# VAR with Flat Prior (`Flat`)

## Description
VAR estimation with flat (uninformative) prior that provides minimal prior restrictions on coefficients. Equivalent to a Minnesota prior with very large λ₁ (> 999), effectively making the prior diffuse.

## Technical Details
- Implements prior = 41 in BEAR5 terminology
- Uses Minnesota prior structure but with λ₁ > 999 to make priors uninformative
- Provides Bayesian estimation with minimal prior influence
- Useful when prior information is limited or when data should drive results

## User Settings (Hyperparameters)

### Inherited Base Settings

#### `Burnin` (double)
- **Description**: Number of burn-in draws for posterior sampling
- **Default**: `0`
- **Details**: Number of initial MCMC draws to discard before collecting posterior samples

#### `StabilityThreshold` (double)
- **Description**: Threshold for maximum eigenvalue magnitude to ensure VAR stability
- **Default**: `Inf` (no stability check)
- **Details**: Maximum allowed eigenvalue magnitude; draws with eigenvalues exceeding this are rejected

#### `MaxNumUnstableAttempts` (double)
- **Description**: Maximum number of unstable sampling attempts before giving up
- **Default**: `1000`
- **Details**: If stability checking is enabled, this limits the number of consecutive unstable draws before termination

### Flat-Specific Settings

#### `BlockExogenous` (logical)
- **Description**: Block exogeneity restriction flag
- **Default**: `false`
- **Details**: Accessed by implementation but block exogeneity logic not implemented in current Flat algorithm

## Implementation Notes
- Implements its own Gibbs sampling algorithm with diffuse (flat) priors directly
- Does not use the Minnesota prior framework or lambda parameters
- Uses Natural Conjugate (Normal-Inverse-Wishart) priors with diffuse parameterization
- Alternates between sampling VAR coefficients β and error covariance Σ
- Accesses `BlockExogenous` setting but lambda parameters are ignored
- Posterior results are dominated by the likelihood (data)

## Usage Recommendations
- **Limited prior information**: Use when you have minimal prior beliefs about coefficients
- **Data-driven analysis**: When you want results to be primarily determined by the data
- **Benchmark comparisons**: Compare against informative priors to assess prior sensitivity
- **Large sample sizes**: Most effective when sample size is sufficient for stable estimation
- **Model exploration**: Useful for initial model exploration before imposing informative priors

## Comparison to Other Estimators
- **vs. Ordinary**: Provides Bayesian uncertainty quantification vs. classical inference
- **vs. Minnesota**: Removes informative shrinkage toward random walk
- **vs. Normal-Diffuse**: Similar philosophy but different technical implementation ???

## Limitations
- May lead to unstable estimates in small samples without prior regularization
- Less efficient than informative priors when prior beliefs are reasonable
- Can produce overfitting in large VAR models without sufficient data