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In Other Words

June 26
Bayesian statistical inference

Member of the Assessment Working Group on Baltic Salmon and Trout (WGBAST) and Bayesian modeler Henni Pulkkinen.
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'Bayesian statistical inference is a field of statistics in which the initial knowledge – such as data and expert views (formulated into a prior distribution) – is updated with the new data (interpreted via likelihood function) to form a new understanding (called posterior distribution) about the parameter we are interested in. These steps can simply be considered as a learning process, like the ones taking place in our minds when tackling questions in our everyday life. A likelihood function is a component used also in traditional statistics which gives an interpretation of the data, specifying how much the observed data supports different plausible values of the parameter.

The concepts of prior and posterior distribution, however, are unique to Bayesian statistics. It is possible to combine any kind of initial knowledge into a prior distribution be it, for example, data from published or unpublished (grey) literature, past studies on related species or expert knowledge. A strict rule is, however, that the data we wish to analyse in our model cannot be used to construct prior distributions or to make decisions about the model structure – for example, the choice of likelihood functions. This would be a double usage of the same data and lead to falsely overconfident results.

Since in Bayesian analyses all quantities of interest are expressed as probability distributions, uncertainty related to these quantities is also estimated. This makes it possible to answer to interesting questions such as “what is the probability that the stock abundance has increased from last year?” Bayesian methods allow us to build complex models that are biologically realistic and yet provide comprehensible answers to practical questions. The downside is that the more complex model we have, the more computational power and time is required to come up with the posterior estimates. The need for fast computers is the reason why Bayesian modelling has only recently become common in many areas of research.

The stock assessment for Baltic salmon has been conducted with Bayesian models for over a decade. The current assessment successfully combines nearly all the versatile but relevant information available of these salmon stocks, and it has improved understanding of the population dynamics of this complex migratory species. Unsurprisingly, the amount of detailed research questions keeps growing as the biological realism and resolution of the assessment increases. The old saying that knowing more shows how little we still know seems to hold true.'

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