Population and Ecological Models
 
 
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  Bayesian models  

 

     
   

For many biological considerations, the concept of an underlying 'true', point, value for a parameter as a premise for statistical inference is somewhat artificial.

Bayesian methods relax that premise, and have some advantages over maximum-likelihood (sometimes called frequentist) approaches.

For example, Bayesian methods permit an analyst to conceptualize that the biological parameter of interest, say a survival rate, is variable over time or space within the population from which data were collected to estimate it.

That is, a parameter is conceptualized as a random variable rather than having a fixed value.

Additionally, Bayesian methods allow an analyst to impose subjective beliefs or objective uncertainties (so-called prior distributions) about parameter values upon an analysis.

Likelihood function minimization can still be an element of the Bayesian approach, but it is used to combine information on parameter values contained in the data with the prior information on the parameters independent of the data, to produce parameter estimates associated with the so-called posterior distributions of the parameter values.

Statistical inference now concerns the posterior probability distributions of the parameter values of interest.

Statistical inference tends to be discussed more in terms of probability than likelihood, since the intent of a imposing a prior distribution is to define a probabilistic domain of a parameter's possible values.

This contrasts with the maximum-likelihood approach of judging statistical confidence in estimating the underlying, and perhaps wrongly-conceived, 'true' values of the parameters.

The appropriateness of maximum-likelihood versus Bayesian approaches to statistical inference is an ongoing debate among practitioners.

Either or both approaches may be prescribed for a particular statistical problem depending upon the analytical questions posed, the data available, and the eventual use of the analytical results.