State-dependent Probability Research Articles

Infectious diseases and social distancing under state-dependent probabilities.

We analyze the implications of infectious diseases and social distancing in an extended SIS framework to allow for the presence of stochastic shocks with state dependent probabilities. Random shocks give rise to the diffusion of a new strain of the disease which affects both the number of infectives and the average biological characteristics of the pathogen causing the disease. The probability of such shock realizations changes with the level of disease prevalence and we analyze how the properties of the state-dependent probability function affect the long run epidemiological outcome which is characterized by an invariant probability distribution supported on a range of positive prevalence levels. We show that social distancing reduces the size of the support of the steady state distribution decreasing thus the variability of disease prevalence, but in so doing it also shifts the support rightward allowing eventually for more infectives than in an uncontrolled framework. Nevertheless, social distancing is an effective control measure since it concentrates most of the mass of the distribution toward the lower extreme of its support.

Tackling the Problem of State Dependent Execution Probability: Empirical Evidence and Order Placement

Tackling the Problem of State Dependent Execution Probability: Empirical Evidence and Order Placement

Intrinsic Fault Resistance for Nonlinear Filters with State-Dependent Probability of Detection

Intrinsic Fault Resistance for Nonlinear Filters with State-Dependent Probability of Detection

A Gaussian Filtering Method for Multitarget Tracking With Nonlinear/Non-Gaussian Measurements

This article proposes a Gaussian filtering method to approximate the single-target updates and normalizing constants for multitarget tracking with nonlinear, non-Gaussian measurements, and a state-dependent probability of detection. The Gaussian approximation is based on the posterior linearization technique, which seeks the optimal affine approximation of the nonlinearities in a mean square error sense. The normalizing constant is approximated using sigma-points based on the posterior. The proposed approach is implemented in a Poisson multi-Bernoulli mixture filter and compared against standard methods to approximate single-target posteriors and normalizing constants in two range-bearings tracking scenarios.

Analysis of Queueing System MMPP/M/K/K with Delayed Feedback

The model of multi-channel queuing system with Markov modulated Poisson process (MMPP) flow and delayed feedback is considered. After the customer is served completely, they will decide either to join the retrial group again for another service (feedback) with some state-dependent probability or to leave the system forever with complimentary probability. Feedback calls organize an orbit of repeated calls (r-calls). If upon arrival of an r-call all the channels of the system are busy, then it either leaves the system with some state-dependent probability or with a complementary probability returns to orbit. Methods to calculate the steady-state probabilities of the appropriate three-dimensional Markov chain as well as performance measures of investigated system are developed. Results of numerical experiments are demonstrated.

Penalized estimation of flexible hidden Markov models for time series of counts

We propose an effectively nonparametric approach to fitting hidden Markov models to time series of counts, where the state-dependent distributions are estimated in a completely data-driven way without the need to specify a parametric family of distributions. To avoid overfitting, a roughness penalty based on higher-order differences between adjacent count probabilities is added to the likelihood, which is demonstrated to produce smooth state-dependent probability mass functions. The feasibility of the suggested approach is assessed in simulation experiments, and further illustrated in two real-data applications, where we model the distributions of (i) major earthquake counts and (ii) acceleration counts of an oceanic whitetip shark (Carcharhinus longimanus) over time. The proposed methodology is implemented in the accompanying R package countHMM, which is available on CRAN.

Multi-Period Mean-Variance Portfolio Selection with State-Dependent Exit Probability and Bankruptcy State

Based on the mean-variance portfolio selection under multi-period criterion, this paper focuses on the study of the uncertain time horizon and the regime-switching market including the bankruptcy state, where the conditional distribution of exit time is followed by the market state. When the market enters the bankruptcy state, investors are assumed to get back δ part of the wealth from the bankrupt company, where δ refers to the retrieval rate. By introducing the Lagrange multiplier λ, we create an innovative expression for the wealth process and the iterative representation of the value function to obtain the analytical expression of the optimal strategy and the corresponding efficient frontier. Besides, some special cases and numerical examples are presented to demonstrate the effects of state-dependent exit probability and bankruptcy state on the investment strategy.

State-Dependent Bandwidth Sharing Policies for Wireless Multirate Loss Networks

We consider a reference cell of fixed capacity in a wireless cellular network while concentrating on next-generation network architectures. The cell accommodates new and handover calls from different service-classes. Arriving calls follow a random or quasi-random process and compete for service in the cell under two bandwidth sharing policies: 1) a probabilistic threshold (PrTH) policy or 2) the multiple fractional channel reservation (MFCR) policy. In the PrTH policy, if the number of in-service calls (new or handover) of a service-class exceeds a threshold (difference between new and handover calls), then an arriving call of the same service-class is accepted in the cell with a predefined state-dependent probability. In the MFCR policy, a real number of channels is reserved to benefit calls of certain service-classes; thus, a service priority is introduced. The cell is modeled as a multirate loss system. Under the PrTH policy, call-level performance measures are determined via accurate convolution algorithms, while under the MFCR policy, via approximate but efficient models. Furthermore, we discuss the applicability of the proposed models in 4G/5G networks. The accuracy of the proposed models is verified through simulation. Comparison against other models reveals the necessity of the new models and policies.

A Probabilistic Threshold-Based Bandwidth Sharing Policy for Wireless Multirate Loss Networks

We propose a probabilistic bandwidth sharing policy, based on the threshold (TH) policy, for a single cell of fixed capacity in a homogeneous wireless cellular network. The cell accommodates random input-traffic originated from $K$ service-classes. We distinguish call requests to new and handover, and therefore, the cell supports $2K$ types of arrivals. If the number of in-service calls (new or handover) of a service-class exceeds a threshold (different for new and handover calls of a service-class), a new or handover arriving call of the same service-class is not always blocked, as it happens in the TH policy, but it is accepted in the system with a predefined state-dependent probability. The cell is analyzed as a multirate loss system, via a reversible continuous-time Markov chain, which leads to a product form solution (PFS) for the steady state distribution. Thanks to the PFS, the calculation of performance measures is accurate, but complex. To reduce the computational complexity, we determine performance measures via a convolution algorithm.

Integrated particle filter for target tracking in clutter

In a typical surveillance situation the number and the trajectories of targets are a priori unknown. Each measurement has an unknown source; either clutter, a target being tracked or a new target. The tracks are initialised and updated using measurements, thus both true and false tracks exist at any given time. The authors present a particle filter approach which recursively calculates the probability of target existence, which may be used as a track quality measure for the false track discrimination. Single target, joint multitarget and linear multitarget versions are presented. The algorithms assume manoeuvring (multiple trajectory propagation models) targets and state dependent probability of target detection.

Multitarget tracking with state dependent detection

Target tracking determines the number and the trajectories of targets in the surveillance area. The sensors provide an imperfect target detection and measurement environment, complicated by clutter measurements. The vast majority of published target tracking algorithms assume that the probability of target detection is independent of the trajectory state. This assumption is often incorrect, with subsequent degradation in the target tracking performance. The authors present two multitarget trackers which incorporate the state-dependent probability of target detection, each of which improves upon the state of the art capabilities of target tracking in such environments.

A delay time model with imperfect and failure-inducing inspections

This paper presents an inspection-based maintenance optimisation model where the inspections are imperfect and potentially failure-inducing. The model is based on the basic delay-time model in which a system has three states: perfectly functioning, defective and failed. The system is deteriorating through these states and to reveal defective systems, inspections are performed periodically using a procedure by which the system fails with a fixed state-dependent probability; otherwise, an inspection identifies a functioning system as defective (false positive) with a fixed probability and a defective system as functioning (false negative) with a fixed probability. The system is correctively replaced upon failure or preventively replaced either at the N'th inspection time or when an inspection reveals the system as defective, whichever occurs first. Replacement durations are assumed to be negligible and costs are associated with inspections, replacements and failures. The problem is to determine the optimal inspection interval T and preventive age replacement limit N that jointly minimise the long run expected cost per unit of time. The system may also be thought of as a passive two-state system subject to random demands; the three states of the model are then functioning, undetected failed and detected failed; and to ensure the renewal property of replacement cycles the demand process generating the ‘delay time’ is then restricted to the Poisson process. The inspiration for the presented model has been passive safety critical valves as used in (offshore) oil and gas production and transportation systems. In light of this the passive system interpretation is highlighted, as well as the possibility that inspection-induced failures are associated with accidents. Two numerical examples are included, and some potential extensions of the model are indicated.

Road network based vehicle navigation using an improved IMM particle filter

This paper presents an improved interacting multiple model (IMM) algorithm for vehicle navigation using road network information. Incorporating extra information like a digital road map can significantly enhance the navigation performance of an intelligent vehicle especially when the standard positioning sensor losses accuracy due to obstruction. The proposed algorithm uses multiple models to associate the vehicle to different road sections, so that the corresponding information, such as road width, speed limits, can be taken into account as system constraints. An IMM filter that can deal with the model constraints is then developed based on the Bayesian framework. The mode transition governed by a state-dependent probability is also embedded in it. The derived Bayesian filter is implemented using a particle filter solution. Comparison results are included to show its performance against some existing algorithms for a vehicle travelling in an urban environment.

State-Dependent Probability Distributions in Non Linear Rational Expectations Models

In this paper, we provide solution methods for non-linear rational expectations models in which regime-switching or the shocks themselves may be endogenous, i.e. follow state-dependent probability distributions. We use the perturbation approach to find determinacy conditions, i.e. conditions for the existence of a unique stable equilibrium. We show that these conditions directly follow from the corresponding conditions in the exogenous regime-switching model. Whereas these conditions are difficult to check in the general case, we provide for easily verifiable and sufficient determinacy conditions and first-order approximation of the solution for purely forward-looking models. Finally, we illustrate our results with a Fisherian model of inflation determination in which the monetary policy rule may change across regimes according to a state-dependent transition probability matrix.

Experimental quantum process tomography of non-trace-preserving maps

The ability of fully reconstructing quantum maps is a fundamental task of quantum information, in particular when coupling with the environment and experimental imperfections of devices are taken into account. In this context, we carry out a quantum process tomography approach for a set of non-trace-preserving maps. We introduce an operator $\mathcal{P}$ to characterize the state-dependent probability of success for the process under investigation. We also evaluate the result of approximating the process with a trace-preserving one.

PERFORMANCE ANALYSIS OF OPTICAL BURST SWITCHED NETWORKS WITH LIMITED-RANGE WAVELENGTH CONVERSION, RETRANSMISSION AND BURST SEGMENTATION

This paper considers the performance of optical burst switched networks with burst segmentation, wavelength conversion and upper-layer retransmission. When a burst arrives at an intermediate node and finds its allocated wavelength occupied, it attempts to find another idle wavelength among a limited number of wavelengths to which the allocated wavelength can be converted. If the incoming burst cannot find any idle wavelength in the range, the ongoing burst in the allocated wavelength is segmented and its tail part which overlaps with the incoming burst is dropped and retransmitted as a retransmitted burst in a later time by upper-layer retransmission mechanisms such as TCP. Focusing on an outgoing optical fiber shared under wavelength division multiplexing, we model it as a multi-server retrial queueing system without waiting room, in which an arriving customer chooses his server out of a group of servers with a state-dependent probability. We formulate a bivariate Markov chain to analyze the model and also perform simulation experiments to validate the analysis model. Numerical examples show that the wavelength conversion technique is effective to lessen the contention of bursts at low traffic intensity and that the degree of contention among bursts is almost insensitive to the retransmission rate. They further reveal that even a small range of wavelength conversion can significantly alleviate the contention among bursts.

Compact Acoustic Models for Embedded Speech Recognition

Speech recognition applications are known to require a significant amount of resources. However, embedded speech recognition only authorizes few KB of memory, few MIPS, and small amount of training data. In order to fit the resource constraints of embedded applications, an approach based on a semicontinuous HMM system using state-independent acoustic modelling is proposed. A transformation is computed and applied to the global model in order to obtain each HMM state-dependent probability density functions, authorizing to store only the transformation parameters. This approach is evaluated on two tasks: digit and voice-command recognition. A fast adaptation technique of acoustic models is also proposed. In order to significantly reduce computational costs, the adaptation is performed only on the global model (using related speaker recognition adaptation techniques) with no need for state-dependent data. The whole approach results in a relative gain of more than 20% compared to a basic HMM-based system fitting the constraints.

Reducing Delays for Medical Appointments: A Queueing Approach

Many primary care offices and other medical practices regularly experience long backlogs for appointments. These backlogs are exacerbated by a significant level of last-minute cancellations or “no-shows,” which have the effect of wasting capacity. In this paper, we conceptualize such an appointment system as a single-server queueing system in which customers who are about to enter service have a state-dependent probability of not being served and may rejoin the queue. We derive stationary distributions of the queue size, assuming both deterministic as well as exponential service times, and compare the performance metrics to the results of a simulation of the appointment system. Our results demonstrate the usefulness of the queueing models in providing guidance on identifying patient panel sizes for medical practices that are trying to implement a policy of “advanced access.”

Bounding the Blocking Probabilities in Multirate CDMA Networks Supporting Elastic Services

Several previous contributions have proposed calculation methods that can be used to determine the steady state (and from it the blocking probabilities) of code-division multiple-access (CDMA) systems. This present work extends the classical Kaufman-Roberts formula such that it becomes applicable in CDMA systems in which elastic services with state-dependent instantaneous bit rate and average-bit-rate-dependent residency time are supported. Our model captures the effect of soft blocking, that is, an arriving session may be blocked in virtually all system states but with a state dependent probability. The core of this method is to approximate the original irreversible Markov chain with a reversible one and to give lower and upper bounds on the so-called partially blocking macro states of the state space. We employ this extended formula to establish lower and upper bounds on the steady state and the classwise blocking probabilities.

Road-map assisted ground moving target tracking

Tracking ground targets with airborne GMTI (ground moving target indicator) sensor measurements proves to be a challenging task due to high target density, high clutter, and low visibility. The exploitation of nonstandard background information such as road maps and terrain information is therefore highly desirable for the enhancement of track quality and track continuity. The present paper presents a Bayesian approach to incorporate such information consistently. It is particularly suited to deal with winding roads and networks of roads. The target dynamics is modeled in quasi one-dimensional road coordinates and mapped onto ground coordinates using linear road segments taking road map errors into account. The case of several intersecting roads with different characteristics, such as mean curvature, slope, or visibility, is treated within an interacting multiple model (IMM) scheme. Targets can be masked both by the clutter notch of the sensor and by terrain obstacles. Both effects are modeled using a sensor-target state dependent detection probability. The iterative filter equations are formulated within a framework of Gaussian sum approximations on the one hand and a particle filter approach on the other hand. Simulation results for single targets taken from a realistic ground scenario show strongly reduced target location errors compared with the case of neglecting road-map information. By modeling the clutter notch of the GMTI sensor, early detection of stopping targets is demonstrated