7 research outputs found
Identifying optimal sequential decisions
We consider conditions that allow us to find an optimal strategy for sequential decisions from a given data situation. For the case where all interventions are unconditional (atomic), identifiability has been discussed by Pearl & Robins (1995). We argue here that an optimal strategy must be conditional, i.e. take the information available at each decision point into account. We show that the identification of an optimal sequential decision strategy is more restrictive, in the sense that conditional interventions might not always be identified when atomic interventions are. We further demonstrate that a simple graphical criterion for the identifiability of an optimal strategy can be given.
von Neumann-Morgenstern and Savage Theorems for Causal Decision Making
Causal thinking and decision making under uncertainty are fundamental aspects
of intelligent reasoning. Decision making under uncertainty has been well
studied when information is considered at the associative (probabilistic)
level. The classical Theorems of von Neumann-Morgenstern and Savage provide a
formal criterion for rational choice using purely associative information.
Causal inference often yields uncertainty about the exact causal structure, so
we consider what kinds of decisions are possible in those conditions. In this
work, we consider decision problems in which available actions and consequences
are causally connected. After recalling a previous causal decision making
result, which relies on a known causal model, we consider the case in which the
causal mechanism that controls some environment is unknown to a rational
decision maker. In this setting we state and prove a causal version of Savage's
Theorem, which we then use to develop a notion of causal games with its
respective causal Nash equilibrium. These results highlight the importance of
causal models in decision making and the variety of potential applications.Comment: Submitted to Journal of Causal Inferenc
Identifying the consequences of dynamic treatment strategies: A decision-theoretic overview
We consider the problem of learning about and comparing the consequences of
dynamic treatment strategies on the basis of observational data. We formulate
this within a probabilistic decision-theoretic framework. Our approach is
compared with related work by Robins and others: in particular, we show how
Robins's 'G-computation' algorithm arises naturally from this
decision-theoretic perspective. Careful attention is paid to the mathematical
and substantive conditions required to justify the use of this formula. These
conditions revolve around a property we term stability, which relates the
probabilistic behaviours of observational and interventional regimes. We show
how an assumption of 'sequential randomization' (or 'no unmeasured
confounders'), or an alternative assumption of 'sequential irrelevance', can be
used to infer stability. Probabilistic influence diagrams are used to simplify
manipulations, and their power and limitations are discussed. We compare our
approach with alternative formulations based on causal DAGs or potential
response models. We aim to show that formulating the problem of assessing
dynamic treatment strategies as a problem of decision analysis brings clarity,
simplicity and generality.Comment: 49 pages, 15 figure
Optimal dynamic treatment strategies
PhD ThesisDynamic treatment regimes are functions of treatment and covariate history which are
used to advise on decisions to be taken. Murphy (2003) and Robins (2004) have proposed
models and developed semi-parametric methods for making inferences about the optimal
dynamic treatment regime in a multi-interval study that provide clear advantages over
traditional parametric approaches.
The main part of the thesis investigates the estimation of optimal dynamic treatment
regimes based on two semi-parametric approaches: G-estimation by James Robins and
Iterative Minimization by Susan Murphy. Moodie et al. (2006) show that Murphy's model
is a special case of Robins' and that the methods are closely related but not equivalent.
In this thesis we rst describe and demonstrate the current theory, then present an alternative method. This method proposes a modelling and estimation strategy which incorporates the regret functions of Murphy (2003) into a regression model for observed responses.
Estimation is fast and diagnostics are available, meaning a variety of candidate models can be compared. The method is illustrated using two simulation scenarios taken from the literature and using a two-armed bandit problem. An application on determination of optimal anticoagulation treatment regimes is presented in detail