Beliefs and expertise in sequential decision making

This work explores a sequential decision making problem with agents having diverse expertise and mismatched beliefs. We consider an N-agent sequential binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on previous agents’ decisions. In addition, the agents have their own beliefs instead of the true prior, and have varying expertise in terms of the noise variance in the private signal. We focus on the risk of the last-acting agent, where precedent agents are selfish. Thus, we call this advisor(s)-advisee sequential decision making. We first derive the optimal decision rule by recursive belief update and conclude, counterintuitively, that beliefs deviating from the true prior could be optimal in this setting. The impact of diverse noise levels (which means diverse expertise levels) in the two-agent case is also considered and the analytical properties of the optimal belief curves are given. These curves, for certain cases, resemble probability weighting functions from cumulative prospect theory, and so we also discuss the choice of Prelec weighting functions as an approximation for the optimal beliefs, and the possible psychophysical optimality of human beliefs. Next, we consider an advisor selection problem where in the advisee of a certain belief chooses an advisor from a set of candidates with varying beliefs. We characterize the decision region for choosing such an advisor and argue that an advisee with beliefs varying from the true prior often ends up selecting a suboptimal advisor, indicating the need for a social planner. We close with a discussion on the implications of the study toward designing artificial intelligence systems for augmenting human intelligence.https://arxiv.org/abs/1812.04419First author draf

A rare case of triplet heterotopic pregnancy with a live intrauterine and bilateral tubal ectopic

Heterotopic pregnancy (HP) is a condition characterized by the coexistence of an ectopic pregnancy (EP) with a viable intrauterine pregnancy (IUP). The occurrence of a triplet heterotopic pregnancy is an exceptionally rare medical condition. Hence, timely diagnosis and management are challenging, but essential to prevent mortality. Authors report the case of a young woman who presented with a heterotopic triplet pregnancy, after in-vitro fertilization (IVF), at 12 weeks of gestation. She had been misdiagnosed as a case of severe ovarian hyperstimulation syndrome but had a ruptured tubal ectopic on the right side and an unruptured ectopic on the left side. Both the ectopics were managed by performing an emergency laparotomy with bilateral salpingectomy. The live intrauterine pregnancy was continued till term with the delivery of a healthy baby. High clinical suspicion and timely treatment can preserve the intrauterine gestation thus, ensuring a successful outcome

Beliefs in Decision-Making Cascades

This work explores a social learning problem with agents having nonidentical noise variances and mismatched beliefs. We consider an $N$-agent binary hypothesis test in which each agent sequentially makes a decision based not only on a private observation, but also on preceding agents' decisions. In addition, the agents have their own beliefs instead of the true prior, and have nonidentical noise variances in the private signal. We focus on the Bayes risk of the last agent, where preceding agents are selfish. We first derive the optimal decision rule by recursive belief update and conclude, counterintuitively, that beliefs deviating from the true prior could be optimal in this setting. The effect of nonidentical noise levels in the two-agent case is also considered and analytical properties of the optimal belief curves are given. Next, we consider a predecessor selection problem wherein the subsequent agent of a certain belief chooses a predecessor from a set of candidates with varying beliefs. We characterize the decision region for choosing such a predecessor and argue that a subsequent agent with beliefs varying from the true prior often ends up selecting a suboptimal predecessor, indicating the need for a social planner. Lastly, we discuss an augmented intelligence design problem that uses a model of human behavior from cumulative prospect theory and investigate its near-optimality and suboptimality.Comment: final version, to appear in IEEE Transactions on Signal Processin

From Neural Tube Formation Through the Differentiation of Spinal Cord Neurons: Ion Channels in Action During Neural Development.

Ion channels are expressed throughout nervous system development. The type and diversity of conductances and gating mechanisms vary at different developmental stages and with the progressive maturational status of neural cells. The variety of ion channels allows for distinct signaling mechanisms in developing neural cells that in turn regulate the needed cellular processes taking place during each developmental period. These include neural cell proliferation and neuronal differentiation, which are crucial for developmental events ranging from the earliest steps of morphogenesis of the neural tube through the establishment of neuronal circuits. Here, we compile studies assessing the ontogeny of ionic currents in the developing nervous system. We then review work demonstrating a role for ion channels in neural tube formation, to underscore the necessity of the signaling downstream ion channels even at the earliest stages of neural development. We discuss the function of ion channels in neural cell proliferation and neuronal differentiation and conclude with how the regulation of all these morphogenetic and cellular processes by electrical activity enables the appropriate development of the nervous system and the establishment of functional circuits adapted to respond to a changing environment

The Information-State Based Approach to Linear System Identification

This paper considers the problem of system identification for linear systems. We propose a new system realization approach that uses an ``information-state" as the state vector, where the ``information-state" is composed of a finite number of past inputs and outputs. The system identification algorithm uses input-output data to fit an autoregressive moving average model (ARMA) to represent the current output in terms of finite past inputs and outputs. This information-state-based approach allows us to directly realize a state-space model using the estimated ARMA or time-varying ARMA parameters for linear time invariant (LTI) or linear time varying (LTV) systems, respectively. The paper develops the theoretical foundation for using ARMA parameters-based system representation using only the concept of linear observability, details the reasoning for exact output modeling using only the finite history, and shows that there is no need to separate the free and the forced response for identification. The proposed approach is tested on various different systems, and the performance is compared with state-of-the-art system identification techniques