Reaaliaikainen käännepisteiden havainta hylkäysvirheaste- ja kommunikaatiorajoitteilla

In a quickest detection problem, the objective is to detect abrupt changes in a stochastic sequence as quickly as possible, while limiting rate of false alarms. The development of algorithms that after each observation decide to either stop and declare a change as having happened, or to continue the monitoring process has been an active line of research in mathematical statistics. The algorithms seek to optimally balance the inherent trade-off between the average detection delay in declaring a change and the likelihood of declaring a change prematurely. Change-point detection methods have applications in numerous domains, including monitoring the environment or the radio spectrum, target detection, financial markets, and others. Classical quickest detection theory focuses settings where only a single data stream is observed. In modern day applications facilitated by development of sensing technology, one may be tasked with monitoring multiple streams of data for changes simultaneously. Wireless sensor networks or mobile phones are examples of technology where devices can sense their local environment and transmit data in a sequential manner to some common fusion center (FC) or cloud for inference. When performing quickest detection tasks on multiple data streams in parallel, classical tools of quickest detection theory focusing on false alarm probability control may become insufficient. Instead, controlling the false discovery rate (FDR) has recently been proposed as a more useful and scalable error criterion. The FDR is the expected proportion of false discoveries (false alarms) among all discoveries. In this thesis, novel methods and theory related to quickest detection in multiple parallel data streams are presented. The methods aim to minimize detection delay while controlling the FDR. In addition, scenarios where not all of the devices communicating with the FC can remain operational and transmitting to the FC at all times are considered. The FC must choose which subset of data streams it wants to receive observations from at a given time instant. Intelligently choosing which devices to turn on and off may extend the devices’ battery life, which can be important in real-life applications, while affecting the detection performance only slightly. The performance of the proposed methods is demonstrated in numerical simulations to be superior to existing approaches. Additionally, the topic of multiple hypothesis testing in spatial domains is briefly addressed. In a multiple hypothesis testing problem, one tests multiple null hypotheses at once while trying to control a suitable error criterion, such as the FDR. In a spatial multiple hypothesis problem each tested hypothesis corresponds to e.g. a geographical location, and the non-null hypotheses may appear in spatially localized clusters. It is demonstrated that implementing a Bayesian approach that accounts for the spatial dependency between the hypotheses can greatly improve testing accuracy

Bayesian Quickest Detection of Propagating Spatial Events

Rapid detection of spatial events that propagate across a sensor network is of wide interest in many modern applications. In particular, in communications, radar, environmental monitoring, and biosurveillance, we may observe propagating fields or particles. In this paper, we propose Bayesian single and multiple change-point detection procedures for the rapid detection of propagating spatial events. It is assumed that the spatial event propagates across a network of sensors according to the physical properties of the source causing the event. The multi-sensor system configuration is arbitrary and sensors may be mobile. We begin by considering a single spatial event and are interested in detecting this event as quickly as possible, while controlling the probability of false alarm. Using a dynamic programming framework we derive the structure of the optimal procedure, which minimizes the average detection delay (ADD) subject to a false alarm probability upper bound. In the rare event regime, the optimal procedure converges to a more practical threshold test on the posterior probability of the change point. A convenient recursive computation of this posterior probability is derived by using the propagation pattern of the spatial event. The ADD of the posterior probability threshold test is analyzed in the asymptotic regime, and specific analysis is conducted in the setting of detecting attenuating random signals. Then, we show how the proposed procedure is easy to extend for detecting multiple propagating spatial events in parallel. A method that provides false discovery rate (FDR) control is proposed. In the simulation section, it is clearly demonstrated that exploiting the spatial properties of the event decreases the ADD compared to procedures that do not utilize this information, even under model mismatch.Comment: 14 pages, 5 figure

Modeling of Dead Wood Potential Based on Tree Stand Data

Here we present a framework for identifying areas with high dead wood potential (DWP) for conservation planning needs. The amount and quality of dead wood and dying trees are some of the most important factors for biodiversity in forests. As they are easy to recognize on site, it is widely used as a surrogate marker for ecological quality of forests. However, wall-to-wall information on dead wood is rarely available on a large scale as field data collection is expensive and local dead wood conditions change rapidly. Our method is based on the forest growth models in the Motti forest simulator, taking into account 168 combinations of tree species, site types, and vegetation zones as well as recommendations on forest management. Simulated estimates of stand-level dead wood volume and mean diameter at breast height were converted into DWP functions. The accuracy of the method was validated on two sites in southern and northeastern Finland, both consisting of managed and conserved boreal forests. Altogether, 203 field plots were measured for living and dead trees. Data on living trees were inserted into corresponding DWP functions and the resulting DWPs were compared to the measured dead wood volumes. Our results show that DWP modeling is an operable tool, yet the accuracy differs between areas. The DWP performs best in near-pristine southern forests known for their exceptionally good quality areas. In northeastern areas with a history of softer management, the differences between near-pristine and managed forests is not as clear. While accurate wall-to-wall dead wood inventory is not available, we recommend using DWP method together with other spatial datasets when assessing biodiversity values of forests

Bayesian Methods for Multiple Change-Point Detection with Reduced Communication

In many modern applications, large-scale sensor networks are used to perform statistical inference tasks. In this article, we propose Bayesian methods for multiple change-point detection using a sensor network in which a fusion center (FC) can receive a data stream from each sensor. Due to communication limitations, the FC monitors only a subset of the sensors at each time slot. Since the number of change points can be high, we adopt the false discovery rate (FDR) criterion for controlling the rate of false alarms, while aiming to minimize the average detection delay (ADD) and the average number of observations (ANO) communicated until discovery. We propose two Bayesian detection procedures that handle the communication limitations by monitoring the subset of the sensors with the highest posterior probabilities of change points having occurred. This monitoring policy aims to minimize the delay between the occurrence of each change point and its declaration using the corresponding posterior probabilities. One of the proposed procedures is more conservative than the second one in terms of having lower FDR at the expense of higher ADD. It is analytically shown that both procedures control the FDR under a specified tolerated level and are also scalable in the sense that they attain ADD and ANO that do not increase asymptotically with the number of sensors. In addition, it is demonstrated that the proposed detection procedures are useful for trading off between reduced ADD and reduced ANO. Numerical simulations are conducted for validating the analytical results and for demonstrating the properties of the proposed procedures.Peer reviewe

Bayesian Quickest Detection of Propagating Spatial Events

Rapid detection of spatial events that propagate across a sensor network is of wide interest in many modern applications. In particular, in communications, radar, IoT, environmental monitoring, and biosurveillance, we may observe propagating fields or particles. In this paper, we propose Bayesian sequential single and multiple change-point detection procedures for the rapid detection of such phenomena. Using a dynamic programming framework we derive the structure of the optimal single-event quickest detection procedure, which minimizes the average detection delay (ADD) subject to a false alarm probability upper bound. The multi-sensor system configuration is arbitrary and sensors may be mobile. In the rare event regime, the optimal procedure converges to a more practical threshold test on the posterior probability of the change point. A convenient recursive computation of this posterior probability is derived by using the propagation characteristics of the spatial event. The ADD of the posterior probability threshold test is analyzed in the asymptotic regime, and specific analysis is conducted in the setting of detecting random Gaussian signals affected by path loss. Then, we show how the proposed procedure is easy to extend for detecting multiple propagating spatial events in parallel in a multiple hypothesis testing setting. A method that provides strict false discovery rate (FDR) control is proposed. In the simulation section, it is demonstrated that exploiting the spatial properties of the event decreases the ADD compared to procedures that do not utilize this information, even under model mismatch.Peer reviewe

Spatial Inference in Sensor Networks using Multiple Hypothesis Testing and Bayesian Clustering

The problem of statistical inference in large-scale sensor networks observing spatially varying fields is addressed. A method based on multiple hypothesis testing and Bayesian clustering is proposed. The method identifies homogeneous regions in a field based on similarity in decision statistics and locations of the sensors. High detection power is achieved while keeping false positives at a tolerable level. A variant of the EM-algorithm is employed to associate sensors with clusters. The performance of the method is studied in simulation using different detection theoretic criteria.Peer reviewe