Bayesian Data Analysis: From Foundations to Applications

Bayesian vs Frequentist Inference: Concepts, Contrasts, and Applications

28 August, Mohammad Ghorbani, SLU.

This introductory session examines the philosophical and practical differences between Bayesian and frequentist approaches to statistical inference. We discuss how these frameworks influence model formulation, parameter interpretation, and uncertainty quantification. Through applied examples, we highlight key decisions in the modeling process and demonstrate how Bayesian methods are used in contemporary research. In addition, the talk will briefly introduce commonly used R packages for Bayesian data analysis and illustrate their role in practical implementation. The seminar is designed to be accessible to a broad audience and serves as a foundation for the subsequent talks in the series.

From snow leopards to house crickets: how a Bayesian approach helps me answer questions in a better way

4 September, Matthew Low, SLU. 

Often I build models in a Bayesian framework that don’t differ in their structure from what I could build more quickly using a likelihood-based R package. So why do I do it? Is it because I like to make my life more complicated? Is it to show off my ‘cool' credentials in being a stats nerd? In this seminar I will show examples from my work in analysing snow leopard prey selection, bird trends across the Great Barrier Reef, and personality traits of insects, and how building my models in a Bayesian framework allows me to ask new questions and answer old ones in a much clearer way. Basically, I use Bayes because it helps me communicate my results.

From ecological data to management decisions: using Bayesian models in carnivore research

18 September, Malin Aronsson, SLU.

A large part of my research focuses on large carnivores, often in situations where ecological uncertainty meets very practical management decisions. In many cases, managers are not primarily asking whether an effect is “significant” or not – they want to know the probability that a management action will lead to a certain outcome. In wildlife management, decisions often need to be made despite substantial uncertainty and incomplete information. Bayesian approaches provide a useful framework for combining ecological data with management goals, and for presenting results in ways that are relevant for practical decision-making. 

In this seminar I will talk about how I use Bayesian models to translate ecological data into directly interpretable probabilities that can be used in both research and wildlife management. I will show examples from work ranging from applied wildlife management to broader ecological questions. Bayesian approaches have helped us develop practical decision-support tools for management authorities, while also improving our understanding of ecological processes. One thing I am particularly interested in is how probabilistic thinking can help bridge the gap between ecological research and applied management of large carnivores.

A Bayesian approach to analyzing the long-term soil fertility experiment

25 September, Rong Lang, SLU.

The treatment effects in the agricultural long-term experiments (LTEs) have been widely analyzed using conventional Frequentist approaches. In contrast, the Bayesian approach based on Bayes’ Theorem incorporates prior information on model parameters and provides greater flexibility on the models and parameters. The aim of this talk is to show how the Bayesian approach can be applied to the LFTs datasets and how results and interpretations differ between the two approaches, using the long-term soil fertility experiment in Sweden as an example. The effects of crop rotation and fertilization on soil carbon (SOC) content in 0-20 cm topsoil were assessed using both the conventional mixed-effects model and a Bayesian approach. The results showed similar trends that rotation with ley slowed SOC loss compared to rotation without ley, and nitrogen fertilization reduced SOC losses.

A Bayesian approach to projecting forest dynamics and related uncertainty: An application to continuous cover forests

2 October, Mari Myllymäki, Luke.

Continuous cover forestry (CCF) is forest management based on ecological principles and this management type is currently re-visited in many countries. CCF woodlands are known for their structural diversity in terms of tree size and species and forest planning in CCF needs to make room for multiple forest development pathways as opposed to only one management target. As forest management diversifies and management types such as CCF become more common, models used for projecting forest development need to have a generic and flexible bottom-up design. They also need to be able to handle uncertainty to a larger extent and more comprehensively than is necessary with single, traditional forest management types. In this study, a spatial tree model was designed for analyzing a data set involving 18 plots from CCF stands in Southern Finland. The tree model has specific ingrowth, growth and mortality model components, each including a spatially explicit competition effect involving neighboring trees. Approximations were presented that allow inference of the model components operating in annual steps based on time-series measurements from several years. We employed Bayesian methodology and posterior predictive distributions to simulate forest development for short- and long-term projections. The Bayesian approach allowed us to incorporate uncertainties related to model parameters in the projections, and we analyzed these uncertainties based on three scenarios: (1) known plot and tree level random effects, (2) known plot level random effects but unknown tree level random effects, and (3) unknown random effects. Our simulations revealed that uncertainties related to plot effects can be rather high, particularly when accumulated across many years whilst the length of the simulation step only had a minor effect. As the plot and tree effects are not known when tree models are applied in practice, in such cases, it may be possible to significantly improve model projections for a single plot by taking one-off individual-tree growth measurements from the plot and using them for calibrating the model. Random plot effects as used in our tree model are also a way of describing environmental conditions in CCF stands where other traditional descriptors based on stand height and stand age fail to be suitable any more.