Re: [r-inla] INLA never recovers true Theta values?
nati.k.asnakew
Pm..
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-------- Original message --------
From: Finn Lindgren <finn.l...@gmail.com>
Date: 2018/04/25 7:22 PM (GMT-03:30)
To: Munji Choi <munji...@gmail.com>
Cc: R-inla discussion group <r-inla-disc...@googlegroups.com>
Subject: Re: [r-inla] INLA never recovers true Theta values?
Ah, I missed that, sorry.
Those theta results perfectly match your true parameters; theta1=log(3) is just above 1, as is the posterior mean; and 0 is also in the credible interval for theta2.
To see that in the natural scale (range and variance), please use inla.spde.result()
If you use inla.spde2.pcmatern, the summary output will already be on the range&sigma scale, but I nla.spde.result() is consistent between the two models.
Finn
> On 25 Apr 2018, at 22:45, Munji Choi <munji...@gmail.com> wrote:
>
> Thank you for the answer.
> In my original post, I included summary output under "model results".
> I'll look forward your comments!
>
> Munji
>
>> On Wednesday, April 25, 2018 at 5:40:34 PM UTC-4, Finn Lindgren wrote:
>> Hi,
>>
>> Could you please supply the summary(spde.sim) output you get?
>>
>> The Matérn covariance parameters are not consistently identifiable from a single realisation, that’s always a possible explanation.
>>
>> I’d recommend using inla.mesh.2d instead of the old create.helper function (though they might possibly point to the same code). I don’t see anything wrong with your coordinate transformations, so that shouldn’t be the issue.
>> However, you can nowadays tell inla.mesh.2d to build the mesh on the sphere without pre-converting the coordinates, as long as you give it a SpatialPoints object with a longlat CRS (or whatever your data CRS is), and specify crs=inla.CRS(“sphere”) as parameter to inla.mesh.2d().
>> This feature is also supported by the inla.mesh.project functions.
>>
>> Using random independent locations as mesh seed points is rarely a good idea, so I wouldn’t do that without a specific reason. You can get a quasi-regular spherical mesh with inla.mesh.create(globe=...) for the whole globe if that might be useful. (See the help documentation)
>>
>> Finn
>>
>>> On 25 Apr 2018, at 19:46, Munji Choi <munji...@gmail.com> wrote:
>>>
>>> Hello
>>>
>>> I am still struggling with recovering the true theta values for simulated data.
>>> This is very simple SPDE model, in which I am just trying to fit normal linear regression with one covariate and spatial random effect. I generated the GRF values with 'inla.qsample'.
>>>
>>> The model results in correct gaussian error terms in the outcome model and correct fixed effect, but the two theta values are completely off from the true simulation values.
>>> I wonder whether this is because I constructed mesh with cartesian-converted values of long/lat.
>>>
>>> Below is my code and verbose output.
>>> Any advice or help would be highly appreciated. Thank you!
>>>
>>>
>>> ps ) I used real data of California census block groups shape files to obtain geographical locations of the centroid of each Block groups.
>>>
>>> --------------------
>>> BG.cent.xyz <- inla.mesh.map(BG.cent@coords, projection="longlat", inverse = TRUE)
>>>
>>> mesh.points <- spsample(CA, 2500, "regular")
>>> mesh.points <- inla.mesh.map(mesh.points@coords, projection="longlat", inverse = TRUE)
>>> mesh.points <- mesh.points[order(mesh.points[ ,1], mesh.points[ ,2], mesh.points[ ,3]), ]
>>>
>>> auto.mesh <- inla.mesh.create.helper(mesh.points, max.edge = 0.005*c(1, 5), cutoff=0.005)
>>>
>>> bg.D <-inla.spde.make.A(auto.mesh, loc=BG.cent.xyz)
>>>
>>> set.seed(1234)
>>> sigma2_y <- 0.5
>>> # fixed effect coefficient
>>> beta <- rnorm(1, mean=2, sd=1) # true value 0.7929
>>> # marginal variance of spatial random effect
>>> sigma2_s <- 1
>>>
>>> erange <- 0.3
>>> kappa <- sqrt(8) / erange
>>> theta2 <- log(kappa)
>>> tau2 <- 1/(4*pi*kappa^2*sigma2_s)
>>> tau0 <- sqrt(tau2)
>>> theta1 <- log(sqrt(tau2))
>>>
>>> spde <- inla.spde2.matern(auto.mesh,
>>> B.tau = cbind(log(tau0), -1, +1), B.kappa = cbind(log(kappa), 0, -1),
>>> theta.prior.mean = c(0, 0), theta.prior.prec = c(0.1, 1) )
>>>
>>> #spde <- inla.spde2.pcmatern(auto.mesh, prior.range = c(0.1, 0.1), prior.sigma=c(1, 0.5))
>>>
>>> Q.true <- inla.spde.precision(spde, c(log(3), 0))
>>>
>>> field.true <- as.numeric(inla.qsample(1, Q=Q.true, seed=50L))
>>>
>>> proj.BGcent <- inla.mesh.projector(auto.mesh, loc = BG.cent.xyz)
>>> field.BGcent <- inla.mesh.project(proj.BGcent, field=field.true)
>>>
>>> BGperCT <- BGperCT %>% mutate(BGmu=beta*ln_totalpop + field) # we've set alpha=0
>>>
>>> # generate Block group level data with BGmu
>>> set.seed(301)
>>> BGsimdata <- rep(NA, nrow(BGperCT))
>>> for(i in 1:nrow(BGperCT)){
>>> BGsimdata[i] <- rnorm(1, BGperCT$BGmu[i], sqrt(sigma2_y));
>>> }
>>>
>>> f.sim.spde <- y ~ -1 + ln_totalpop + f(i, model=spde)
>>>
>>> stk.sim.bg <- inla.stack(data=list(y=BGperCT$BGsimdata, nBG_inv=1), A=list(bg.D,1),
>>> effects=list(i=1:auto.mesh$n,
>>> data.frame(ln_totalpop=BGperCT$ln_totalpop)
>>> ), tag='dat.bg')
>>>
>>> spde.sim <- inla(f.sim.spde,
>>> control.comput=list(dic=TRUE), verbose =TRUE,
>>> data=inla.stack.data(stk.sim.bg),
>>> family="gaussian",
>>> control.predictor=list(A=inla.stack.A(stk.sim.bg), compute=TRUE),
>>> scale = (nBG_inv)^2,
>>> control.inla=list(correct=TRUE, correct.factor=10)
>>> )
>>> ---------------------
>>> Model result
>>> ---------------------
>>> Time used:
>>> Pre-processing Running inla Post-processing Total
>>> 1.0756 36.6679 1.1832 38.9267
>>>
>>> Fixed effects:
>>> mean sd 0.025quant 0.5quant 0.975quant mode kld
>>> ln_totalpop 0.7805 0.0077 0.7655 0.7805 0.7955 0.7805 0
>>>
>>> Random effects:
>>> Name Model
>>> i SPDE2 model
>>>
>>> Model hyperparameters:
>>> mean sd 0.025quant 0.5quant 0.975quant mode
>>> Precision for the Gaussian observations 2.0021 0.0192 1.9647 2.0021 2.0401 2.0019
>>> Theta1 for i 1.1228 0.3056 0.6122 1.0892 1.7961 0.9636
>>> Theta2 for i 0.1601 0.3173 -0.3692 0.1248 0.8606 -0.0070
>>>
>>> Expected number of effective parameters(std dev): 94.54(5.402)
>>> Number of equivalent replicates : 232.77
>>>
>>> Deviance Information Criterion (DIC) ...: 47275.17
>>> Effective number of parameters .........: 95.90
>>>
>>> Marginal log-Likelihood: -23744.41
>>> Posterior marginals for linear predictor and fitted values computed
>>>
>>> _________________
>>> True theta values
>>>
>>> > theta1;theta2
>>> [1] -3.509206
>>> [1] 2.243694
>>> _________________
>>>
>>>
>>> ----------------------------
>>> Verbose outcome
>>> ------------------------------
>>>
>>> hgid: 29c6a7f1b1ff date: Thu Jun 15 19:50:23 2017 +0800
>>> Report bugs to <he...@r-inla.org>
>>> Processing file [/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/Model.ini] max_threads=[4]
>>> inla_build...
>>> number of sections=[8]
>>> parse section=[0] name=[INLA.libR] type=[LIBR]
>>> inla_parse_libR...
>>> section[INLA.libR]
>>> R_HOME=[/Library/Frameworks/R.framework/Resources]
>>> parse section=[7] name=[INLA.Expert] type=[EXPERT]
>>> inla_parse_expert...
>>> section[INLA.Expert]
>>> disable.gaussian.check=[0]
>>> cpo.manual=[0]
>>> jp.Rfile=[(null)]
>>> jp.RData=NULL
>>> jp.func=[(null)]
>>> parse section=[1] name=[INLA.Model] type=[PROBLEM]
>>> inla_parse_problem...
>>> name=[INLA.Model]
>>> openmp.strategy=[default]
>>> store results in directory=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/results.files]
>>> output:
>>> cpo=[0]
>>> po=[0]
>>> dic=[1]
>>> kld=[1]
>>> mlik=[1]
>>> q=[0]
>>> graph=[0]
>>> gdensity=[0]
>>> hyperparameters=[1]
>>> summary=[1]
>>> return.marginals=[1]
>>> nquantiles=[3] [ 0.025 0.5 0.975 ]
>>> ncdf=[0] [ ]
>>> parse section=[3] name=[Predictor] type=[PREDICTOR]
>>> inla_parse_predictor ...
>>> section=[Predictor]
>>> dir=[predictor]
>>> PRIOR->name=[loggamma]
>>> hyperid=[53001|Predictor]
>>> PRIOR->from_theta=[function (x) <<NEWLINE>>exp(x)]
>>> PRIOR->to_theta = [function (x) <<NEWLINE>>log(x)]
>>> PRIOR->PARAMETERS=[1, 1e-05]
>>> initialise log_precision[12]
>>> fixed=[1]
>>> user.scale=[1]
>>> n=[4247]
>>> m=[22007]
>>> ndata=[22007]
>>> compute=[1]
>>> read offsets from file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52]
>>> read n=[52508] entries from file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52]
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 0/26254 (idx,y) = (0, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 1/26254 (idx,y) = (1, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 2/26254 (idx,y) = (2, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 3/26254 (idx,y) = (3, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 4/26254 (idx,y) = (4, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 5/26254 (idx,y) = (5, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 6/26254 (idx,y) = (6, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 7/26254 (idx,y) = (7, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 8/26254 (idx,y) = (8, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 9/26254 (idx,y) = (9, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 10/26254 (idx,y) = (10, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 11/26254 (idx,y) = (11, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 12/26254 (idx,y) = (12, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 13/26254 (idx,y) = (13, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 14/26254 (idx,y) = (14, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 15/26254 (idx,y) = (15, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 16/26254 (idx,y) = (16, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 17/26254 (idx,y) = (17, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 18/26254 (idx,y) = (18, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5077e414c52] 19/26254 (idx,y) = (19, 0)
>>> Aext=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50770f9dc3f]
>>> AextPrecision=[3.269e+06]
>>> output:
>>> summary=[1]
>>> return.marginals=[1]
>>> nquantiles=[3] [ 0.025 0.5 0.975 ]
>>> ncdf=[0] [ ]
>>> parse section=[2] name=[INLA.Data1] type=[DATA]
>>> inla_parse_data [section 1]...
>>> tag=[INLA.Data1]
>>> family=[GAUSSIAN]
>>> likelihood=[GAUSSIAN]
>>> file->name=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file507468d2779]
>>> file->name=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5075d1a9d1e]
>>> read n=[66021] entries from file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file507468d2779]
>>> 0/22007 (idx,a,y,d) = (0, 1, 9.84086, 1)
>>> 1/22007 (idx,a,y,d) = (1, 1, 8.70613, 1)
>>> 2/22007 (idx,a,y,d) = (2, 1, 10.1688, 1)
>>> 3/22007 (idx,a,y,d) = (3, 1, 10.3216, 1)
>>> 4/22007 (idx,a,y,d) = (4, 1, 9.77952, 1)
>>> 5/22007 (idx,a,y,d) = (5, 1, 10.2504, 1)
>>> 6/22007 (idx,a,y,d) = (6, 1, 10.9513, 1)
>>> 7/22007 (idx,a,y,d) = (7, 1, 9.40776, 1)
>>> 8/22007 (idx,a,y,d) = (8, 1, 9.98893, 1)
>>> 9/22007 (idx,a,y,d) = (9, 1, 10.3875, 1)
>>> 10/22007 (idx,a,y,d) = (10, 1, 11.6129, 1)
>>> 11/22007 (idx,a,y,d) = (11, 1, 10.489, 1)
>>> 12/22007 (idx,a,y,d) = (12, 1, 9.46471, 1)
>>> 13/22007 (idx,a,y,d) = (13, 1, 9.51823, 1)
>>> 14/22007 (idx,a,y,d) = (14, 1, 9.31658, 1)
>>> 15/22007 (idx,a,y,d) = (15, 1, 9.72785, 1)
>>> 16/22007 (idx,a,y,d) = (16, 1, 9.64929, 1)
>>> 17/22007 (idx,a,y,d) = (17, 1, 10.1083, 1)
>>> 18/22007 (idx,a,y,d) = (18, 1, 9.64805, 1)
>>> 19/22007 (idx,a,y,d) = (19, 1, 10.8802, 1)
>>> likelihood.variant=[0]
>>> initialise log_precision[4]
>>> fixed=[0]
>>> PRIOR->name=[loggamma]
>>> hyperid=[65001|INLA.Data1]
>>> PRIOR->from_theta=[function (x) <<NEWLINE>>exp(x)]
>>> PRIOR->to_theta = [function (x) <<NEWLINE>>log(x)]
>>> PRIOR->PARAMETERS=[1, 5e-05]
>>> Link model [IDENTITY]
>>> Link order [-1]
>>> Link variant [-1]
>>> Link ntheta [0]
>>> mix.use[0]
>>> parse section=[5] name=[i] type=[FFIELD]
>>> inla_parse_ffield...
>>> section=[i]
>>> dir=[random.effect00000001]
>>> model=[spde2]
>>> PRIOR0->name=[mvnorm]
>>> hyperid=[23001|i]
>>> PRIOR0->from_theta=[function (x) <<NEWLINE>>x]
>>> PRIOR0->to_theta = [function (x) <<NEWLINE>>x]
>>> PRIOR0->PARAMETERS0[0]=[0]
>>> PRIOR0->PARAMETERS0[1]=[0]
>>> PRIOR0->PARAMETERS0[2]=[0.1]
>>> PRIOR0->PARAMETERS0[3]=[0]
>>> PRIOR0->PARAMETERS0[4]=[0]
>>> PRIOR0->PARAMETERS0[5]=[1]
>>> correct=[-1]
>>> constr=[0]
>>> diagonal=[0]
>>> id.names=<not present>
>>> compute=[1]
>>> nrep=[1]
>>> ngroup=[1]
>>> read covariates from file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30]
>>> read n=[8494] entries from file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30]
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 0/4247 (idx,y) = (0, 78)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 1/4247 (idx,y) = (1, 79)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 2/4247 (idx,y) = (2, 80)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 3/4247 (idx,y) = (3, 81)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 4/4247 (idx,y) = (4, 82)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 5/4247 (idx,y) = (5, 83)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 6/4247 (idx,y) = (6, 84)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 7/4247 (idx,y) = (7, 85)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 8/4247 (idx,y) = (8, 86)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 9/4247 (idx,y) = (9, 87)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 10/4247 (idx,y) = (10, 88)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 11/4247 (idx,y) = (11, 89)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 12/4247 (idx,y) = (12, 90)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 13/4247 (idx,y) = (13, 91)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 14/4247 (idx,y) = (14, 92)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 15/4247 (idx,y) = (15, 93)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 16/4247 (idx,y) = (16, 94)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 17/4247 (idx,y) = (17, 95)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 18/4247 (idx,y) = (18, 96)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50771ad1a30] 19/4247 (idx,y) = (19, 97)
>>> spde2.prefix = [/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file5071b927f9e/file50713091aa8.]
>>> spde2.transform = [identity]
>>> ntheta (max) = [2]
>>> initialise theta[0]=[0]
>>> fixed[0]=[0]
>>> initialise theta[1]=[0]
>>> fixed[1]=[0]
>>> ntheta (used) = [2]
>>> computed/guessed rank-deficiency = [0]
>>> output:
>>> summary=[1]
>>> return.marginals=[1]
>>> nquantiles=[3] [ 0.025 0.5 0.975 ]
>>> ncdf=[0] [ ]
>>> section=[4] name=[ln_totalpop] type=[LINEAR]
>>> inla_parse_linear...
>>> section[ln_totalpop]
>>> dir=[fixed.effect00000001]
>>> file for covariates=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b]
>>> read n=[8494] entries from file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b]
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 0/4247 (idx,y) = (0, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 1/4247 (idx,y) = (1, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 2/4247 (idx,y) = (2, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 3/4247 (idx,y) = (3, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 4/4247 (idx,y) = (4, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 5/4247 (idx,y) = (5, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 6/4247 (idx,y) = (6, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 7/4247 (idx,y) = (7, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 8/4247 (idx,y) = (8, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 9/4247 (idx,y) = (9, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 10/4247 (idx,y) = (10, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 11/4247 (idx,y) = (11, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 12/4247 (idx,y) = (12, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 13/4247 (idx,y) = (13, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 14/4247 (idx,y) = (14, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 15/4247 (idx,y) = (15, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 16/4247 (idx,y) = (16, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 17/4247 (idx,y) = (17, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 18/4247 (idx,y) = (18, 0)
>>> file=[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/data.files/file50723eae60b] 19/4247 (idx,y) = (19, 0)
>>> prior mean=[0]
>>> prior precision=[0.001]
>>> compute=[1]
>>> output:
>>> summary=[1]
>>> return.marginals=[1]
>>> nquantiles=[3] [ 0.025 0.5 0.975 ]
>>> ncdf=[0] [ ]
>>> Index table: number of entries[4], total length[27008]
>>> tag start-index length
>>> APredictor 0 22007
>>> Predictor 22007 4247
>>> i 26254 753
>>> ln_totalpop 27007 1
>>> parse section=[6] name=[INLA.Parameters] type=[INLA]
>>> inla_parse_INLA...
>>> section[INLA.Parameters]
>>> lincomb.derived.only = [Yes]
>>> lincomb.derived.correlation.matrix = [No]
>>> global_node.factor = 2.000
>>> global_node.degree = 2147483647
>>> reordering = -1
>>> Contents of ai_param 0x7fd0357aeb30
>>> Optimiser: DEFAULT METHOD
>>> Option for domin-BFGS: epsx = 0.005
>>> Option for domin-BFGS: epsf = 1e-05 (rounding error)
>>> Option for domin-BFGS: epsg = 0.005
>>> Option for GSL-BFGS2: tol = 0.1
>>> Option for GSL-BFGS2: step_size = 1
>>> Option for GSL-BFGS2: epsx = 0.005
>>> Option for GSL-BFGS2: epsf = 0.000353553
>>> Option for GSL-BFGS2: epsg = 0.005
>>> Restart: 0
>>> Mode known: No
>>> Gaussian approximation:
>>> abserr_func = 0.0005
>>> abserr_step = 0.0005
>>> optpar_fp = 0
>>> optpar_nr_step_factor = -0.1
>>> Gaussian data: Yes
>>> Strategy: Use a mean-skew corrected Gaussian by fitting a Skew-Normal
>>> Fast mode: On
>>> Use linear approximation to log(|Q +c|)? Yes
>>> Method: Compute the derivative exact
>>> Parameters for improved approximations
>>> Number of points evaluate: 9
>>> Step length to compute derivatives numerically: 0.000100002
>>> Stencil to compute derivatives numerically: 5
>>> Cutoff value to construct local neigborhood: 0.0001
>>> Log calculations: On
>>> Log calculated marginal for the hyperparameters: On
>>> Integration strategy: Automatic (GRID for dim(theta)=1 and 2 and otherwise CCD)
>>> f0 (CCD only): 1.100000
>>> dz (GRID only): 0.750000
>>> Adjust weights (GRID only): On
>>> Difference in log-density limit (GRID only): 6.000000
>>> Skip configurations with (presumed) small density (GRID only): On
>>> Gradient is computed using Central difference with step-length 0.010000
>>> Hessian is computed using Central difference with step-length 0.100000
>>> Hessian matrix is forced to be a diagonal matrix? [No]
>>> Compute effective number of parameters? [Yes]
>>> Perform a Monte Carlo error-test? [No]
>>> Interpolator [Auto]
>>> CPO required diff in log-density [3]
>>> Stupid search mode:
>>> Status [On]
>>> Max iter [1000]
>>> Factor [1.05]
>>> Numerical integration of hyperparameters:
>>> Maximum number of function evaluations [100000]
>>> Relative error ....................... [1e-05]
>>> Absolute error ....................... [1e-06]
>>> To stabilise the numerical optimisation:
>>> Minimum value of the -Hessian [-inf]
>>> CPO manual calculation[No]
>>> Laplace-correction is Enabled with correction factor[10.0000]
>>> strategy = [simplified.laplace]
>>> verbose = [FALSE]
>>>
>>> inla_build: check for unused entries in[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/Model.ini]
>>> inla_INLA...
>>> Strategy = [DEFAULT]
>>> Size is [27008]
>>> Chose OpenMP-strategy [LARGE]
>>> Chose density-strategy [HIGH]
>>> Size of graph=[27008] constraints=[0]
>>> Found optimal reordering=[amdc] nnz(L)=[294780] and use_global_nodes(user)=[no]
>>> List of hyperparameters:
>>> theta[0] = [Log precision for the Gaussian observations]
>>> theta[1] = [Theta1 for i]
>>> theta[2] = [Theta2 for i]
>>> Optimise using DEFAULT METHOD
>>> max.logdens= -274954.453470 fn= 1 theta= 4.000000 -0.010000 0.000000 range=[-0.728 14.398]
>>> max.logdens= -274920.678137 fn= 2 theta= 4.000000 0.000000 -0.010000 range=[-0.735 14.400]
>>> max.logdens= -272086.366128 fn= 5 theta= 3.990000 0.000000 0.000000 range=[-0.731 14.398]
>>> max.logdens= -97586.285270 fn= 7 theta= 3.000035 0.006017 -0.005840 range=[-0.357 14.359]
>>> max.logdens= -97579.363328 fn= 9 theta= 3.000035 0.006017 -0.015840 range=[-0.360 14.360]
>>> max.logdens= -96603.486375 fn= 12 theta= 2.990035 0.006017 -0.005840 range=[-0.353 14.359]
>>> max.logdens= -86291.751128 fn= 14 theta= -5.999648 0.060173 -0.058399 range=[0.544 12.924]
>>> max.logdens= -86291.740039 fn= 17 theta= -5.999648 0.060173 -0.048399 range=[0.569 12.915]
>>> max.logdens= -86181.920049 fn= 18 theta= -5.989648 0.060173 -0.058399 range=[0.549 12.929]
>>> Iter=1 |grad|=1.1e+04 |x-x.old|=5.77 |f-f.old|=1.89e+05
>>> max.logdens= -86160.888364 fn= 21 theta= -5.987466 0.796310 -0.735122 range=[-0.003 13.935]
>>> max.logdens= -86160.828985 fn= 23 theta= -5.987466 0.786310 -0.735122 range=[-0.014 13.929]
>>> max.logdens= -86051.060155 fn= 24 theta= -5.977466 0.796310 -0.735122 range=[0.003 13.938]
>>> max.logdens= -85998.541939 fn= 28 theta= -5.951611 2.962863 -2.726813 range=[0.000 14.478]
>>> max.logdens= -85996.838820 fn= 29 theta= -5.951611 2.952863 -2.726813 range=[0.000 14.478]
>>> max.logdens= -85889.502076 fn= 31 theta= -5.941611 2.962863 -2.726813 range=[0.000 14.478]
>>> max.logdens= -85873.830602 fn= 39 theta= -5.948300 2.558717 -2.355285 range=[0.002 14.444]
>>> Iter=2 |grad|=1.09e+04 |x-x.old|=1.96 |f-f.old|=309
>>> max.logdens= -85365.860242 fn= 42 theta= -5.902095 2.542685 -2.340724 range=[0.002 14.442]
>>> max.logdens= -85364.654562 fn= 44 theta= -5.902095 2.532685 -2.340724 range=[0.002 14.443]
>>> max.logdens= -85256.584570 fn= 46 theta= -5.892095 2.542685 -2.340724 range=[0.002 14.442]
>>> max.logdens= -79812.602742 fn= 49 theta= -5.396258 2.398396 -2.209668 range=[0.006 14.425]
>>> max.logdens= -79811.393755 fn= 51 theta= -5.396258 2.388396 -2.209668 range=[0.006 14.425]
>>> max.logdens= -79703.426204 fn= 53 theta= -5.386258 2.398396 -2.209668 range=[0.006 14.424]
>>> max.logdens= -32053.310812 fn= 56 theta= -0.843717 1.099792 -1.030164 range=[0.152 14.371]
>>> max.logdens= -32052.378659 fn= 58 theta= -0.843717 1.089792 -1.030164 range=[0.156 14.370]
>>> max.logdens= -32052.369424 fn= 59 theta= -0.843717 1.099792 -1.020164 range=[0.153 14.370]
>>> max.logdens= -31967.460869 fn= 60 theta= -0.833717 1.099792 -1.030164 range=[0.150 14.371]
>>> max.logdens= -28622.923075 fn= 64 theta= -0.418497 0.978499 -0.919996 range=[0.116 14.370]
>>> max.logdens= -28622.062953 fn= 65 theta= -0.418497 0.978499 -0.909996 range=[0.116 14.369]
>>> max.logdens= -28549.581689 fn= 68 theta= -0.408497 0.978499 -0.919996 range=[0.113 14.370]
>>> max.logdens= -26541.291129 fn= 71 theta= -0.111633 0.890967 -0.840491 range=[0.080 14.369]
>>> max.logdens= -26540.569409 fn= 73 theta= -0.111633 0.880967 -0.840491 range=[0.085 14.368]
>>> max.logdens= -26540.517233 fn= 74 theta= -0.111633 0.890967 -0.830491 range=[0.079 14.368]
>>> max.logdens= -26480.921759 fn= 75 theta= -0.101633 0.890967 -0.840491 range=[0.077 14.369]
>>> max.logdens= -25314.683507 fn= 78 theta= 0.110811 0.827515 -0.782859 range=[0.050 14.369]
>>> max.logdens= -25314.056246 fn= 79 theta= 0.110811 0.817515 -0.782859 range=[0.055 14.368]
>>> max.logdens= -25313.991238 fn= 81 theta= 0.110811 0.827515 -0.772859 range=[0.049 14.368]
>>> max.logdens= -25266.542412 fn= 82 theta= 0.120811 0.827515 -0.782859 range=[0.047 14.369]
>>> max.logdens= -24542.007189 fn= 85 theta= 0.290711 0.776199 -0.736249 range=[0.023 14.368]
>>> max.logdens= -24541.472393 fn= 87 theta= 0.290711 0.766199 -0.736249 range=[0.029 14.367]
>>> max.logdens= -24505.954770 fn= 88 theta= 0.300711 0.776199 -0.736249 range=[0.020 14.368]
>>> max.logdens= -24027.737986 fn= 92 theta= 0.461617 0.727449 -0.691970 range=[-0.003 14.368]
>>> max.logdens= -24027.307232 fn= 94 theta= 0.461617 0.717449 -0.691970 range=[0.003 14.367]
>>> max.logdens= -24027.223944 fn= 95 theta= 0.461617 0.727449 -0.681970 range=[-0.004 14.367]
>>> max.logdens= -24005.370349 fn= 96 theta= 0.471617 0.727449 -0.691970 range=[-0.006 14.368]
>>> max.logdens= -23774.484028 fn= 99 theta= 0.623977 0.681136 -0.649904 range=[-0.029 14.367]
>>> max.logdens= -23774.172025 fn= 100 theta= 0.623977 0.671136 -0.649904 range=[-0.023 14.366]
>>> max.logdens= -23767.472850 fn= 102 theta= 0.633977 0.681136 -0.649904 range=[-0.032 14.367]
>>> Iter=3 |grad|=754 |x-x.old|=4.07 |f-f.old|=6.22e+04
>>> max.logdens= -23766.949962 fn= 107 theta= 0.624380 0.550274 -0.461636 range=[0.051 14.349]
>>> max.logdens= -23766.946144 fn= 109 theta= 0.624380 0.540274 -0.461636 range=[0.058 14.349]
>>> max.logdens= -23766.838532 fn= 110 theta= 0.624380 0.550274 -0.451636 range=[0.051 14.349]
>>> max.logdens= -23760.068624 fn= 111 theta= 0.634380 0.550274 -0.461636 range=[0.048 14.350]
>>> max.logdens= -23759.790200 fn= 118 theta= 0.634455 0.525983 -0.426690 range=[0.065 14.347]
>>> Iter=4 |grad|=737 |x-x.old|=0.157 |f-f.old|=7.84
>>> max.logdens= -23753.293341 fn= 121 theta= 0.645755 0.529896 -0.431912 range=[0.059 14.348]
>>> max.logdens= -23753.240349 fn= 122 theta= 0.645755 0.529896 -0.421912 range=[0.059 14.347]
>>> max.logdens= -23748.644528 fn= 125 theta= 0.655755 0.529896 -0.431912 range=[0.055 14.348]
>>> max.logdens= -23740.683060 fn= 128 theta= 0.693844 0.538731 -0.443703 range=[0.036 14.350]
>>> max.logdens= -23740.624502 fn= 130 theta= 0.693844 0.538731 -0.433703 range=[0.036 14.349]
>>> Iter=5 |grad|=8.82 |x-x.old|=0.0419 |f-f.old|=26
>>> max.logdens= -23739.605072 fn= 136 theta= 0.693964 0.737085 -0.133476 range=[-0.067 14.345]
>>> max.logdens= -23739.527092 fn= 137 theta= 0.693964 0.737085 -0.143476 range=[-0.069 14.345]
>>> max.logdens= -23739.499540 fn= 141 theta= 0.693964 0.747085 -0.133476 range=[-0.075 14.345]
>>> max.logdens= -23739.483234 fn= 149 theta= 0.693945 0.716379 -0.181501 range=[-0.062 14.346]
>>> Iter=6 |grad|=11.5 |x-x.old|=0.18 |f-f.old|=1.11
>>> max.logdens= -23739.097277 fn= 151 theta= 0.692609 0.850039 -0.118933 range=[-0.147 14.349]
>>> max.logdens= -23739.093047 fn= 153 theta= 0.692609 0.840039 -0.118933 range=[-0.140 14.348]
>>> max.logdens= -23739.082068 fn= 154 theta= 0.692609 0.850039 -0.108933 range=[-0.145 14.348]
>>> Iter=7 |grad|=17.5 |x-x.old|=0.0905 |f-f.old|=0.478
>>> max.logdens= -23739.071543 fn= 161 theta= 0.695342 0.857149 -0.105494 range=[-0.150 14.349]
>>> max.logdens= -23739.065557 fn= 170 theta= 0.694200 0.854176 -0.106931 range=[-0.148 14.348]
>>> Iter=8 |grad|=2.52 |x-x.old|=0.00281(pass) |f-f.old|=0.0143
>>> Number of function evaluations = 172
>>> Compute the Hessian using central differences and step_size[0.1]. Matrix-type [dense]
>>> max.logdens= -23739.043039 fn= 182 theta= 0.694200 0.954176 -0.016931 range=[-0.199 14.349]
>>>
>>> Mode not sufficient accurate; switch to a stupid local search strategy.
>>>
>>> 10948.867523 -35.367498 35.166208
>>> -35.367498 113.212621 -104.629919
>>> 35.166208 -104.629919 105.929121
>>> Eigenvectors of the Hessian
>>> 0.999989 -0.004646 -0.000066
>>> -0.003296 -0.719303 0.694688
>>> 0.003275 0.694681 0.719311
>>> Eigenvalues of the Hessian
>>> 10949.099246
>>> 214.032473
>>> 4.877546
>>> StDev/Correlation matrix (scaled inverse Hessian)
>>> 0.009562 0.001926 -0.007805
>>> 0.318369 0.955388
>>> 0.329142
>>> Compute corrected stdev for theta[0]: negative 1.002389 positive 0.998277
>>> Compute corrected stdev for theta[1]: negative 0.926966 positive 1.091919
>>> Compute corrected stdev for theta[2]: negative 0.596360 positive 1.278915
>>> config 0/15=[ -1.10 -1.02 -0.66] log(rel.dens)=-1.58, [2] accept, compute, 0.36s
>>> config 1/15=[ 1.10 -1.02 -0.66] log(rel.dens)=-1.57, [3] accept, compute, 0.35s
>>> config 2/15=[ 0.00 0.00 0.00] log(rel.dens)=-0.00, [0] accept, compute, 0.36s
>>> config 3/15=[ -0.00 -1.77 0.00] log(rel.dens)=-1.86, [1] accept, compute, 0.37s
>>> config 4/15=[ 1.90 -0.00 0.00] log(rel.dens)=-1.81, [0] accept, compute, 0.37s
>>> config 5/15=[ -1.10 1.20 1.41] log(rel.dens)=-1.90, [2] accept, compute, 0.38s
>>> config 6/15=[ 0.00 -0.00 2.44] log(rel.dens)=-1.63, [1] accept, compute, 0.38s
>>> config 7/15=[ 1.10 1.20 1.41] log(rel.dens)=-1.89, [3] accept, compute, 0.38s
>>> config 8/15=[ -1.91 0.00 -0.00] log(rel.dens)=-1.82, [0] accept, compute, 0.36s
>>> config 9/15=[ -1.10 1.20 -0.66] log(rel.dens)=-1.40, [2] accept, compute, 0.36s
>>> config 10/15=[ 0.00 0.00 -1.14] log(rel.dens)=-1.11, [1] accept, compute, 0.36s
>>> config 11/15=[ 1.10 1.20 -0.66] log(rel.dens)=-1.39, [3] accept, compute, 0.35s
>>> config 12/15=[ 1.10 -1.02 1.41] log(rel.dens)=-1.98, [2] accept, compute, 0.34s
>>> config 13/15=[ -1.10 -1.02 1.41] log(rel.dens)=-1.99, [1] accept, compute, 0.34s
>>> config 14/15=[ 0.00 2.08 -0.00] log(rel.dens)=-1.83, [0] accept, compute, 0.35s
>>> Combine the densities with relative weights:
>>> config 0/15=[ 0.00 0.00 0.00] weight = 1.000 neff = 95.07
>>> config 1/15=[ 1.90 -0.00 0.00] weight = 0.341 neff = 95.59
>>> config 2/15=[ -1.91 0.00 -0.00] weight = 0.340 neff = 94.55
>>> config 3/15=[ 0.00 2.08 -0.00] weight = 0.333 neff = 84.05
>>> config 4/15=[ -0.00 -1.77 0.00] weight = 0.325 neff = 105.12
>>> config 5/15=[ 0.00 -0.00 2.44] weight = 0.408 neff = 93.65
>>> config 6/15=[ 0.00 0.00 -1.14] weight = 0.691 neff = 95.63
>>> config 7/15=[ -1.10 -1.02 1.41] weight = 0.286 neff = 99.66
>>> config 8/15=[ -1.10 -1.02 -0.66] weight = 0.432 neff = 100.84
>>> config 9/15=[ -1.10 1.20 1.41] weight = 0.314 neff = 87.54
>>> config 10/15=[ -1.10 1.20 -0.66] weight = 0.517 neff = 88.64
>>> config 11/15=[ 1.10 -1.02 1.41] weight = 0.287 neff = 100.28
>>> config 12/15=[ 1.10 -1.02 -0.66] weight = 0.434 neff = 101.46
>>> config 13/15=[ 1.10 1.20 1.41] weight = 0.315 neff = 88.11
>>> config 14/15=[ 1.10 1.20 -0.66] weight = 0.519 neff = 89.21
>>> Done.
>>> Expected effective number of parameters: 94.543(5.403), eqv.#replicates: 232.773
>>> DIC:
>>> Mean of Deviance................. 47179.3
>>> Deviance at Mean................. 47083.4
>>> Effective number of parameters... 95.9018
>>> DIC.............................. 47275.2
>>> Marginal likelihood: Integration -23744.283874 Gaussian-approx -23744.412943
>>> Compute the marginal for each of the 3 hyperparameters
>>> Interpolation method: Auto
>>> Compute the marginal for theta[0] to theta[2] using numerical integration...
>>> Compute the marginal for theta[0] to theta[2] using numerical integration... Done.
>>> Compute the marginal for the hyperparameters... done.
>>> Store results in directory[/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/results.files]
>>>
>>> Wall-clock time used on [/var/folders/dp/xjtz25ld6vn9sjzdh7mjkg45pvp7bw/T//Rtmpti6Toq/file5073ab5155b/Model.ini]
>>> Preparations : 0.050 seconds
>>> Approx inference: 34.842 seconds [2.6|0.0|85.2|8.2|4.0]%
>>> Output : 1.690 seconds
>>> ---------------------------------
>>> Total : 36.582 seconds
>>>
>>> --
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