Maximum A Posteriori probability estimate (MAP)

Source: R/map_estimate.R

Find the Highest Maximum A Posteriori probability estimate (MAP) of a posterior, i.e., the value associated with the highest probability density (the "peak" of the posterior distribution). In other words, it is an estimation of the mode for continuous parameters. Note that this function relies on estimate_density(), which by default uses a different smoothing bandwidth ("SJ") compared to the legacy default implemented the base R density() function ("nrd0").

map_estimate(x, ...)

# S3 method for class 'numeric'
map_estimate(x, precision = 2^10, method = "kernel", verbose = TRUE, ...)

# S3 method for class 'brmsfit'
map_estimate(
  x,
  precision = 2^10,
  method = "kernel",
  effects = "fixed",
  component = "conditional",
  parameters = NULL,
  verbose = TRUE,
  ...
)

# S3 method for class 'data.frame'
map_estimate(
  x,
  precision = 2^10,
  method = "kernel",
  rvar_col = NULL,
  verbose = TRUE,
  ...
)

# S3 method for class 'get_predicted'
map_estimate(
  x,
  precision = 2^10,
  method = "kernel",
  use_iterations = FALSE,
  verbose = TRUE,
  ...
)

Arguments

x

Vector representing a posterior distribution, or a data frame of such vectors. Can also be a Bayesian model. bayestestR supports a wide range of models (see, for example, methods("hdi")) and not all of those are documented in the 'Usage' section, because methods for other classes mostly resemble the arguments of the .numeric or .data.framemethods.

...

Currently not used.

precision

Number of points of density data. See the n parameter in density.

method

Density estimation method. Can be "kernel" (default), "logspline" or "KernSmooth".

verbose

Toggle off warnings.

effects

Should variables for fixed effects ("fixed"), random effects ("random") or both ("all") be returned? Only applies to mixed models. May be abbreviated.

For models of from packages brms or rstanarm there are additional options:

  • "fixed" returns fixed effects.

  • "random_variance" return random effects parameters (variance and correlation components, e.g. those parameters that start with sd_ or cor_).

  • "grouplevel" returns random effects group level estimates, i.e. those parameters that start with r_.

  • "random" returns both "random_variance" and "grouplevel".

  • "all" returns fixed effects and random effects variances.

  • "full" returns all parameters.

component

Which type of parameters to return, such as parameters for the conditional model, the zero-inflated part of the model, the dispersion term, etc. See details in section Model Components. May be abbreviated. Note that the conditional component also refers to the count or mean component - names may differ, depending on the modeling package. There are three convenient shortcuts (not applicable to all model classes):

  • component = "all" returns all possible parameters.

  • If component = "location", location parameters such as conditional, zero_inflated, smooth_terms, or instruments are returned (everything that are fixed or random effects - depending on the effects argument - but no auxiliary parameters).

  • For component = "distributional" (or "auxiliary"), components like sigma, dispersion, beta or precision (and other auxiliary parameters) are returned.

parameters

Regular expression pattern that describes the parameters that should be returned. Meta-parameters (like lp__ or prior_) are filtered by default, so only parameters that typically appear in the summary() are returned. Use parameters to select specific parameters for the output.

rvar_col

A single character - the name of an rvar column in the data frame to be processed. See example in p_direction().

use_iterations

Logical, if TRUE and x is a get_predicted object, (returned by insight::get_predicted()), the function is applied to the iterations instead of the predictions. This only applies to models that return iterations for predicted values (e.g., brmsfit models).

Value

A numeric value if x is a vector. If x is a model-object, returns a data frame with following columns:

  • Parameter: The model parameter(s), if x is a model-object. If x is a vector, this column is missing.

  • MAP_Estimate: The MAP estimate for the posterior or each model parameter.

Model components

Possible values for the component argument depend on the model class. Following are valid options:

  • "all": returns all model components, applies to all models, but will only have an effect for models with more than just the conditional model component.

  • "conditional": only returns the conditional component, i.e. "fixed effects" terms from the model. Will only have an effect for models with more than just the conditional model component.

  • "smooth_terms": returns smooth terms, only applies to GAMs (or similar models that may contain smooth terms).

  • "zero_inflated" (or "zi"): returns the zero-inflation component.

  • "location": returns location parameters such as conditional, zero_inflated, or smooth_terms (everything that are fixed or random effects - depending on the effects argument - but no auxiliary parameters).

  • "distributional" (or "auxiliary"): components like sigma, dispersion, beta or precision (and other auxiliary parameters) are returned.

For models of class brmsfit (package brms), even more options are possible for the component argument, which are not all documented in detail here. See also ?insight::find_parameters.

Examples

# \donttest{
library(bayestestR)

posterior <- rnorm(10000)
map_estimate(posterior)
#> MAP Estimate
#> 
#> Parameter | MAP_Estimate
#> ------------------------
#> x         |         0.06

plot(density(posterior))
abline(v = as.numeric(map_estimate(posterior)), col = "red")


model <- rstanarm::stan_glm(mpg ~ wt + cyl, data = mtcars)
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 3.1e-05 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.31 seconds.
#> Chain 1: Adjust your expectations accordingly!
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#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 1.3e-05 seconds
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#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 4).
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map_estimate(model)
#> MAP Estimate
#> 
#> Parameter   | MAP_Estimate
#> --------------------------
#> (Intercept) |        39.82
#> wt          |        -3.13
#> cyl         |        -1.53

model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
#> Compiling Stan program...
#> Start sampling
#> 
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 1.1e-05 seconds
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map_estimate(model)
#> MAP Estimate
#> 
#> Parameter   | MAP_Estimate
#> --------------------------
#> b_Intercept |        39.67
#> b_wt        |        -3.06
#> b_cyl       |        -1.58
# }