Beginnings

I have the beginnings of a first chapter. If you want to have a look, email me!

Update of Research Statement

This isn't what I promised in the last post, but it's an update of something!

First, I am interested in the reliability of risk assessment methods in dealing with uncertainty. Specifically, I am focused on the reliability of such methods in population viability analysis. "Population viability analysis" is a term that includes many kinds of risk assessment methods, which typically purport to measure either the probability distribution over the time to (quasi-)extinction or the cumulative probability that some population becomes (quasi-)extinct within some time frame. Currently, Bayesian frameworks for population viability analysis are on the rise, and I am interested in the reliability of such systematic approaches to population viability analysis, Bayesian or otherwise. I am also interested in a logically prior question to the question about the reliability of such methods: what is the proper "target" of conservation, and hence, population viability analysis? Second, and at a much more abstract level, I am interested in theory structure, and, in particular, the inferentialist or algorithmic structure one finds in, for example, conservation biology. In my dissertation work, I plan to work on these two sets of problems. Finally, I am also interested in decision making under uncertainty and looking at theory structure in other sciences such as, say, economics. In the interest of scope, however, such topics will most likely have to be relegated to post-dissertation work.

Plan of Attack

I'll probably be able to update this blog with another lengthy post about where my dissertation research is headed in a couple of weeks. Until then, here's a list of books I plan on reading, and a list of courses I plan on taking in the near future. In other words, my plan of attack over the next year or so.

Courses List
Spring 2012 Courses
Probability
Statistical Modeling
Research/Independent Study

Fall 2012 Courses
Stochastic Processes in Biology
Dynamic Modeling in Biology
Prospectus
Complex Adaptive Systems?

Spring 2013 Courses
Bayesian Modeling in the Life Sciences
Computability and Incompleteness OR Applied Multivariate Analysis
Research

Reading List (Recommendations Helpful!)
Currently Reading
Idea of Biodiversity (Takacs)
Data Analysis with Regression (Gelman)
Computability (Cutland)
Logic of Reliable Inquiry (Kelly)
Articulating Reasons (Brandom)
Making it Explicit (Brandom)

Future Reading
Introduction to Stochastic Processes (Allen)
Bayesian Choice (Robert)
Statistical Decision Theory and Bayesian Analysis (Burger)
Bayesian Data Analysis (Gelman et al)
Probability Theory (Jaynes)
Risk Assessment in Conservation Biology (Burgman et al)
Matrix Population Models (Caswell)
Likelihood (Edwards)
Model Selection and Multimodel Inference (Burnham & Anderson)
Ecological Detective (Hilborn & Mangel)
Nature of Scientific Evidence (Taper & Lele)
Statistical Decision Functions (Wald)
Games and Information (Rasmusen)
Evolution of the Social Contract (Skyrms)
Enterprise of Knowledge (Levi)
Unified Neutral Theory of Biodiversity and Biogeography (Hubbell)
Scientific Image (van Fraassen)
Dappled World (Cartwright)
Method in Ecology (Shrader-Frechette)
Unsimple Truths (Mitchell)
Stochastic Population Dynamics in Ecology and Conservation (Lande et al)
Mathematical Modeling in Biology (Edelstein-Keshet)
Complexity (Mitchel)
Scientific Reasoning (Howson & Urbach)
Linear Causal Modeling with Structural Equations (Mulaik)
Structural Equations with Latent Variables (Bollen)

Big Picture: Extinction Systems and Reliable Decision-Making

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.

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.

Communication Between Ecologists and Conservationists

I've done some significant "narrowing down" with respect to my research these last two weeks. I started with a vague notion that I wanted to do a sort of methodological trajectory of how conservationists have dealt with and deal with uncertainty (specifically, interventional uncertainty and counterfactual uncertainty...more in later posts) in their models. Now, I would like to look at this history from the angle of communication between those who make ecological predictions and those who engage in conservation policy. More specifically, the type of communication I am interested in is visual representations, e.g., diagrams. The questions, then, are: how do (have) ecologists visually represent(ed) to conservationists how they are (were) dealing with uncertainty (if at all) of the kinds mentioned parenthetically above and how this helps (helped) decision-makers evaluate the effects of management under uncertainty (if at all).

Currently, many meta-scientists (e.g., Sarkar) and scientists (e.g., Goodman and Wade) believe that the gap between science and policy in conservation and managerial contexts can be filled with some sort of a Bayesian framework. One such framework, the Bayesian Belief Network (BBN) causal modeling framework, is increasingly being used in conservation biology. I plan to start focusing on this framework as it relies heavily on diagrammatic representations in communicating causal and probabilistic information. Later, I would like to look at this topic by focusing on Island Biogeography-inspired conservation and the (in)famous single-large or several-small (SLOSS) debate on reserve design. The ultimate goal is to measure to what degree of progress (if any) has been made in dealing with uncertainty through communicating with visual representations. Moreover, if such progress (at least, methodological progress) can be shown to be, in part, the result of visual representations, then we might consider what sort of structure conservation biology/practice has. Rather than a general and theoretical end-product (as in, say, physics), conservation biology/practice may be instead a general algorithm or procedure that outputs reliable decision protocols in the face of uncertainty (where the construction of diagrams is central). Along the way, a taxonomy of diagrams may be built as well. Excited yet?

Framing

I don't know about you, but I can't read.

Let me make this more explicit: I can't just read. When I'm doing research, I have to have some research questions in mind or at least a frame of mind when approaching the material. At the beginning of research (and I am most certainly at the beginning stages right now) it is not always easy to have precise questions in mind.

However, typically one has some sort of presuppositions about the topic of interest or some sort of "frame of mind" about (i) the current literature and (ii) how to approach it. For me, my current frame of mind or hunch about my topic of interest is that a philosophical (and methodological) history of why conservation practitioners attempt to overcome problems of uncertainty in the manner in which they do, would be an important "gap-filler" in the current literature. It seems to me that there are many histories on the practice of conservation that focus on the sociological and legislative contexts of why conservationists attempt to conserve biodiversity in the face of uncertainty in the way that they do. Although, I think these "histories" are important, they do not reveal a complete picture of the trajectory of conservation practice.

So, I want to start with a more philosophical (and methodological) frame of mind. Now, I can start reading.