Description Usage Arguments Details Value Note Author(s) References See Also Examples

This function estimates taxonomic compositions of algal communities
based on biomarker field data. More precisely, it estimates the probability distributions of a sample composition
based on an **input ratio matrix**, `A`

that contains
prior estimates of biomarker ratios in different taxa, and an **input data matrix**,
`B`

, containing biomarker ratios measured in field samples.

Probability distributions are estimated based on an adaptive metropolis
MCMC method, function `modMCMC`

from package `FME`

.

1 2 3 4 |

`A ` |
input (group) ratio matrix; can be a matrix or a dataframe |

`B ` |
input (field) data matrix; can be a matrix or a dataframe |

`Wa ` |
elementwise weight matrix for A, with the same dimensions as A.
is minimized |

`Wb ` |
elementwise weight matrix for B, with the same dimensions as B.
is minimized |

`jmpType ` |
one of "default", "estimate" or "covar"; if default, jmpA and jmpX are the jump lengths. if jmpA or jmpX is a number, then this is the jump length for all elements of A resp. X. If "estimate", the initial jump length is proportional to an estimated covariance matrix for the tlsce fit for A and the lsei fit of X (or Q if Xratios). jmpA and jmpX are then used as rescaling factors for the jump covariance matrix. If "covar", a jump covariance matrix with the correct dimensions, obtained from a previous run, is given as parameter jmpCovar. Covariances can be calculated from the result. |

`jmpA ` |
jump length of A: a number or a matrix with dim(A); see details jmpType |

`jmpX ` |
jump lenth of X: a number or a matrix with dim(X); see details jmpType |

`jmpCovar ` |
only if jmpType="covar", the covariance matrix to initiate the jumps - see details jmpType |

`initX ` |
composition matrix used to start the markov chain: default the tlsce solution of Ax=B |

`initA ` |
ratio matrix used to start the markov chain: default the input ratio matrix A |

`priorA ` |
"normal" (gaussian - default) or "uniform". |

`minA ` |
minimum values for A |

`maxA ` |
maximum values for A |

`var0 ` |
initial model variance; if 'NULL', then the model variance of tlsce(A,B,...) is used |

`wvar0 ` |
relative weight of the initial model variance (see modMCMC). Ideally this would be 0 (initial model variance is not taken into account); because wvar0=0 is a special case in modMCMC() (fixed model variance), the default value is set to a small number (wvar0=1e-6) |

`Xratios ` |
does the composition matrix contain ratios (TRUE) or estimated biomass concentrations (TRUE) per sample? In the latter case, B must contain the pigment concentrations as measured in the samples (not rescaled) |

`verbose ` |
when |

`... ` |
arguments to pass on to modMCMC() |

The function `bce1`

searches probability distributions for all
elements of a taxonomical composition matrix `X`

and a ratio
matrix `A`

for which:

*A%*%X ~= B*

It does this by returning `niter`

samples for A and X, organized
in three-dimensional arrays. The input
data matrix `B`

and ratio matrix `A`

should be
in the following formats, with the relative concentrations per
biomarker organized in columns:

data matrix B:

sample1 | sample2 | sample3 | sample4 | |

marker1 | 0.14 | 0.005 | 0.35 | 0.033 |

marker2 | 0.15 | 0.004 | 0.36 | 0.034 |

marker3 | 0.13 | 0.004 | 0.31 | 0.030 |

marker4 | 0.13 | 0.005 | 0.33 | 0.031 |

marker5 | 0.14 | 0.008 | 0.33 | 0.036 |

marker6 | 0.11 | 0.082 | 0.34 | 0.044 |

and ratio matrix A:

species1 | species2 | species3 | species4 | |

marker1 | 0.27 | 0.13 | 0.35 | 0.076 |

marker2 | 0.084 | 0 | 0.5 | 0.24 |

marker3 | 0.195 | 0.3 | 0 | 0.1 |

marker4 | 0.06 | 0 | 0 | 0 |

marker5 | 0 | 0 | 0 | 0 |

marker6 | 0 | 0 | 0 | 0 |

An object of class bce and _modMCMC_ (returned by the function modMCMC). This object has methods for the generic functions 'summary', 'plot', 'pairs'- see ?modMCMC. It is distinguished from other modMCMC objects by 3 extra attributes that allow to extract matrices A and X from the mcmc result: "dim_A" (dimensions of A), "A_not_null" (which elements of A are not zero and thus included in the mcmc) and Xratios (whether X was rescaled, yes or no).

Producing sensible output:

Markov Chain Monte Carlo simulations are not as straightforward as one might wish; several preliminary runs might be necessary to determine the desired number of iterations, burn-in length and jump length. For all estimated values of Rat and X, their trace (evolution of the values over all iterations) has to display random behaviour; no obvious trends should appear. A few parameters can be tuned to obtain such behaviour:

**jump length**The jump length determines how big the jumps are for each step in the random walk. A longer jump length will make you jump around faster in the parameter space, but acceptance of new points can get very low. Smaller jump lengths increase the acceptance rate, but the algorithm will move too slowly, and a lot more runs will be needed to scan the whole parameter space. A good way to find a good jump length, is look at the number of points accepted. If the output is saved under the name`MCMC`

, you can find the number of accepted points under`MCMC$naccepted`

. It is also given if you run the model with`verbose=TRUE`

(default). This value should be somewhere between 5% and 40%. For long runs, 5 % can be acceptable, for short runs, you will prefer a higher acceptance in order to have enough different points. 20% accepted is usually a good number. Do some preliminary runs with`niter=1000-10000`

and tune the jump length parameters`jmpRat`

and`jmpX`

. You can set different jump lengths for each column of the ratio matrix, or 1 jump length for the whole ratio matrix, and 1 jump length for the composition matrix. Decreasing the jump lengths will generally increase the acceptance rate and vice versa. Also the mixing rate (the speed with which accepted points change their values) will be influenced. You want this mixing rate to be as high as possible, whilst maintaining enough accepted points.**burninlength**The program uses the solution of lsei using the original ratio matrix as starting values for the MCMC. This might in some cases be far from the optimal solution, and the MCMC algorithm will start with moving towards this optimal solution. This is called a burn-in. When there is a slow mixing rate, this can take a considerable number of cycles. As it can influence the averages and standard deviations, you might want to remove it from the mcmc objects. By defining a burnin length, the first '`burninlength`

' cycles will not be written to the output. Look at some plots to determine if you need to specify a burnin length.**niter**the number of iterations: start with 10000 runs or less; check the output and estimate how many runs you will need to get a random pattern in the output.

Karel Van den Meersche <[email protected]>, Karline Soetaert <[email protected]>.

Van den Meersche, K., K. Soetaert and J.J. Middelburg (2008) *A
Bayesian compositional estimator for microbial taxonomy
based on biomarkers*, Limnology and Oceanography Methods 6, 190-199

`summary.bce`

, `plot.bce`

,
`export.bce`

, `pairs.bce`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 | ```
##====================================
# example using bceInput data
# !!! should be weighted to correspond better to example of BCE!!!
A <- t(bceInput$Rat)
B <- t(bceInput$Dat)
result <- bce1(A,B,niter=1000)
## the number of accepted runs is zero;
## try different starting values
result <- bce1(A,B,niter=1000,initX=matrix(1/ncol(A),ncol(A),ncol(B)))
## number of accepted runs is still low;
## smaller jumps
result <- bce1(A,B,niter=1000,initX=matrix(1/ncol(A),ncol(A),ncol(B)),jmpA=.01,jmpX=.01)
Sum <-summary(result)
## did the algorithm converge?
plot(result$SS,type="l")
## no
## more runs, using the output of previous run as input.
result <- bce1(A,B,niter=1e4,jmpA=.01,jmpX=.01,updatecov=1e3,
initX=Sum$lastX,initA=Sum$lastA,
jmpCovar=Sum$covar*2.4^2/ncol(result$pars),
)
Sum <-summary(result)
## we inspect the output:
plot(result$SS,type="l")
plot(result,ask=TRUE)
## looks already pretty good; to get a better result, repeat one more
## time with a longer run. Uncomment the following paragraph and run.
## go get some coffee, this might take a while (~30s).
## result <- bce1(A,B,niter=1e5,jmpA=.01,jmpX=.01,updatecov=1e3,
## outputlength=1e3,burninlength=.35e5,
## initX=Sum$lastX,initA=Sum$lastA,
## jmpCovar=Sum$covar*2.4^2/ncol(result$pars),
## )
## Sum <-summary(result)
## plot(result$SS,type="l")
## plot(result,ask=TRUE)
# show results as mean with ranges
print(Sum$meanX)
# plot estimated means and ranges (lbX=lower, ubX=upper bound)
xlim <- range(c(Sum$lbX,Sum$ubX))
# first the mean
dotchart(x=t(Sum$meanX),xlim=xlim,
main="Taxonomic composition",
sub="using bce",pch=16)
# then ranges
nr <- nrow(Sum$meanX)
nc <- ncol(Sum$meanX)
for (i in 1:nr)
{ip <-(nr-i)*(nc+2)+1
cc <- ip : (ip+nc-1)
segments(t(Sum$lbX[i,]),cc,t(Sum$ubX[i,]),cc)
}
``` |

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