Specification and validation of POUMM/PMM settings.
specifyPOUMM(z = NULL, tree = NULL, zMin = 10, zMean = 0, zMax = 10, zVar = 4, zSD = sqrt(zVar), tMin = 0.1, tMean = 2, tMax = 10, parMapping = NULL, parLower = NULL, parUpper = NULL, g0Prior = NULL, parInitML = NULL, control = NULL, parPriorMCMC = NULL, parInitMCMC = NULL, parScaleMCMC = NULL, nSamplesMCMC = 1e+05, nAdaptMCMC = nSamplesMCMC, thinMCMC = 100, accRateMCMC = 0.01, gammaMCMC = 0.50001, nChainsMCMC = 3, samplePriorMCMC = TRUE, parallelMCMC = FALSE, validateSpec = TRUE) specifyPOUMM_ATS(z = NULL, tree = NULL, zMin = 10, zMean = 0, zMax = 10, zVar = 4, zSD = sqrt(zVar), tMin = 0.1, tMean = 2, tMax = 10, parMapping = NULL, parLower = NULL, parUpper = NULL, g0Prior = NULL, parInitML = NULL, control = NULL, parPriorMCMC = NULL, parInitMCMC = NULL, parScaleMCMC = NULL, nSamplesMCMC = 1e+05, nAdaptMCMC = nSamplesMCMC, thinMCMC = 100, accRateMCMC = 0.01, gammaMCMC = 0.50001, nChainsMCMC = 3, samplePriorMCMC = TRUE, parallelMCMC = FALSE, sigmaeFixed = 0) specifyPOUMM_ATSG0(z = NULL, tree = NULL, zMin = 10, zMean = 0, zMax = 10, zVar = 4, zSD = sqrt(zVar), tMin = 0.1, tMean = 2, tMax = 10, parMapping = NULL, parLower = NULL, parUpper = NULL, g0Prior = NULL, parInitML = NULL, control = NULL, parPriorMCMC = NULL, parInitMCMC = NULL, parScaleMCMC = NULL, nSamplesMCMC = 1e+05, nAdaptMCMC = nSamplesMCMC, thinMCMC = 100, accRateMCMC = 0.01, gammaMCMC = 0.50001, nChainsMCMC = 3, samplePriorMCMC = TRUE, parallelMCMC = FALSE, sigmaeFixed = 0) specifyPOUMM_ATSSeG0(z = NULL, tree = NULL, zMin = 10, zMean = 0, zMax = 10, zVar = 4, zSD = sqrt(zVar), tMin = 0.1, tMean = 2, tMax = 10, parMapping = NULL, parLower = NULL, parUpper = NULL, g0Prior = NULL, parInitML = NULL, control = NULL, parPriorMCMC = NULL, parInitMCMC = NULL, parScaleMCMC = NULL, nSamplesMCMC = 1e+05, nAdaptMCMC = nSamplesMCMC, thinMCMC = 100, accRateMCMC = 0.01, gammaMCMC = 0.50001, nChainsMCMC = 3, samplePriorMCMC = TRUE, parallelMCMC = FALSE) specifyPMM(z = NULL, tree = NULL, zMin = 10, zMean = 0, zMax = 10, zVar = 4, zSD = sqrt(zVar), tMin = 0.1, tMean = 2, tMax = 10, parMapping = NULL, parLower = NULL, parUpper = NULL, g0Prior = NULL, parInitML = NULL, control = NULL, parPriorMCMC = NULL, parInitMCMC = NULL, parScaleMCMC = NULL, nSamplesMCMC = 1e+05, nAdaptMCMC = nSamplesMCMC, thinMCMC = 100, accRateMCMC = 0.01, gammaMCMC = 0.50001, nChainsMCMC = 3, samplePriorMCMC = TRUE, parallelMCMC = FALSE) specifyPMM_SSeG0(z = NULL, tree = NULL, zMin = 10, zMean = 0, zMax = 10, zVar = 4, zSD = sqrt(zVar), tMin = 0.1, tMean = 2, tMax = 10, parMapping = NULL, parLower = NULL, parUpper = NULL, g0Prior = NULL, parInitML = NULL, control = NULL, parPriorMCMC = NULL, parInitMCMC = NULL, parScaleMCMC = NULL, nSamplesMCMC = 1e+05, nAdaptMCMC = nSamplesMCMC, thinMCMC = 100, accRateMCMC = 0.01, gammaMCMC = 0.50001, nChainsMCMC = 3, samplePriorMCMC = TRUE, parallelMCMC = FALSE) specifyPOUMM_ATH2tMeanSe(z = NULL, tree = NULL, zMin = 10, zMean = 0, zMax = 10, zVar = 4, zSD = sqrt(zVar), tMin = 0.1, tMean = 2, tMax = 10, parMapping = NULL, parLower = NULL, parUpper = NULL, g0Prior = NULL, parInitML = NULL, control = NULL, parPriorMCMC = NULL, parInitMCMC = NULL, parScaleMCMC = NULL, nSamplesMCMC = 1e+05, nAdaptMCMC = nSamplesMCMC, thinMCMC = 100, accRateMCMC = 0.01, gammaMCMC = 0.50001, nChainsMCMC = 3, samplePriorMCMC = TRUE, parallelMCMC = FALSE) specifyPOUMM_ATH2tMeanSeG0(z = NULL, tree = NULL, zMin = 10, zMean = 0, zMax = 10, zVar = 4, zSD = sqrt(zVar), tMin = 0.1, tMean = 2, tMax = 10, parMapping = NULL, parLower = NULL, parUpper = NULL, g0Prior = NULL, parInitML = NULL, control = NULL, parPriorMCMC = NULL, parInitMCMC = NULL, parScaleMCMC = NULL, nSamplesMCMC = 1e+05, nAdaptMCMC = nSamplesMCMC, thinMCMC = 100, accRateMCMC = 0.01, gammaMCMC = 0.50001, nChainsMCMC = 3, samplePriorMCMC = TRUE, parallelMCMC = FALSE) specifyPMM_H2tMeanSe(z = NULL, tree = NULL, zMin = 10, zMean = 0, zMax = 10, zVar = 4, zSD = sqrt(zVar), tMin = 0.1, tMean = 2, tMax = 10, parMapping = NULL, parLower = NULL, parUpper = NULL, g0Prior = NULL, parInitML = NULL, control = NULL, parPriorMCMC = NULL, parInitMCMC = NULL, parScaleMCMC = NULL, nSamplesMCMC = 1e+05, nAdaptMCMC = nSamplesMCMC, thinMCMC = 100, accRateMCMC = 0.01, gammaMCMC = 0.50001, nChainsMCMC = 3, samplePriorMCMC = TRUE, parallelMCMC = FALSE) specifyPMM_H2tMeanSeG0(z = NULL, tree = NULL, zMin = 10, zMean = 0, zMax = 10, zVar = 4, zSD = sqrt(zVar), tMin = 0.1, tMean = 2, tMax = 10, parMapping = NULL, parLower = NULL, parUpper = NULL, g0Prior = NULL, parInitML = NULL, control = NULL, parPriorMCMC = NULL, parInitMCMC = NULL, parScaleMCMC = NULL, nSamplesMCMC = 1e+05, nAdaptMCMC = nSamplesMCMC, thinMCMC = 100, accRateMCMC = 0.01, gammaMCMC = 0.50001, nChainsMCMC = 3, samplePriorMCMC = TRUE, parallelMCMC = FALSE)
z, tree  a numeric vector and a phylo object on which the fit is to be done. These arguments are used in order to guess meaningful values for the parLower, parUpper and parPriorMCMC arguments. See also, zMin,zMean,...,tMax below. 

zMin, zMean, zMax, zVar, zSD, tMin, tMean, tMax  summary statistics of the observed tipvalues (z) and roottip distances (t). Some of these values are used for constructing default parameter values and limits; These arguments are given default values which will most likely be meaningless in your specific usecase. The default values will be overwritten with the corresponding statistics from the z and tree arguments if these were specified. If none of tree and z, nor these parameters are specified, then the arguments parLower, parUpper, parPriorMCMC must be specified explicitly. 
parMapping  An Rfunction that can handle, both, a numeric vector
or a numeric matrix as argument. This function should transform the input
vector or each rowvector (if the input is matrix) into a (row)vector of
the POUMM parameters alpha, theta, sigma, sigmae, g0. For a vector input
the function should return a vector with named elements alpha, theta,
sigma, sigmae, g0. For a matrix input the function should return a matrix
with the same number of rows and columns alpha, theta, sigma, sigmae, g0.
Only finite nonnegative values are allowed for alpha, sigma, and sigmae.
Returning Inf, Inf, NA or NaN for any of these parameters will result in
an error during likelihood calculation. Only finite numerical values are
allowed for theta. The parameter
g0 is treated in a special way and can assume either a finite numerical
value or one of NA or NaN. If g0 = finite value, this value is used
together
with the corresponding values of alpha, theta, sigma, and sigmae for
likelihood calcuation. If g0 = NA (meaing value Not Avaiable), the value of
g0 is calculated analytically during likelihood calculation in order to
maximise one of the following:
If g0 = NaN (meaning Not a Number), then the likelihood is marginalized w.r.t.
the g0's prior distribution (see g0Prior), i.e. the likelihood returned is:
\(pdf(z  \alpha, \theta, \sigma, \sigma_e, tree) = Integral(pdf(z\alpha,\theta,\sigma,\sigma_e,g0) x pdf(g0) d g0; g0 from \infty to +\infty) \)
In this case (g0=NaN), if g0Prior is not specified,
it is assumed that g0Prior is the stationary OU normal distribution with
mean, theta, and variance, varOU(Inf, alpha, sigma). # Default for POUMM: identity for alpha, theta, sigma, sigmae, NA for g0. parMapping = function(par) { if(is.matrix(par)) { atsseg0 < cbind(par[, 1:4, drop = FALSE], NA) colnames(atsseg0) < c("alpha", "theta", "sigma", "sigmae", "g0") } else { atsseg0 < c(par[1:4], NA) names(atsseg0) < c("alpha", "theta", "sigma", "sigmae", "g0") } atsseg0 } 
parLower, parUpper  two named numeric vectors of the same length
indicating the boundaries of the search region for the MLfit. Calling
parMapping on parLower and parUpper should result in appropriate values of
the POUMM parameters alpha, theta, sigma sigmae and g0. By default, the
upper limit for alpha is set to 69.31 / tMean, which corresponds to a value
of alpha so big that the time for halfway convergence towards theta from
any initial trait value is 100 times shorter than the mean roottip distance
in the tree. Examples: # Default for POUMM: parLower = c(alpha = 0, theta = zMin  2 * (zMax  zMin), sigma = 0, sigmae = 0) parUpper = c(alpha = 69.31 / tMean, theta = zMax + 2 * (zMax  zMin), sigma = sigmaOU(H2 = .99, alpha = 69.31 / tMean, sigmae = 2 * zSD, t = tMean), sigmae = 2 * zSD) 
g0Prior  Either NULL or a list with named numeric or character members "mean" and "var". Specifies a prior normal distribution for the parameter g0. If characters, the members "mean" and "var" are evaluated as Rexpressions  useful if these are functions of some of other parameters. Note that if g0Prior is not NULL and g0 is not NaN (either a fixed number or NA), then the likelihood maximization takes into account the prior for g0, that is, the optimization is done over the product p(g0) x lik(datag0, other parameters and tree). This can be helpful to prevent extremely big or low estimates of g0. To avoid this behavior and always maximize the likelihood, use g0Prior = NULL. 
parInitML  A named vector (like parLower and parUpper) or a list of such vectors  starting points for optim. 
control  List of parameters passed on to optim in the MLfit, default list(factr=1e9), see ?optim. 
parPriorMCMC  A function of a numeric parametervector returning the
logprior for this parameter vector. Example: # Default for POUMM: parPriorMCMC = function(par) { dexp(par[1], rate = tMean / 6.931, TRUE) + dnorm(par[2], zMean, 10 * zSD, TRUE) + dexp(par[3], rate = sqrt(tMean / (zVar * 0.6931)), TRUE) + dexp(par[4], rate = 2 / zSD, TRUE) } 
parInitMCMC  a function(chainNo, fitML) returning an initial state of
an MCMC as a vector. The argument fitML can be used to specify an initial
state, close to a previously found likelihood optimum. Example: # Default for POUMM: parInitMCMC = function(chainNo, fitML) { if(!is.null(fitML)) { parML < fitML$par } else { parML < NULL } init < rbind( c(alpha = 0, theta = 0, sigma = 1, sigmae = 0), parML, c(alpha = 0, theta = 0, sigma = 1, sigmae = 1) ) init[(chainNo  1) %% nrow(init) + 1, ] } 
parScaleMCMC  Numeric matrix indicating the initial jumpdistribution matrix for the MCMC fit. Default for POUMM is diag(4); 
nSamplesMCMC  Integer indicating the length of each MCMC chain. Defaults to 1e5. 
nAdaptMCMC  Logical indicating whether adaptation of the MCMC jump distribution should be done with respect to the target acceptance rate (accRateMCMC) or integer indicating how many initial MCMC iterations should be used for adaptation of the jumpdistribution matrix (see details in ?POUMM). Defaults to nSamplesMCMC meaning continuous adaptation throughout the MCMC. 
thinMCMC  Integer indicating the thinning interval of the mcmcchains. Defaults to 100. 
accRateMCMC  numeric between 0 and 1 indicating the target acceptance rate of the adaptive Metropolis sampling (see details in ?POUMM). Default 0.01. 
gammaMCMC  controls the speed of adaption. Should be in the interval (0.5,1]. A lower gamma leads to faster adaption. Default value is 0.50001. 
nChainsMCMC  integer indicating the number of chains to run. Defaults to 3 chains, from which the first one is a sample from the prior distribution (see samplePriorMCMC). 
samplePriorMCMC  Logical indicating if sampling from the prior should be done for the first chain (see nChainsMCMC). This is useful to compare mcmc's for an overlap between prior and posterior distributions. Default is TRUE. 
parallelMCMC  Logical indicating whether the MCMC chains should be run
in parallel. Setting this option to TRUE results in using

validateSpec  Logical indicating whether the passed parameters should be validated. This parameter is used internally and should always be TRUE. 
sigmaeFixed  fixed value for the sigmae parameter (used in specifyPOUMM_ATS and specifyPOUMM_ATSG0). 
A named list to be passed as a spec argument to POUMM.
specifyPOUMM
: Specify parameters for fitting a POUMM model.
Parameter vector is c(alpha, theta, sigma, sigmae). Default model settings.
specifyPOUMM_ATS
: Fitting a POU model with fixed sigmae.
Parameter vector is c(alpha, theta, sigma).
specifyPOUMM_ATSG0
: Fitting a POU model with fixed sigmae.
Parameter vector is c(alpha, theta, sigma, g0).
specifyPOUMM_ATSSeG0
: Fitting a POUMM model with sampling of g0.
Parameter vector is c(alpha, theta, sigma, sigmae, g0).
specifyPMM
: Specify parameter for fitting a PMM model.
Parameter vector is c(sigma, sigmae)
specifyPMM_SSeG0
: Specify parameter for fitting a PMM model with
sampling of g0. Parameter vector is c(sigma, sigmae, g0).
specifyPOUMM_ATH2tMeanSe
: Fitting a POUMM model with a uniform prior for
the phylogenetic heritability at mean roottip distance. Parameter vector is
c(alpha, theta, H2tMean, sigmae).
specifyPOUMM_ATH2tMeanSeG0
: Fitting a POUMM model with a uniform prior for
the phylogenetic heritability at mean roottip with sampling of g0.
Parameter vector is c(alpha, theta, H2tMean, sigmae, g0).
specifyPMM_H2tMeanSe
: Fitting a PMM model with a uniform prior for
the phylogenetic heritability at mean roottip distance. Parameter vector is
c(H2tMean, sigmae).
specifyPMM_H2tMeanSeG0
: Fitting a PMM model with a uniform prior for
the phylogenetic heritability at mean roottip distance with sampling of G0.
Parameter vector is c(H2tMean, sigmae, g0).