHICHING', 'LAC QUI PARLE', 'LAKE', 'LAKE OF THE WOODS', 'LE SUEUR', 'LINCOLN', 'LYON', 'MAHNOMEN', 'MARSHALL', 'MARTIN', 'MCLEOD', 'MEEKER', 'MILLE LACS', 'MORRISON', 'MOWER', 'MURRAY', 'NICOLLET', 'NOBLES', 'NORMAN', 'OLMSTED', 'OTTER TAIL', 'PENNINGTON', 'PINE', 'PIPESTONE', 'POLK', 'POPE', 'RAMSEY', 'REDWOOD', 'RENVILLE', 'RICE', 'ROCK', 'ROSEAU', 'SCOTT', 'SHERBURNE', 'SIBLEY', 'ST LOUIS', 'STEARNS', 'STEELE', 'STEVENS', 'SWIFT', 'TODD', 'TRAVERSE', 'WABASHA', 'WADENA', 'WASECA', 'WASHINGTON', 'WATONWAN', 'WILKIN', 'WINONA', 'WRIGHT', 'YELLOW MEDICINE'], dtype='<U17')
array(['intercept', 'slope'], dtype='<U9')
array([ 1, 2, 3, ..., 917, 918, 919])
array([[[0.80789947, 0.65931313, 1.34828739, ..., 1.88969097, 1.37028872, 1.78836638], [0.85039413, 0.70463773, 1.38048993, ..., 1.91158204, 1.40207222, 1.81218725], [0.94746714, 0.8323246 , 1.36622457, ..., 1.78576906, 1.38327385, 1.7072506 ], ..., [0.9781602 , 0.85559295, 1.42392027, ..., 1.87051815, 1.44206893, 1.7869366 ], [0.98584921, 0.87753208, 1.3797836 , ..., 1.77445838, 1.39582223, 1.70059433], [1.12266773, 1.02300934, 1.48511146, ..., 1.8482364 , 1.49986798, 1.78027696]], [[0.96821547, 0.85535318, 1.37868 , ..., 1.78991599, 1.39539163, 1.71295248], [0.99142483, 0.89012753, 1.35982906, ..., 1.72892571, 1.37482825, 1.65984864], [0.8660374 , 0.73006738, 1.3605415 , ..., 1.85597502, 1.38067472, 1.7632538 ], ... [1.01052875, 0.89377887, 1.43513188, ..., 1.86053304, 1.45241915, 1.78091849], [0.92246085, 0.80316932, 1.35630762, ..., 1.79096979, 1.37397123, 1.70962203], [0.8625068 , 0.72998713, 1.34446246, ..., 1.82732396, 1.36408479, 1.73695562]], [[0.94993567, 0.82749591, 1.39523211, ..., 1.84136549, 1.41336189, 1.75787087], [0.96417744, 0.84683134, 1.39094894, ..., 1.81852256, 1.4083245 , 1.73850144], [0.94011961, 0.81618353, 1.39085795, ..., 1.84244346, 1.40920929, 1.75792846], ..., [1.07345867, 0.98111563, 1.40929748, ..., 1.74576749, 1.4229708 , 1.68279656], [1.12312947, 1.0310123 , 1.45814686, ..., 1.79379391, 1.47178674, 1.73097699], [1.00365109, 0.88037614, 1.45198498, ..., 1.90116151, 1.47023842, 1.81709736]]])
array([[-0.54417626, -0.59160681, -0.53388747, ..., -0.62052845, -0.62739942, -0.72623561], [-0.59230356, -0.74427519, -0.7027961 , ..., -0.60183736, -0.62571873, -0.60544757], [-0.72027605, -0.60138213, -0.63006106, ..., -0.68669638, -0.61964099, -0.72250962], [-0.54222656, -0.77720862, -0.63139076, ..., -0.65421649, -0.81114096, -0.68708442]])
array([[[0.88412065, 0.79607225, 1.39784523, ..., 1.74843142, 1.57555505, 1.66292039], [0.92913664, 0.87283224, 1.39328495, ..., 1.7358453 , 1.60953416, 1.66678422], [0.87201355, 0.87673791, 1.4564779 , ..., 1.801204 , 1.40439383, 1.75627175], ..., [1.26661271, 0.80678944, 1.34635269, ..., 1.48410783, 1.57128887, 1.59748227], [0.39286964, 0.99742921, 1.57425917, ..., 1.9153411 , 1.57720541, 1.34381829], [1.15331268, 0.81838478, 1.47683596, ..., 1.90674101, 1.46075288, 1.32432165]], [[0.77096671, 0.9882212 , 1.51448631, ..., 1.7562554 , 1.46692903, 1.34608326], [0.82111217, 0.84183925, 1.22266708, ..., 1.45448711, 1.49046179, 1.40539755], [1.00262666, 0.8734182 , 1.51922672, ..., 1.9414069 , 1.5022222 , 1.88061454], ... [1.29926444, 0.83562718, 1.19907934, ..., 1.87645596, 1.39366518, 1.99862254], [0.62175743, 0.88156744, 1.50594828, ..., 1.69663238, 1.45569531, 1.41189992], [0.91455264, 0.70054955, 1.33835333, ..., 1.67611266, 1.65367054, 1.59883488]], [[0.98009683, 0.82560485, 1.25320499, ..., 1.96314737, 1.53083973, 1.84366968], [0.99409576, 0.97397453, 1.44908872, ..., 1.89508418, 1.57960817, 1.7061964 ], [0.92906692, 0.74349466, 1.43568375, ..., 1.85484899, 1.36993343, 1.64904105], ..., [0.89597629, 0.87248668, 1.39604344, ..., 1.89698124, 1.77455671, 1.74754542], [1.0583367 , 0.84551587, 1.36935571, ..., 1.75434781, 1.72304073, 1.727473 ], [0.95580915, 0.87467843, 1.3349354 , ..., 1.80042171, 1.65504724, 1.64149426]]])
array([[[ 0.41432373, 0.74339642, 0.26938695, ..., -0.76785989, 1.11578847, -0.68190039], [ 0.42611312, 0.91018034, 0.06923993, ..., -0.95099493, 1.12267505, -0.78684481], [-0.94111822, 0.55395868, 1.12571259, ..., 0.19251701, 0.26342554, 0.61143145], ..., [ 1.47881329, -0.25020161, -0.39766672, ..., -1.98101487, 0.66247358, -0.97127801], [-1.81191075, 0.36635813, 0.59424033, ..., 0.4304818 , 0.55423519, -1.0901663 ], [ 0.18348915, -1.22520629, -0.04955021, ..., 0.3503011 , -0.23420487, -2.73006968]], [[-1.16115488, 0.78216131, 0.79945828, ..., -0.19815156, 0.42112302, -2.15966864], [-0.89406726, -0.25349242, -0.72004065, ..., -1.44068312, 0.60702571, -1.33575741], [ 0.8328738 , 0.87410341, 0.96760721, ..., 0.52093384, 0.74115424, 0.71562492], ... [ 2.35143797, -0.47358225, -1.92239096, ..., 0.12967486, -0.47848716, 1.77296248], [-2.01788314, 0.52609396, 1.00417009, ..., -0.63305522, 0.54841291, -1.99787695], [ 0.3780273 , -0.21381554, -0.04437279, ..., -1.09830107, 2.10336346, -1.00321963]], [[ 0.2922006 , -0.0183205 , -1.37595568, ..., 1.17982022, 1.13812274, 0.83121701], [ 0.29411191, 1.24988087, 0.57154294, ..., 0.75263885, 1.68380379, -0.31757456], [-0.07710414, -0.50708136, 0.31270714, ..., 0.08654164, -0.27399052, -0.75960438], ..., [-0.9258692 , -0.56668275, -0.06914208, ..., 0.78883409, 1.83411206, 0.33777426], [-0.40199985, -1.15089279, -0.55089518, ..., -0.24473911, 1.55887854, -0.02174018], [-0.25780462, -0.03070311, -0.63074204, ..., -0.54285396, 0.99587453, -0.94626794]]])
array([[0.73528044, 0.72817112, 0.72865881, ..., 0.73396615, 0.72662638, 0.7480746 ], [0.75164279, 0.75563737, 0.74644034, ..., 0.75512848, 0.76671025, 0.76323502], [0.78303403, 0.73270549, 0.72401043, ..., 0.75767707, 0.76426799, 0.75643395], [0.73124151, 0.76892993, 0.77637449, ..., 0.74229922, 0.78183814, 0.79638447]])
array([[[1.45480744, 0.93884367], [1.48498122, 0.92096264], [1.4487691 , 0.72752878], ..., [1.51178749, 0.77444185], [1.45743506, 0.68440242], [1.55655555, 0.6296921 ]], [[1.45958984, 0.71312108], [1.43244807, 0.64004758], [1.45801704, 0.85912735], ..., [1.46561475, 0.66176208], [1.45520875, 0.83703939], [1.48119879, 0.85816438]], [[1.46821501, 0.80312117], [1.4676747 , 0.76403997], [1.47823896, 0.81647138], ..., [1.51882869, 0.7376848 ], [1.44182651, 0.75374425], [1.43946448, 0.83732631]], [[1.48300795, 0.77363636], [1.47507318, 0.74145203], [1.47970648, 0.78309085], ..., [1.47549727, 0.58347 ], [1.52418473, 0.5820429 ], [1.54035954, 0.77891347]]])
array([[[ 0.33994438, 0.88412065, 0.88412065, ..., 1.57555505, 1.66292039, 1.66292039], [ 0.33752983, 0.92913664, 0.92913664, ..., 1.60953416, 1.66678422, 1.66678422], [ 0.33812608, 0.87201355, 0.87201355, ..., 1.40439383, 1.75627175, 1.75627175], ..., [ 0.64608426, 1.26661271, 1.26661271, ..., 1.57128887, 1.59748227, 1.59748227], [-0.23452978, 0.39286964, 0.39286964, ..., 1.57720541, 1.34381829, 1.34381829], [ 0.42707706, 1.15331268, 1.15331268, ..., 1.46075288, 1.32432165, 1.32432165]], [[ 0.17866315, 0.77096671, 0.77096671, ..., 1.46692903, 1.34608326, 1.34608326], [ 0.07683698, 0.82111217, 0.82111217, ..., 1.49046179, 1.40539755, 1.40539755], [ 0.29983057, 1.00262666, 1.00262666, ..., 1.5022222 , 1.88061454, 1.88061454], ... [ 0.61256806, 1.29926444, 1.29926444, ..., 1.39366518, 1.99862254, 1.99862254], [ 0.00211644, 0.62175743, 0.62175743, ..., 1.45569531, 1.41189992, 1.41189992], [ 0.19204302, 0.91455264, 0.91455264, ..., 1.65367054, 1.59883488, 1.59883488]], [[ 0.43787026, 0.98009683, 0.98009683, ..., 1.53083973, 1.84366968, 1.84366968], [ 0.21688714, 0.99409576, 0.99409576, ..., 1.57960817, 1.7061964 , 1.7061964 ], [ 0.29767616, 0.92906692, 0.92906692, ..., 1.36993343, 1.64904105, 1.64904105], ..., [ 0.24175981, 0.89597629, 0.89597629, ..., 1.77455671, 1.74754542, 1.74754542], [ 0.24719574, 1.0583367 , 1.0583367 , ..., 1.72304073, 1.727473 , 1.727473 ], [ 0.26872473, 0.95580915, 0.95580915, ..., 1.65504724, 1.64149426, 1.64149426]]])
array([[0.18396527, 0.18479251, 0.0801744 , ..., 0.19505675, 0.32726754, 0.16701233], [0.16987292, 0.19049199, 0.16399755, ..., 0.12006289, 0.0669287 , 0.04485562], [0.14600644, 0.13807689, 0.17344577, ..., 0.12279112, 0.14901925, 0.13767747], [0.10322071, 0.10172424, 0.14334754, ..., 0.19169271, 0.16117612, 0.1855744 ]])
Dataset (xarray.Dataset) Dimensions: (chain: 4, draw: 500, obs_id: 919) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499 * obs_id (obs_id) int64 1 2 3 4 5 6 7 8 ... 912 913 914 915 916 917 918 919 Data variables: y (chain, draw, obs_id) float64 0.8789 0.008412 ... 0.9402 2.318 Attributes: created_at: 2020-10-22T21:54:06.926568 arviz_version: 0.10.0 inference_library: Soss
array([0, 1, 2, 3])
array([ 0, 1, 2, ..., 497, 498, 499])
array([ 1, 2, 3, ..., 917, 918, 919])
array([[[ 0.87890761, 0.00841201, 1.2032543 , ..., 2.18442294, 2.25680978, 1.30930848], [ 0.19670509, 1.81854798, 1.25554941, ..., 2.66142395, 1.63371097, 1.70732784], [ 2.84396372, 0.71780581, 0.58953519, ..., 0.8565214 , 2.61458195, 2.64357121], ..., [ 0.25484339, 2.0495833 , 2.66912583, ..., 0.45132302, 1.98085069, 2.57418379], [-0.54946281, 0.38149868, -0.00337138, ..., 2.64432683, 0.86354637, 0.06539837], [ 0.85343477, 1.19588563, 0.57260635, ..., 2.06146424, 1.07942 , 0.66164841]], [[ 0.62749845, 2.14803817, 0.36659753, ..., 1.45529307, 1.82845882, 1.23586327], [-0.13039018, 1.02875794, 0.64763085, ..., 2.28346964, 2.06134395, 0.6045999 ], [ 0.65132636, 0.87079846, 0.41989008, ..., 1.43575645, 1.99014674, 1.58364901], ... [ 0.23789382, 0.58270823, 1.02158837, ..., 1.80374595, 2.18084344, 2.41590006], [ 0.0686027 , 0.23685781, 0.41520892, ..., 2.01683942, 1.08291052, 1.29554788], [ 0.6732404 , 0.79507764, 2.09001568, ..., 1.17896983, 0.78457522, 1.75853194]], [[ 1.40281964, 2.33836912, 0.59432641, ..., 1.46901039, 2.18444404, 1.46015995], [ 0.10020749, 2.18962905, 0.59361526, ..., 3.09323053, 3.21697795, 1.79863717], [-0.25899983, 0.8995789 , 0.66914131, ..., 1.3208745 , 2.33765325, 2.51609932], ..., [-0.64926085, 0.51188126, 0.33844466, ..., 3.01775151, 1.39938745, 2.98593113], [ 1.02245731, -0.25511736, -0.19100069, ..., 1.90368094, 1.07860718, 1.86491461], [ 1.55637825, 1.02706777, 0.56636067, ..., 1.71984767, 0.94015731, 2.3184378 ]]])
Dataset (xarray.Dataset) Dimensions: (chain: 4, draw: 500, obs_id: 919) Coordinates: * chain (chain) int64 0 1 2 3 * draw (draw) int64 0 1 2 3 4 5 6 7 8 ... 492 493 494 495 496 497 498 499 * obs_id (obs_id) int64 1 2 3 4 5 6 7 8 ... 912 913 914 915 916 917 918 919 Data variables: y (chain, draw, obs_id) float64 -0.7975 -0.6199 ... -0.7788 -0.9535 Attributes: created_at: 2020-10-22T21:54:11.323164 arviz_version: 0.10.0
array([0, 1, 2, 3])
array([ 0, 1, 2, ..., 497, 498, 499])
array([ 1, 2, 3, ..., 917, 918, 919])
array([[[-0.79747851, -0.61989882, -0.64159665, ..., -0.61249698, -0.72771682, -0.94239165], [-0.79346104, -0.62038155, -0.61905164, ..., -0.60171934, -0.72288056, -0.94354298], [-0.79336793, -0.60896359, -0.63735697, ..., -0.64198163, -0.7913442 , -1.05277245], ..., [-0.62845985, -0.82185134, -0.64748163, ..., -0.61099694, -0.68724634, -0.87309724], [-1.59062848, -0.74779059, -1.02704124, ..., -0.60057955, -0.60078815, -0.67336756], [-0.74536937, -0.74762421, -0.63569997, ..., -0.64843812, -0.62891437, -0.68890392]], [[-0.96253364, -0.6337152 , -0.70980783, ..., -0.65141788, -0.63470568, -0.70351095], [-1.08218999, -0.63967861, -0.69070765, ..., -0.65114031, -0.64699507, -0.7403823 ], [-0.84075562, -0.66766074, -0.62995787, ..., -0.63681461, -0.92039892, -1.22388862], ... [-0.66838567, -0.86869661, -0.68935716, ..., -0.68199089, -1.05645622, -1.40109034], [-1.17939995, -0.6738893 , -0.81805739, ..., -0.67033508, -0.65928344, -0.75328544], [-0.95062934, -0.65369243, -0.65950117, ..., -0.64150815, -0.71354243, -0.88909281]], [[-0.72085884, -0.64026846, -0.61262175, ..., -0.61170366, -0.8739072 , -1.17331154], [-0.93245433, -0.69194371, -0.66039997, ..., -0.65693558, -0.79004743, -1.00417601], [-0.86562186, -0.68221875, -0.68108081, ..., -0.71340158, -0.76211081, -0.94905156], ..., [-0.89214603, -0.63142583, -0.64677133, ..., -0.64567598, -0.79598546, -1.04403579], [-0.91246628, -0.73240757, -0.67286423, ..., -0.68338736, -0.81653037, -1.03212654], [-0.90421864, -0.71334462, -0.70061493, ..., -0.69290528, -0.77877054, -0.95353624]]])
Dataset (xarray.Dataset) Dimensions: (chain: 1, county: 85, draw: 2000, g_coef: 2, obs_id: 919) Coordinates: * chain (chain) int64 0 * draw (draw) int64 0 1 2 3 4 5 6 ... 1993 1994 1995 1996 1997 1998 1999 * county (county) <U17 'AITKIN' 'ANOKA' ... 'WRIGHT' 'YELLOW MEDICINE' * obs_id (obs_id) int64 1 2 3 4 5 6 7 8 ... 913 914 915 916 917 918 919 * g_coef (g_coef) <U9 'intercept' 'slope' Data variables: a (chain, draw, county) float64 -6.048 -4.706 ... -9.087 -18.01 a_county (chain, draw, county) float64 -7.022 -3.851 ... -9.28 -18.33 b (chain, draw) float64 1.373 1.119 -0.3245 ... 0.4427 -1.223 za_county (chain, draw, county) float64 -0.59 0.5183 ... -0.435 -0.7183 sigma (chain, draw) float64 2.462 0.8884 1.655 ... 0.4859 2.017 0.09474 theta (chain, draw, obs_id) float64 -5.648 -7.022 ... -18.33 -18.33 g (chain, draw, g_coef) float64 -11.89 -8.481 ... -10.89 -20.03 sigma_a (chain, draw) float64 1.65 0.005178 1.134 ... 1.34 0.08033 0.4442 Attributes: created_at: 2020-10-22T21:54:09.502672 arviz_version: 0.10.0 inference_library: Soss
array([0])
array([ 0, 1, 2, ..., 1997, 1998, 1999])
array(['AITKIN', 'ANOKA', 'BECKER', 'BELTRAMI', 'BENTON', 'BIG STONE', 'BLUE EARTH', 'BROWN', 'CARLTON', 'CARVER', 'CASS', 'CHIPPEWA', 'CHISAGO', 'CLAY', 'CLEARWATER', 'COOK', 'COTTONWOOD', 'CROW WING', 'DAKOTA', 'DODGE', 'DOUGLAS', 'FARIBAULT', 'FILLMORE', 'FREEBORN', 'GOODHUE', 'HENNEPIN', 'HOUSTON', 'HUBBARD', 'ISANTI', 'ITASCA', 'JACKSON', 'KANABEC', 'KANDIYOHI', 'KITTSON', 'KOOCHICHING', 'LAC QUI PARLE', 'LAKE', 'LAKE OF THE WOODS', 'LE SUEUR', 'LINCOLN', 'LYON', 'MAHNOMEN', 'MARSHALL', 'MARTIN', 'MCLEOD', 'MEEKER', 'MILLE LACS', 'MORRISON', 'MOWER', 'MURRAY', 'NICOLLET', 'NOBLES', 'NORMAN', 'OLMSTED', 'OTTER TAIL', 'PENNINGTON', 'PINE', 'PIPESTONE', 'POLK', 'POPE', 'RAMSEY', 'REDWOOD', 'RENVILLE', 'RICE', 'ROCK', 'ROSEAU', 'SCOTT', 'SHERBURNE', 'SIBLEY', 'ST LOUIS', 'STEARNS', 'STEELE', 'STEVENS', 'SWIFT', 'TODD', 'TRAVERSE', 'WABASHA', 'WADENA', 'WASECA', 'WASHINGTON', 'WATONWAN', 'WILKIN', 'WINONA', 'WRIGHT', 'YELLOW MEDICINE'], dtype='<U17')
array([ 1, 2, 3, ..., 917, 918, 919])
array(['intercept', 'slope'], dtype='<U9')
array([[[ -6.04826367, -4.70602877, -10.92978584, ..., -15.82048284, -11.12853193, -14.90518063], [ 20.86553893, 20.98997513, 20.41298171, ..., 19.95957392, 20.39455632, 20.04442995], [ -7.0882975 , -7.30627511, -6.29554315, ..., -5.50129881, -6.26326698, -5.64994298], ..., [ -0.95454099, -0.69509331, -1.89811622, ..., -2.8434649 , -1.9365329 , -2.66654129], [ 1.38015563, 0.45879277, 4.73102459, ..., 8.08819151, 4.86745173, 7.45989204], [ 2.91191667, 6.08207017, -8.61749199, ..., -20.16857018, -9.08689985, -18.00676636]]])
array([[[ -7.02161778, -3.85090246, -10.6123104 , ..., -15.008368 , -9.56537684, -12.88224525], [ 20.87063352, 20.99004494, 20.42369996, ..., 19.9578306 , 20.39946771, 20.04287203], [ -7.18761635, -8.08891779, -5.4314606 , ..., -5.95796736, -4.04448155, -4.41314248], ..., [ -2.43698682, 0.02161689, -3.21233007, ..., -5.9943565 , -1.08246757, -3.50746778], [ 1.34602234, 0.34918024, 4.78005316, ..., 8.09077312, 4.82183391, 7.54309334], [ 2.57791008, 6.63126032, -8.69409773, ..., -20.23782327, -9.28011947, -18.32582136]]])
array([[ 1.37312134, 1.11858113, -0.32449665, ..., -0.03551086, 0.44271637, -1.22322431]])
array([[[-0.59001127, 0.51834595, 0.19244187, ..., 0.49227399, 0.94752681, 1.22622862], [ 0.98386594, 0.01348036, 2.06990512, ..., -0.33666923, 0.94848699, -0.30086475], [-0.08755121, -0.68991247, 0.76170306, ..., -0.40256088, 1.95589606, 1.0902601 ], ..., [-1.10625905, 0.53483718, -0.98071777, ..., -2.35131852, 0.63733694, -0.62753222], [-0.42489457, -1.36446764, 0.61031253, ..., 0.0321361 , -0.56785508, 1.035698 ], [-0.75195677, 1.23640451, -0.17246427, ..., -0.15591108, -0.4349998 , -0.71829593]]])
array([[2.46153442, 0.88841353, 1.6549757 , ..., 0.48585206, 2.01736696, 0.09473966]])
array([[[ -5.64849644, -7.02161778, -7.02161778, ..., -9.56537684, -12.88224525, -12.88224525], [ 21.98921465, 20.87063352, 20.87063352, ..., 20.39946771, 20.04287203, 20.04287203], [ -7.51211299, -7.18761635, -7.18761635, ..., -4.04448155, -4.41314248, -4.41314248], ..., [ -2.47249768, -2.43698682, -2.43698682, ..., -1.08246757, -3.50746778, -3.50746778], [ 1.78873871, 1.34602234, 1.34602234, ..., 4.82183391, 7.54309334, 7.54309334], [ 1.35468578, 2.57791008, 2.57791008, ..., -9.28011947, -18.32582136, -18.32582136]]])
array([[[-11.89202051, -8.48091901], [ 20.32377465, -0.78625088], [ -6.13927719, 1.37729282], ..., [ -2.08411164, -1.63932167], [ 5.39154034, 5.82163662], [-10.89014309, -20.03063338]]])
array([[1.64972122, 0.00517813, 1.13440866, ..., 1.34005307, 0.08033355, 0.44418323]])
Dataset (xarray.Dataset) Dimensions: (chain: 1, draw: 2000, obs_id: 919) Coordinates: * chain (chain) int64 0 * draw (draw) int64 0 1 2 3 4 5 6 7 ... 1993 1994 1995 1996 1997 1998 1999 * obs_id (obs_id) int64 1 2 3 4 5 6 7 8 ... 912 913 914 915 916 917 918 919 Data variables: y (chain, draw, obs_id) float64 -7.96 -6.003 -5.829 ... -18.52 -18.48 Attributes: created_at: 2020-10-22T21:54:09.488524 arviz_version: 0.10.0 inference_library: Soss
array([0])
array([ 0, 1, 2, ..., 1997, 1998, 1999])
array([ 1, 2, 3, ..., 917, 918, 919])
array([[[ -7.95990701, -6.00255287, -5.82878515, ..., -9.29544629, -12.17677522, -16.19540162], [ 20.50894809, 20.91422028, 19.93031133, ..., 21.70649567, 19.02338229, 20.99364111], [-12.29825178, -8.3076492 , -5.85233324, ..., -0.50914043, -6.52568469, -4.44121602], ..., [ -2.18163433, -2.15146575, -3.12716976, ..., -0.5524566 , -3.5617786 , -3.32026735], [ 2.53050193, 3.24240271, -1.43215436, ..., 8.06971877, 9.21055718, 8.99138635], [ 1.29369871, 2.54627158, 2.66162123, ..., -9.24484113, -18.51945978, -18.48185627]]])
Dataset (xarray.Dataset) Dimensions: (county: 85, g_coef: 2, level: 2, obs_id: 919) Coordinates: * obs_id (obs_id) int64 1 2 3 4 5 6 7 8 ... 912 913 914 915 916 917 918 919 * county (county) <U17 'AITKIN' 'ANOKA' ... 'WRIGHT' 'YELLOW MEDICINE' * g_coef (g_coef) <U9 'intercept' 'slope' * level (level) <U8 'basement' 'floor' Data variables: y (obs_id) float64 0.7885 0.7885 1.065 0.0 ... 1.609 1.308 1.065 Attributes: created_at: 2020-10-22T21:54:12.429962 arviz_version: 0.10.0
array([ 1, 2, 3, ..., 917, 918, 919])
array(['AITKIN', 'ANOKA', 'BECKER', 'BELTRAMI', 'BENTON', 'BIG STONE', 'BLUE EARTH', 'BROWN', 'CARLTON', 'CARVER', 'CASS', 'CHIPPEWA', 'CHISAGO', 'CLAY', 'CLEARWATER', 'COOK', 'COTTONWOOD', 'CROW WING', 'DAKOTA', 'DODGE', 'DOUGLAS', 'FARIBAULT', 'FILLMORE', 'FREEBORN', 'GOODHUE', 'HENNEPIN', 'HOUSTON', 'HUBBARD', 'ISANTI', 'ITASCA', 'JACKSON', 'KANABEC', 'KANDIYOHI', 'KITTSON', 'KOOCHICHING', 'LAC QUI PARLE', 'LAKE', 'LAKE OF THE WOODS', 'LE SUEUR', 'LINCOLN', 'LYON', 'MAHNOMEN', 'MARSHALL', 'MARTIN', 'MCLEOD', 'MEEKER', 'MILLE LACS', 'MORRISON', 'MOWER', 'MURRAY', 'NICOLLET', 'NOBLES', 'NORMAN', 'OLMSTED', 'OTTER TAIL', 'PENNINGTON', 'PINE', 'PIPESTONE', 'POLK', 'POPE', 'RAMSEY', 'REDWOOD', 'RENVILLE', 'RICE', 'ROCK', 'ROSEAU', 'SCOTT', 'SHERBURNE', 'SIBLEY', 'ST LOUIS', 'STEARNS', 'STEELE', 'STEVENS', 'SWIFT', 'TODD', 'TRAVERSE', 'WABASHA', 'WADENA', 'WASECA', 'WASHINGTON', 'WATONWAN', 'WILKIN', 'WINONA', 'WRIGHT', 'YELLOW MEDICINE'], dtype='<U17')
array(['intercept', 'slope'], dtype='<U9')
array(['basement', 'floor'], dtype='<U8')
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Dataset (xarray.Dataset) Dimensions: (J_dim_0: 1, county: 85, g_coef: 2, level: 2, obs_id: 919) Coordinates: * obs_id (obs_id) int64 1 2 3 4 5 6 7 8 ... 913 914 915 916 917 918 919 * J_dim_0 (J_dim_0) int64 0 * county (county) <U17 'AITKIN' 'ANOKA' ... 'WRIGHT' 'YELLOW MEDICINE' * g_coef (g_coef) <U9 'intercept' 'slope' * level (level) <U8 'basement' 'floor' Data variables: floor_idx (obs_id) int64 1 0 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 1 0 0 0 0 0 0 0 J (J_dim_0) int64 85 county_idx (obs_id) int64 1 1 1 1 2 2 2 2 2 ... 84 84 84 84 84 84 84 85 85 uranium (county) float64 -0.689 -0.8473 -0.1135 ... -0.09002 0.3553 Attributes: created_at: 2020-10-22T21:54:14.149337 arviz_version: 0.10.0
array([ 1, 2, 3, ..., 917, 918, 919])
array([0], dtype=int64)
array(['AITKIN', 'ANOKA', 'BECKER', 'BELTRAMI', 'BENTON', 'BIG STONE', 'BLUE EARTH', 'BROWN', 'CARLTON', 'CARVER', 'CASS', 'CHIPPEWA', 'CHISAGO', 'CLAY', 'CLEARWATER', 'COOK', 'COTTONWOOD', 'CROW WING', 'DAKOTA', 'DODGE', 'DOUGLAS', 'FARIBAULT', 'FILLMORE', 'FREEBORN', 'GOODHUE', 'HENNEPIN', 'HOUSTON', 'HUBBARD', 'ISANTI', 'ITASCA', 'JACKSON', 'KANABEC', 'KANDIYOHI', 'KITTSON', 'KOOCHICHING', 'LAC QUI PARLE', 'LAKE', 'LAKE OF THE WOODS', 'LE SUEUR', 'LINCOLN', 'LYON', 'MAHNOMEN', 'MARSHALL', 'MARTIN', 'MCLEOD', 'MEEKER', 'MILLE LACS', 'MORRISON', 'MOWER', 'MURRAY', 'NICOLLET', 'NOBLES', 'NORMAN', 'OLMSTED', 'OTTER TAIL', 'PENNINGTON', 'PINE', 'PIPESTONE', 'POLK', 'POPE', 'RAMSEY', 'REDWOOD', 'RENVILLE', 'RICE', 'ROCK', 'ROSEAU', 'SCOTT', 'SHERBURNE', 'SIBLEY', 'ST LOUIS', 'STEARNS', 'STEELE', 'STEVENS', 'SWIFT', 'TODD', 'TRAVERSE', 'WABASHA', 'WADENA', 'WASECA', 'WASHINGTON', 'WATONWAN', 'WILKIN', 'WINONA', 'WRIGHT', 'YELLOW MEDICINE'], dtype='<U17')
array(['intercept', 'slope'], dtype='<U9')
array(['basement', 'floor'], dtype='<U8')
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array([85], dtype=int64)
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array([-0.6890476 , -0.84731286, -0.11345877, -0.59335253, -0.14289048, 0.38705671, 0.27161366, 0.2775787 , -0.33231549, 0.09586457, -0.60821981, 0.27368456, -0.73532009, 0.34378118, -0.05986041, -0.50499598, 0.33956032, -0.6333907 , -0.02414516, 0.26385546, 0.15571232, 0.29502505, 0.41491366, 0.22420699, 0.19661065, -0.09652081, 0.50352907, -0.40059698, -0.75187223, -0.66334763, 0.30902028, -0.05338601, 0.10973294, -0.00780337, -0.88182892, 0.31102988, -0.69159638, -0.68170885, 0.19444774, 0.44490375, 0.39473441, 0.14960034, 0.01376483, 0.16586184, 0.14042259, 0.02395087, -0.21005952, -0.09322665, 0.26093247, 0.39884994, 0.24804687, 0.40545177, 0.26522172, 0.24315008, -0.20473037, -0.07402767, -0.16329217, 0.47860404, 0.26611108, 0.28114827, -0.41805351, 0.36632226, 0.38057798, 0.19314609, 0.52802487, -0.21204536, 0.06311563, -0.68343648, 0.23721212, -0.47467372, 0.11639541, 0.26980574, 0.47077833, 0.31602898, -0.04684007, 0.49759448, 0.15008242, -0.67202973, 0.2124142 , -0.14748428, 0.1832378 , 0.23603608, 0.46321187, -0.09002427, 0.35528698])
idata.to_netcdf("soss.nc")
"soss.nc"
versioninfo()
Julia Version 1.5.2 Commit 539f3ce943 (2020-09-23 23:17 UTC) Platform Info: OS: macOS (x86_64-apple-darwin18.7.0) CPU: Intel(R) Core(TM) i5-3470S CPU @ 2.90GHz WORD_SIZE: 64 LIBM: libopenlibm LLVM: libLLVM-9.0.1 (ORCJIT, ivybridge)
using Pkg
Pkg.status()
Status `~/.julia/environments/v1.5/Project.toml` [131c737c] ArviZ v0.4.8 [31c24e10] Distributions v0.23.8 [7073ff75] IJulia v1.21.4 [682c06a0] JSON v0.21.1 [d9ec5142] NamedTupleTools v0.13.6 [438e738f] PyCall v1.92.1 [8ce77f84] Soss v0.15.3 [9a3f8284] Random