My last post was very specific. I said that the big picture wasn't quite clear yet. Well, it's not. But it's not entirely unclear so as not to be blogged about! Here's a brief outline of what I'm thinking now.
So, the first chapter studies the problem of making reliable decisions given priors and hypothetical inputs (management plans or intended outcomes) to a Bayesian model and a complex system of extinction (perhaps in general or something like frogs in particular). (The previous post details where I'm heading with respect to this chapter.)
The second and third chapters go together. We will take the decision-making process one-step further by considering the adaptive management framework in conservation biology. So, now we can make plans and decisions by considering updated priors and new hypothetical inputs. In the second chapter we will introduce adaptive management and discuss the conditions a system must meet to be amenable to adaptive management. In the third chapter we will discuss Bayesian adaptive management and some other popular framework(s) (so, might have to include these in the first chapter discussion as well) and compare them for optimal decision making in the adaptive management framework. One might be optimal for this context, the other that, etc. Whatever.
The fourth and fifth chapters go together. We will take note that the previous chapters have the beginnings of an algorithm or heuristic device for making decisions under various kinds of uncertainty (from highest level of uncertainty to less degrees of it). In the fourth chapter we will make the case that current algorithms in conservation biology are good but lacking/bad but not unsalvageable. Again, whatever. In the fifth chapter we will present our algorithm and consider extensions to other forms of uncertainty and systems relevant to extinction concerns.
Finally, in the sixth chapter we will examine how this algorithmic structure of conservation biology fits with accounts of discipline/theory structure from the philosophy of science. It's not laws, it's not syntactic, it's not semantic, it's algorithmic. Input a particular problem and system of uncertainty and output a reliable decision making protocol.
Obviously this will change (and it has changed; I just haven't shared every version). But, it's a start.
Thursday, October 13, 2011
Wednesday, October 12, 2011
Justifying Probabilities: Reliable Decision-Making in Contexts of Biodiversity Catastrophe
Probably needless to say, my ideas for a thesis have changed. Though the grand picture is still unclear, here is something specific I've been working on.
Many conservation biologists (Ellison 1996; Goodman 2002; Wade 2000, 2002) and philosophers of biology (Sarkar 2005) argue that given uncertainty is ubiquitous in conservation contexts, a Bayesian future is in store. From the perspective of uncertainty, Bayesian methodologies have many advantages over frequentist methodologies from the choice of data sets and estimating parameters to updating model structure and providing a formal framework for decision-making. One particular branch of Bayesian methodologies, causal Bayes nets, has become increasingly popular in the literature not only as a framework for accounting for various types of uncertainty, but also as a reaction against deterministic modeling more generally (Reckhow 1999).
An essential aspect (and central point of contention) of Bayesian methodologies in general and causal Bayes nets in particular is the estimation of prior probability distributions. Typically negative responses to Bayesian methodologies have focused on trying to undercut this practice by arguing that it is, at best, arbitrary to assign prior probability distributions before confronting the data. Objective Bayesians generally respond by assigning uniform probability distributions of the variables of interest, whereas subjective Bayesians opt to make use of "background assumptions." In other words, to be a subjective Bayesian in the contexts of conservation biology implies using information from the biological domain to assign prior probability distributions.
Communicating to decision-makers about how and why prior probability distributions were assigned the way they were is important whether one is an objective or a subjective Bayesian. In the philosophy of climate modeling, Parker (2010) has provided a list of three conditions that ought to be met before scientists present a probability distribution to decision-makers. The first is ownership. Scientists must be willing to claim the probability distribution as a representation of their own degree of belief and uncertainty before presenting it to decision-makers. The second is justification. Scientists must justify why they have chosen this particular distribution as opposed to others. Finally, the third is robustness. Scientists must present probability distributions that do not rely on contentious assumptions.
All three conditions apply to the subjective Bayesian and the last two apply to the objective Bayesian. When conservation biologists present their causal Bayes nets to decision-makers, they should not only be explicit about posterior probability distributions, they should also be explicit about prior probability distributions. In particular, whether one is of the objective or subjective camp, one ought to provide justification for how and why one assigned prior probability distributions and be ready to show that such an assignment is robust. I focus on analyzing Parker's notion of justification in these contexts, and I aim to develop one strategy scientists could use to justify the assignment of prior probability distributions given a particular context.
My argument is as follows. Though some causes C have low probabilities, C may have high consequences on the probability distribution P(V) over the values v of the variable V estimating an attribute of the species of interest. Given some data set of C and V, one might be able to estimate the the prior P(V). However, C is, by definition, practically incalculable because we typically have a small sample size of observation on it. Supposing C causes V, if C is practically incalculable, then P(V|C) will be practically incalculable and any estimation of the prior P(V) will likely overestimate the expectation E(V) and underestimate the variance Var(V) and risk of making a decision E(V)U(V), where U is a utility function of V. Hence, when assigning prior P(V), the P(V) must be assumed, not generated from data.
One way to justify assuming a P(V) is by picking the one makes decision-making reliable given this domain of C. That is, given the problem of decision-making under risk of C causing V, P(V) can be justified by making decision-making reliable. A Gaussian distribution is risky in these contexts because it is unreliable in accounting for C. A power law distribution (e.g., Zipf's law distribution) is less risky and more reliable in accounting for C than the Gaussian distribution. Assuming a power law distribution is more reliable in the following sense. Whereas one cannot discover that the true P(V) is a power law distribution by initially assuming it is a Gaussian distribution, one can discover that the true P(V) is Gaussian by assuming it is a power law distribution. Therefore, we have good reason to assume a power law distribution for our prior P(V) given this domain of C.
Many conservation biologists (Ellison 1996; Goodman 2002; Wade 2000, 2002) and philosophers of biology (Sarkar 2005) argue that given uncertainty is ubiquitous in conservation contexts, a Bayesian future is in store. From the perspective of uncertainty, Bayesian methodologies have many advantages over frequentist methodologies from the choice of data sets and estimating parameters to updating model structure and providing a formal framework for decision-making. One particular branch of Bayesian methodologies, causal Bayes nets, has become increasingly popular in the literature not only as a framework for accounting for various types of uncertainty, but also as a reaction against deterministic modeling more generally (Reckhow 1999).
An essential aspect (and central point of contention) of Bayesian methodologies in general and causal Bayes nets in particular is the estimation of prior probability distributions. Typically negative responses to Bayesian methodologies have focused on trying to undercut this practice by arguing that it is, at best, arbitrary to assign prior probability distributions before confronting the data. Objective Bayesians generally respond by assigning uniform probability distributions of the variables of interest, whereas subjective Bayesians opt to make use of "background assumptions." In other words, to be a subjective Bayesian in the contexts of conservation biology implies using information from the biological domain to assign prior probability distributions.
Communicating to decision-makers about how and why prior probability distributions were assigned the way they were is important whether one is an objective or a subjective Bayesian. In the philosophy of climate modeling, Parker (2010) has provided a list of three conditions that ought to be met before scientists present a probability distribution to decision-makers. The first is ownership. Scientists must be willing to claim the probability distribution as a representation of their own degree of belief and uncertainty before presenting it to decision-makers. The second is justification. Scientists must justify why they have chosen this particular distribution as opposed to others. Finally, the third is robustness. Scientists must present probability distributions that do not rely on contentious assumptions.
All three conditions apply to the subjective Bayesian and the last two apply to the objective Bayesian. When conservation biologists present their causal Bayes nets to decision-makers, they should not only be explicit about posterior probability distributions, they should also be explicit about prior probability distributions. In particular, whether one is of the objective or subjective camp, one ought to provide justification for how and why one assigned prior probability distributions and be ready to show that such an assignment is robust. I focus on analyzing Parker's notion of justification in these contexts, and I aim to develop one strategy scientists could use to justify the assignment of prior probability distributions given a particular context.
My argument is as follows. Though some causes C have low probabilities, C may have high consequences on the probability distribution P(V) over the values v of the variable V estimating an attribute of the species of interest. Given some data set of C and V, one might be able to estimate the the prior P(V). However, C is, by definition, practically incalculable because we typically have a small sample size of observation on it. Supposing C causes V, if C is practically incalculable, then P(V|C) will be practically incalculable and any estimation of the prior P(V) will likely overestimate the expectation E(V) and underestimate the variance Var(V) and risk of making a decision E(V)U(V), where U is a utility function of V. Hence, when assigning prior P(V), the P(V) must be assumed, not generated from data.
One way to justify assuming a P(V) is by picking the one makes decision-making reliable given this domain of C. That is, given the problem of decision-making under risk of C causing V, P(V) can be justified by making decision-making reliable. A Gaussian distribution is risky in these contexts because it is unreliable in accounting for C. A power law distribution (e.g., Zipf's law distribution) is less risky and more reliable in accounting for C than the Gaussian distribution. Assuming a power law distribution is more reliable in the following sense. Whereas one cannot discover that the true P(V) is a power law distribution by initially assuming it is a Gaussian distribution, one can discover that the true P(V) is Gaussian by assuming it is a power law distribution. Therefore, we have good reason to assume a power law distribution for our prior P(V) given this domain of C.
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