Compute a Bayesian equivalent of the *p*-value, related to the odds that a parameter (described by its posterior distribution) has against the null hypothesis (*h0*) using Mills' (2014, 2017) *Objective Bayesian Hypothesis Testing* framework. It corresponds to the density value at 0 divided by the density at the Maximum A Posteriori (MAP).

## Usage

```
p_map(x, precision = 2^10, method = "kernel", ...)
p_pointnull(x, precision = 2^10, method = "kernel", ...)
# S3 method for stanreg
p_map(
x,
precision = 2^10,
method = "kernel",
effects = c("fixed", "random", "all"),
component = c("location", "all", "conditional", "smooth_terms", "sigma",
"distributional", "auxiliary"),
parameters = NULL,
...
)
# S3 method for brmsfit
p_map(
x,
precision = 2^10,
method = "kernel",
effects = c("fixed", "random", "all"),
component = c("conditional", "zi", "zero_inflated", "all"),
parameters = NULL,
...
)
```

## 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.frame`

methods.- precision
Number of points of density data. See the

`n`

parameter in`density`

.- method
Density estimation method. Can be

`"kernel"`

(default),`"logspline"`

or`"KernSmooth"`

.- ...
Currently not used.

- effects
Should results for fixed effects, random effects or both be returned? Only applies to mixed models. May be abbreviated.

- component
Should results for all parameters, parameters for the conditional model or the zero-inflated part of the model be returned? May be abbreviated. Only applies to brms-models.

- 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.

## Details

Note that this method is sensitive to the density estimation `method`

(see the section in the examples below).

### Strengths and Limitations

**Strengths:** Straightforward computation. Objective property of the posterior distribution.
**Limitations:** Limited information favoring the null hypothesis. Relates on density approximation. Indirect relationship between mathematical definition and interpretation. Only suitable for weak / very diffused priors.

## References

Makowski D, Ben-Shachar MS, Chen SHA, Lüdecke D (2019) Indices of Effect Existence and Significance in the Bayesian Framework. Frontiers in Psychology 2019;10:2767. doi:10.3389/fpsyg.2019.02767

Mills, J. A. (2018). Objective Bayesian Precise Hypothesis Testing. University of Cincinnati.

## Examples

```
library(bayestestR)
p_map(rnorm(1000, 0, 1))
#> MAP-based p-value: 1.00
p_map(rnorm(1000, 10, 1))
#> MAP-based p-value: 0.00
if (FALSE) {
library(rstanarm)
model <- stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)
p_map(model)
library(emmeans)
p_map(emtrends(model, ~1, "wt"))
library(brms)
model <- brms::brm(mpg ~ wt + cyl, data = mtcars)
p_map(model)
library(BayesFactor)
bf <- ttestBF(x = rnorm(100, 1, 1))
p_map(bf)
# ---------------------------------------
# Robustness to density estimation method
set.seed(333)
data <- data.frame()
for (iteration in 1:250) {
x <- rnorm(1000, 1, 1)
result <- data.frame(
"Kernel" = p_map(x, method = "kernel"),
"KernSmooth" = p_map(x, method = "KernSmooth"),
"logspline" = p_map(x, method = "logspline")
)
data <- rbind(data, result)
}
data$KernSmooth <- data$Kernel - data$KernSmooth
data$logspline <- data$Kernel - data$logspline
summary(data$KernSmooth)
summary(data$logspline)
boxplot(data[c("KernSmooth", "logspline")])
}
```