tboot: tilted bootstrapping and Bayesian marginal reconstruction.

Description

tboot: tilted bootstrapping and Bayesian marginal reconstruction.

Author(s)

Nathan Morris morris_nathan@lilly.com

References

https://github.com/njm18/tboot

Function post_bmr

Description

Simulates the joint posterior based upon a dataset and specified marginal posterior distribution of the mean of selected variables.

Usage

post_bmr(nsims, weights_bmr)

Arguments

Value

A matrix of simulations from the posterior.

See Also

tweights_bmr

Examples

#Use winsorized marginal to keep marginal simulation within feasible bootstrap region
winsor=function(marginalSims,y)  {
  l=min(y)
  u=max(y)
  ifelse(marginalSims<l,l,ifelse(marginalSims>u,u, marginalSims))
}
#Create an example marginal posterior
marginal = list(Sepal.Length=winsor(rnorm(10000,mean=5.8, sd=.2),iris$Sepal.Length),
               Sepal.Width=winsor(rnorm(10000,mean=3,sd=.2), iris$Sepal.Width),
               Petal.Length=winsor(rnorm(10000,mean=3.7,sd=.2), iris$Petal.Length)
)

#simulate
w = tweights_bmr(dataset = iris, marginal = marginal, silent = TRUE)
post_sims = post_bmr(1000, weights = w)

Function tboot

Description

Bootstrap nrow rows of dataset using the given row-level weights.

Usage

tboot(nrow, weights, dataset = weights$dataset, fillMissingAug = TRUE)

Arguments

Details

Bootstrap samples from a dataset using the tilted weights. Details are further described in the vignette.

Value

A simulated dataset with 'nrow' rows.

See Also

tweights

Examples

 target=c(Sepal.Length=5.5, Sepal.Width=2.9, Petal.Length=3.4)
 w = tweights(dataset = iris, target = target, silent = TRUE)
 simulated_data = tboot(nrow = 1000, weights = w)

Function tboot_bmr

Description

Bootstrap nrow rows of dataset using the given row-level weights.

Usage

tboot_bmr(nrow, weights_bmr, tol_rel_sd = 0.01)

Arguments

Details

Simulates a dataset by first simulating from the posterior distribution of the column means and then simulating a dataset with that underlying mean. Details a further documented in the vignette.

Value

A simulated dataset with 'nrow' rows. The underlying 'true' posterior parameter value is an attribute which can be extracted useing attr(ret, "post_bmr") where 'ret' is the matrix.

See Also

tweights

Examples

#Use winsorized marginal to keep marginal simulation within feasible bootstrap region
winsor=function(marginalSims,y)  {
  l=min(y)
  u=max(y)
  ifelse(marginalSims<l,l,ifelse(marginalSims>u,u, marginalSims))
}
#Create an example marginal posterior
marginal = list(Sepal.Length=winsor(rnorm(10000,mean=5.8, sd=.2),iris$Sepal.Length),
               Sepal.Width=winsor(rnorm(10000,mean=3,sd=.2), iris$Sepal.Width),
               Petal.Length=winsor(rnorm(10000,mean=3.7,sd=.2), iris$Petal.Length)
)

#simulate
w = tweights_bmr(dataset = iris, marginal = marginal, silent = TRUE)
sample_data = tboot_bmr(1000, weights = w)

Function tweights

Description

Returns a vector p of resampling probabilities such that the column means of tboot(dataset = dataset, p = p) equals target on average.

Usage

tweights(dataset, target = apply(dataset, 2, mean), distance = "klqp",
  maxit = 1000, tol = 1e-08, warningcut = 0.05, silent = FALSE,
  Nindependent = 0)

Arguments

Details

Let p_i = 1/n be the probability of sampling subject i from a dataset with n individuals (i.e. rows of the dataset) in the classic resampling with replacement scheme. Also, let q_i be the probability of sampling subject i from a dataset with n individuals in our new resampling scheme. Let d(q,p) represent a distance between the two resampling schemes. The tweights function seeks to solve the problem:

q = argmin_p d(q,p)

Subject to the constraint that:

sum_i q_i = 1

and

dataset' q = target

where dataset is a n x K matrix of variables input to the function.

d_{euclidian}(q,p) = sqrt( \sum_i (p_i-q_i)^2 )

d_{kl}(q,p) = \sum_i (log(p_i) - log(q_i))

Optimization for Euclidean distance is a quadratic program and utilizes the ipop function in kernLab. Optimization for the others utilize a Newton-Raphson type iterative algorithm.

If the original target cannot be achieved. Something close to the original target will be selected. A warning will be produced and the new target displayed.

The 'Nindependent' option augments the dataset by assuming some additional specified number of patients. These patients are assumed to made up of a random bootstrapped sample from the dataset for each variable marginally leading to independent variables.

Value

An object of type tweights. This object contains the following components:

weights

Tilted weights for resampling

originalTarget

Will be null if target was not changed.

target

Actual target that was attempted.

achievedMean

Achieved mean from tilting.

dataset

Inputed dataset.

X

Reformated dataset.

Nindependent

Inputed 'Nindependent' option.

See Also

tboot

Examples

 target=c(Sepal.Length=5.5, Sepal.Width=2.9, Petal.Length=3.4)
 w = tweights(dataset = iris, target = target, silent = TRUE)
 simulated_data = tboot(nrow = 1000, weights = w)

Function tweights_bmr

Description

Set up the needed prerequisites in order to prepare for Bayesian marginal reconstruction (including a call to tweights). Takes as input simulations from the posterior marginal distribution of variables in a dataset.

Usage

tweights_bmr(dataset, marginal, distance = "klqp", maxit = 1000,
  tol = 1e-08, warningcut = 0.05, silent = FALSE, Nindependent = 1)

Arguments

Details

Reconstructs a correlated joint posterior from simulations from a marginal posterior. The algorithm is summarized more fully in the vignettes. The 'Nindependent' option augments the dataset by assuming some additional specified number of patients. These patients are assumed to made up of a random bootstrapped sample from the dataset for each variable marginally leading to independent variables.

Value

An object of type tweights. This object conains the following components:

Csqrt

Matrix square root of the covariance.

tweights

Result from the call to tweigths.

marginal

Input marginal simulations.

dataset

Formatted dataset.

target

Attempted target.

distance,maxit,tol, Nindependent, warningcut

Inputed values to 'tweights_bmr'.

Nindependent

Inputed 'Nindependent' option.

augmentWeights

Used for 'Nindependent' option weights for each variable.

weights

Tilted weights for resampling

originalTarget

Will be null if target was not changed.

marginal_sd

Standard deviation of the marginals.

See Also

tweights

Examples

#Use winsorized marginal to keep marginal simulation within feasible bootstrap region
winsor=function(marginalSims,y)  {
  l=min(y)
  u=max(y)
  ifelse(marginalSims<l,l,ifelse(marginalSims>u,u, marginalSims))
}
#Create an example marginal posterior
marginal = list(Sepal.Length=winsor(rnorm(10000,mean=5.8, sd=.2),iris$Sepal.Length),
               Sepal.Width=winsor(rnorm(10000,mean=3,sd=.2), iris$Sepal.Width),
               Petal.Length=winsor(rnorm(10000,mean=3.7,sd=.2), iris$Petal.Length)
)

#simulate
w = tweights_bmr(dataset = iris, marginal = marginal, silent = TRUE)
post1 = post_bmr(1000, weights = w)