Phan Hong Giang

Two axiomatic approaches to decision making using possibility theory

This paper proposes a utility theory for decision making under uncertainty that is described by possibility theory. We show that our approach is a natural generalization of the two axiomatic systems that correspond to pessimistic and optimistic decision criteria proposed by Dubois et al. The generalization is achieved by removing axioms that are supposed to reflect attitudes toward uncertainty, namely, pessimism and optimism. In their place we adopt an axiom that imposes an order on a class of canonical lotteries that realize either in the best or in the worst prize. We prove an expected utility theorem for the generalized axiomatic system based on the newly introduced concept of binary utility.

Decision making on the sole basis of statistical likelihood

This paper presents a new axiomatic decision theory for choice under uncertainty. Unlike Bayesian decision theory where uncertainty is represented by a probability function, in our theory, uncertainty is given in the form of a likelihood function extracted from statistical evidence. The likelihood principle in statistics stipulates that likelihood functions encode all relevant information obtainable from experimental data. In particular, we do not assume any knowledge of prior probabilities. Consequently, a Bayesian conversion of likelihoods to posterior probabilities is not possible in our setting. We make an assumption that defines the likelihood of a set of hypotheses as the maximum likelihood over the elements of the set. We justify an axiomatic system similar to that used by von Neumann and Morgenstern for choice under risk. Our main result is a representation theorem using the new concept of binary utility. We also discuss how ambiguity attitudes are handled. Applied to the statistical inference problem, our theory suggests a novel solution. The results in this paper could be useful for probabilistic model selection.

Sampling Semantics of Duration Calculus

In the paper, the problem of discretization of continuous time in Duration Calculus (DC) is addressed. For a DC formula D, for a sampling step h, a sampling semantics [D]h is defined to express the properties of discrete observations of its models, while original semantics [D] expresses the properties of the models. In practice, only sampling semantics is implemented. So, an implementation D of a system specified by S, where both are written in DC, is correct iff \([[D]]_h \subseteq [[S]]\). Some rules for proving the correctness of an implementation are given. The problem of digitization is also considered in the paper. Some forms of digitizable DC formulas are shown. Then we apply the obtained results to a non-trivial example, namely, a Biphase Mark Protocol introduced in [11]. That protocol uses 18-cycle cell for one bit of message. A cell is formed by 5-cycle mark subcell followed by 13-cycle code subcell. We adopt the same assumptions about physical environment as in [11]. However, we are able to show a stronger property than in [11]: The protocol works correctly provided the ratio of the writers and readers clock is within 30%.

A decision theory for partially consonant belief functions

Partially consonant belief functions (pcb), studied by Walley, are the only class of Dempster-Shafer belief functions that are consistent with the likelihood principle of statistics. Structurally, the set of foci of a pcb is partitioned into non-overlapping groups and within each group, foci are nested. The pcb class includes both probability function and Zadehs possibility function as special cases. This paper studies decision making under uncertainty described by pcb. We prove a representation theorem for preference relation over pcb lotteries to satisfy an axiomatic system that is similar in spirit to von Neumann and Morgensterns axioms of the linear utility theory. The closed-form expression of utility of a pcb lottery is a combination of linear utility for probabilistic lottery and two-component (binary) utility for possibilistic lottery. In our model, the uncertainty information, risk attitude and ambiguity attitude are separately represented. A tractable technique to extract ambiguity attitude from a decision maker behavior is also discussed.

Decision Making Under Ignorance

Ignorance is an extreme form of uncertainty. In most narrow and technical sense, it means inability to assign a meaningful probability to the phenomena of interest. In more general sense, the state of ignorance is the result of the absence of knowledge about structural factors that influence the issues, the lack of reliable information or inability to completely determine the space of alternatives and consequences. We argue that the practice of casually papering over the ignorance with subjective judgments and analytic assumptions can have serious consequences. This chapter provides a structured survey (and necessarily selective) of significant ideas and proposals for decision making under ignorance, from the ground breaking work by Hurwicz and Arrow to the latest result of τ-anchor utility theory. A careful analysis and isolation of ignorance in the system of knowledge about a subject or a problem is of particular importance in the context of risk assessment and risk management.

Sequence of Functional Loss and Recovery in Nursing Homes

PURPOSE OF THE STUDY This study provides benchmarks for likelihood, number of days until, and sequence of functional decline and recovery. DESIGN AND METHODS We analyzed activities of daily living (ADLs) of 296,051 residents in Veteran Affairs nursing homes between January 1, 2000 and October 9, 2012. ADLs were extracted from standard minimum data set assessments. Because of significant overlap between short- and long-stay residents, we did not distinguish between these populations. Twenty-five combinations of ADL deficits described the experience of 84.3% of all residents. A network model described transitions among these 25 combinations. The network was used to calculate the shortest, longest, and maximum likelihood paths using backward induction methodology. Longitudinal data were used to derive a Bayesian network that preserved the sequence of occurrence of 9 ADL deficits. RESULTS The majority of residents (57%) followed 4 pathways in loss of function. The most likely sequence, in order of occurrence, was bathing, grooming, walking, dressing, toileting, bowel continence, urinary continence, transferring, and feeding. The other three paths occurred with reversals in the order of dressing/toileting and bowel/urinary continence. ADL impairments persisted without any change for an average of 164 days (SD = 62). Residents recovered partially or completely from a single impairment in 57% of cases over an average of 119 days (SD = 41). Recovery rates declined as residents developed more than 4 impairments. IMPLICATIONS Recovery of deficits among those studied followed a relatively predictable path, and although more than half recovered from a single functional deficit, recovery exceeded 100 days suggesting time to recover often occurs over many months.

Shared Homes as an Alternative to Nursing Home Care: Impact of VA’s Medical Foster Home Program on Hospitalization

PURPOSE OF THE STUDY This study compares hospitalization rates for common conditions in the Veteran Affairs (VA) Medical Foster Home (MFH) program to VA nursing homes, known as Community Living Centers (CLCs). DESIGN AND METHODS We used a nested, matched, case control design. We examined 817 MFH residents and matched each to 3 CLC residents selected from a pool of 325,031. CLC and MFH cases were matched on (a) baseline time period, (b) follow-up time period, (c) age, (d) gender, (e) race, (f) risk of mortality calculated from comorbidities, and (g) history of hospitalization for the selected condition during the baseline period. Odds ratio (OR) and related confidence interval (CI) were calculated to contrast MFH cases and matched CLC controls. RESULTS Compared with matched CLC cases, MFH residents were less likely to be hospitalized for adverse care events, (OR = 0.13, 95% CI = 0.03-0.53), anxiety disorders (OR = 0.52, 95% CI = 0.33-0.80), mood disorders (OR = 0.57, 95% CI = 0.42-0.79), skin infections (OR = 0.22, 95% CI = 0.10-0.51), pressure ulcers (OR = 0.22, 95% CI = 0.09-0.50) and bacterial infections other than tuberculosis or septicemia (OR = 0.54, 95% CI = 0.31-0.92). MFH cases and matched CLC controls did not differ in rates of urinary tract infections, pneumonia, septicemia, suicide/self-injury, falls, other injury besides falls, history of injury, delirium/dementia/cognitive impairments, or adverse drug events. Hospitalization rates were not higher for any conditions studied in the MFH cohort compared with the CLC cohort. IMPLICATIONS MFH participants had the same or lower rates of hospitalizations for conditions examined compared with CLC controls suggesting that noninstitutional care by a nonfamilial caregiver does not increase hospitalization rates for common medical conditions.

Decision making under uncertainty comprising complete ignorance and probability

This paper investigates a model of decision making under uncertainty comprising opposite epistemic states of complete ignorance and probability. In the first part, a new utility theory under complete ignorance is developed that combines Hurwicz-Arrows theory of decision under ignorance with Anscombe-Aumanns idea of reversibility and monotonicity used to characterize subjective probability. The main result is a representation theorem for preference under ignorance by a particular one-parameter function - the ?-anchor utility function. In the second part, we study decision making under uncertainty comprising an ignorant variable and a probabilistic variable. We show that even if the variables are independent, they are not reversible in Anscombe-Aumanns sense. This insight leads to the development of a new proposal for decision under uncertainty represented by a preference relation that satisfies the weak order and monotonicity assumptions but rejects the reversibility assumption. A distinctive feature of the new proposal is that the certainty equivalent of a mapping from the state space of uncertain variables to the prize space depends on the order in which the variables are revealed. Explicit modeling of the order of variables explains some of the puzzles in multiple-prior model and the models for decision making with Dempster-Shafer belief function.

A machine learning approach to create blocking criteria for record linkage

Record linkage, a part of data cleaning, is recognized as one of most expensive steps in data warehousing. Most record linkage (RL) systems employ a strategy of using blocking filters to reduce the number of pairs to be matched. A blocking filter consists of a number of blocking criteria. Until recently, blocking criteria are selected manually by domain experts. This paper proposes a new method to automatically learn efficient blocking criteria for record linkage. Our method addresses the lack of sufficient labeled data for training. Unlike previous works, we do not consider a blocking filter in isolation but in the context of an accompanying matcher which is employed after the blocking filter. We show that given such a matcher, the labels (assigned to record pairs) that are relevant for learning are the labels assigned by the matcher (link/nonlink), not the labels assigned objectively (match/unmatch). This conclusion allows us to generate an unlimited amount of labeled data for training. We formulate the problem of learning a blocking filter as a Disjunctive Normal Form (DNF) learning problem and use the Probably Approximately Correct (PAC) learning theory to guide the development of algorithm to search for blocking filters. We test the algorithm on a real patient master file of 2.18 million records. The experimental results show that compared with filters obtained by educated guess, the optimal learned filters have comparable recall but reduce throughput (runtime) by an order-of-magnitude factor.

Decision with Dempster--Shafer belief functions: Decision under ignorance and sequential consistency

This paper examines proposals for decision making with Dempster-Shafer belief functions from the perspectives of requirements for rational decision under ignorance and sequential consistency. The focus is on the proposals by Jaffray & Wakker and Giang & Shenoy applied for partially consonant belief functions. We formalize the concept of sequential consistency of an evaluation model and prove results about sequential consistency of Jaffray-Wakkers model and Giang-Shenoys model under various conditions. We demonstrate that the often neglected assumption about two-stage resolution of uncertainty used in Jaffray-Wakkers model actually disambiguates the foci of a belief function, and therefore, makes it a partially consonant on the extended state space.