diff --git a/doc/dynare.texi b/doc/dynare.texi
index 731692d33..d48175b6f 100644
--- a/doc/dynare.texi
+++ b/doc/dynare.texi
@@ -4353,10 +4353,20 @@ Specifies a starting value for the posterior mode optimizer or the
 maximum likelihood estimation. If unset, defaults to the prior mean.
 
 @item @var{LOWER_BOUND}
-Specifies a lower bound for the parameter value in maximum likelihood estimation
+@anchor{lower_bound} Specifies a lower bound for the parameter value in maximum
+likelihood estimation. In a Bayesian estimation context, sets a lower bound
+only effective while maximizing the posterior kernel. This lower bound does not
+modify the shape of the prior density, and is only aimed at helping the
+optimizer in identifying the posterior mode (no consequences for the MCMC). For
+some prior densities (namely inverse gamma, gamma, uniform or beta) it is
+possible to shift the default lower bound (zero) on the left or the right using
+@ref{prior_3rd_parameter}. In this case the prior density is effectively
+modified (note that the truncated Gaussian density is not implemented in
+Dynare). If unset, defaults to minus infinity (ML) or the natural lower bound
+of the prior (Bayesian estimation).
 
 @item @var{UPPER_BOUND}
-Specifies an upper bound for the parameter value in maximum likelihood estimation
+Same as @ref{lower_bound}, but specifying an upper bound instead.
 
 @item @var{PRIOR_SHAPE}
 A keyword specifying the shape of the prior density.
@@ -4368,16 +4378,18 @@ that @code{inv_gamma_pdf} is equivalent to
 @code{inv_gamma1_pdf}
 
 @item @var{PRIOR_MEAN}
-The mean of the prior distribution
+@anchor{prior_mean} The mean of the prior distribution
 
 @item @var{PRIOR_STANDARD_ERROR}
-The standard error of the prior distribution
+@anchor{prior_standard_error} The standard error of the prior distribution
 
 @item @var{PRIOR_3RD_PARAMETER}
+@anchor{prior_3rd_parameter}
 A third parameter of the prior used for generalized beta distribution,
 generalized gamma and for the uniform distribution. Default: @code{0}
 
 @item @var{PRIOR_4TH_PARAMETER}
+@anchor{prior_4th_parameter}
 A fourth parameter of the prior used for generalized beta distribution
 and for the uniform distribution. Default: @code{1}
 
@@ -5731,16 +5743,29 @@ estimates using a higher tapering are usually more reliable.
 
 @deffn Command model_comparison @var{FILENAME}[(@var{DOUBLE})]@dots{};
 @deffnx Command model_comparison (marginal_density = laplace | modifiedharmonicmean) @var{FILENAME}[(@var{DOUBLE})]@dots{};
-
+@anchor{model_comparison}
 @descriptionhead
 
-This command computes odds ratios and estimate a posterior density
-over a collection of models 
-(see e.g. @cite{Koop (2003), Ch. 1}). The priors over models can be specified
-as the @var{DOUBLE} values, otherwise a uniform prior over all models is assumed. 
-In contrast to frequentist econometrics, the models to be compared do not need to be nested. 
-However, as the computation of posterior odds ratios is a Bayesian technique, 
-the comparison of models estimated with maximum likelihood is not supported.
+This command computes odds ratios and estimate a posterior density over a
+collection of models (see e.g. @cite{Koop (2003), Ch. 1}). The priors over
+models can be specified as the @var{DOUBLE} values, otherwise a uniform prior
+over all models is assumed.  In contrast to frequentist econometrics, the
+models to be compared do not need to be nested.  However, as the computation of
+posterior odds ratios is a Bayesian technique, the comparison of models
+estimated with maximum likelihood is not supported.
+
+It is important to keep in mind that model comparison of this type is only
+valid with proper priors.  If the prior does not integrate to one for all
+compared models, the comparison is not valid. This may be the case if part of
+the prior mass is implicitly truncated because Blanchard and Kahn conditions
+(instability or indeterminacy of the model) are not fulfilled, or because for
+some regions of the parameters space the deterministic steady state is
+undefined (or Dynare is unable to find it). The compared marginal densities
+should be renormalized by the effective prior mass, but this not done by
+Dynare: it is the user's responsibility to make sure that model comparison is
+based on proper priors. Note that, for obvious reasons, this is not an issue if
+the compared marginal densities are based on Laplace approximations.
+
 
 @examplehead