Bayesian Maximum A Posteriori Research Articles

Dynamical system identification, model selection, and model uncertainty quantification by Bayesian inference.

This study presents a Bayesian maximum a posteriori (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational justification for the choice of the residual and regularization terms, respectively, from the negative logarithms of the likelihood and prior distributions. In addition to the estimation of model coefficients, the Bayesian interpretation gives access to the full apparatus for Bayesian inference, including the ranking of models, the quantification of model uncertainties, and the estimation of unknown (nuisance) hyperparameters. Two Bayesian algorithms, joint MAP and variational Bayesian approximation, are compared to the least absolute shrinkage and selection operator (LASSO), ridge regression, and the sparse identification of nonlinear dynamics (SINDy) algorithms for sparse regression by application to several dynamical systems with added Gaussian or Laplace noise. For multivariate Gaussian likelihood and prior distributions, the Bayesian formulation gives Gaussian posterior and evidence distributions, in which the numerator terms can be expressed in terms of the Mahalanobis distance or "Gaussian norm" ||y-y^||M-12=(y-y^)⊤M-1(y-y^), where y is a vector variable, y^ is its estimator, and M is the covariance matrix. The posterior Gaussian norm is shown to provide a robust metric for quantitative model selection for the different systems and noise models examined.

Saliva as a noninvasive sampling matrix for therapeutic drug monitoring of intravenous busulfan in Chinese patients undergoing hematopoietic stem cell transplantation: A prospective population pharmacokinetic and simulation study.

Therapeutic drug monitoring (TDM) of busulfan (BU) is currently performed by plasma sampling in patients undergoing hematopoietic stem cell transplantation (HSCT). Saliva samples are considered a noninvasive TDM matrix. Currently, no salivary population pharmacokinetics (PopPKs) model for BU available. This study aimed to develop a PopPK model that can describe the relationship between plasma and saliva kinetics in patients receiving intravenous BU. The performance of the model in predicting the area under the concentration-time curve at steady state (AUCss ) based on saliva samples is evaluated. Sixty-six patients with HSCT were recruited and administered 0.8 mg/kg BU intravenously. A PopPK model for saliva and plasma was developed using the nonlinear mixed effects model. Bayesian maximum a posteriori (MAP) optimization was used to estimate the model's predictive performance. Plasma and saliva PKs were adequately described with a one-compartment model and a scaled central compartment. Body surface area correlated positively with both clearance and apparent volume of distribution (Vd), whereas alkaline phosphatase correlated negatively with Vd. Simulations demonstrated that the percentage root mean squared prediction error and lower and upper limits of agreements reduced to 10.02% and -16.96% to 22.86% based on five saliva samples. Saliva can be used as an alternative matrix to plasmain TDM of BU. The AUCss can be predicted from saliva concentration by Bayesian MAP optimization, which can be used to design personalized dosing for BU.

Optimal exposure to docetaxel in adjuvant chemotherapy for early-stage breast cancer.

Drug-induced neutropenia is the main reason for the dose limitation of docetaxel in patients with breast cancer. The area under the drug concentration-time curve (AUC) of docetaxel is associated with neutropenia. However, the optimal exposure to docetaxel for receiving postoperative adjuvant chemotherapy remains unclear. Therefore, we aimed to evaluate the relationship between the docetaxel AUC and neutropenia, identify potential influencing factors, and explore the best monitoring target for docetaxel when treating patients with early-stage breast cancer using a population pharmacokinetic (PopPK) model. Docetaxel plasma concentration, demographics, clinical data, and related laboratory data were collected. PopPK analyses were performed using a nonlinear mixed-effect modelling program. The docetaxel AUC was determined using the maximum a posteriori Bayesian (MAPB) method. The docetaxel exposure-toxicity threshold measured from the AUC for neutropenia was determined using the receiver operating characteristic (ROC) curve. The correlation between docetaxel exposure and neutropenia was analysed using multivariable logistic regression. Among the 70 participants, 47 (67.1%) developed severe neutropenia. The PopPK analysis showed that the typical drug clearance (CL) rate was 37.4L/h. Age was a significant covariate of CL rate, and aspartate aminotransferase and albumin levels were covariables of the volume of distribution. The multivariable regression analysis showed that AUC >3.0mg.h/L (odds ratio [OR], 5.940; 95% confidence interval [CI], 1.693-20.843; P=0.005), platinum use (OR, 0.156; 95% CI, 0.043-0.562; P=0.005) and baseline haemoglobin level (OR, 0.938; 95% CI, 0.887-0.993; P=0.027) were significant factors influencing the occurrence of grade 3/4 neutropenia. The AUC of first cycle may not predict the occurrence rates of grade 3/4 neutropenia in later cycles. We developed a docetaxel PopPK model for patients with early-stage breast cancer. Age and AST and ALB levels were significant covariates. AUC estimated using the MAPB method can predict the toxicity of docetaxel in patients with breast cancer. Docetaxel AUC >3.0mg.h/L, absence of platinum use and low baseline haemoglobin level were risk factors for docetaxel-induced grade 3/4 neutropenia. Chinese Clinical Trial Center Registry (ChiCTR2200056460).

Optimal exposure targets for vancomycin in the treatment of neonatal coagulase-negative Staphylococcus infection: A retrospective study based on electronic medical records

The currently advocated ratio of area under the curve (AUC) over 24h to minimum inhibitory concentration (AUC/MIC)>400 and AUC<600mgh/L as the therapeutic drug monitoring (TDM) target of vancomycin is based on data from multiple observational studies in adult patients with methicillin-resistant Staphylococcus aureus (MRSA) infection. It may not be applicable to newborns with coagulase-negative Staphylococcus (CoNS) infection. We conducted a retrospective study to identify the optimal exposure targets for vancomycin in the treatment of neonatal CoNS infection. Based on the inclusion and exclusion criteria, serum vancomycin concentration, demographics, clinical data, and related laboratory data of newborns who received vancomycin intravenous infusion from June 1, 2016 to February 1, 2021 were collected retrospectively. The AUC was calculated using the maximum a posteriori Bayesian (MAPB) method. The vancomycin exposure threshold of AUC/MIC for efficacy and AUC for toxicity (acute kidney injury, AKI) were determined based on receiver operating characteristic (ROC) curve analysis. The correlation between vancomycin exposure and both clinical effect and nephrotoxicity was analyzed using logistic multivariate regression. In total, 153 patients and 245 vancomycin concentrations (160 trough and 85 peak concentrations) were included. The ROC curve analysis showed that the exposure thresholds of AUC/MIC for clinical efficacy and AUC for nephrotoxicity were 281 and 602mgh/L, respectively. The multivariate regression analysis showed that AUC/MIC>280 was a predictor of efficacy (OR: 13.960, 95% CI: 1.891-103.078, P<0.05) and AUC>600mgh/L was associated with AKI (OR: 9.008, 95% CI: 2.706-29.983, P<0.05). The vancomycin AUC/MIC threshold for treating neonatal CoNS infection with vancomycin is lower than the currently advocated AUC/MIC >400. The optimal exposure targets for vancomycin in neonatal CoNS infection were AUC/MIC>280 and AUC<600mgh/L.

Despeckling method of ultrasound images using closed-form shrinkage function based on cauchy distribution in wavelet domain

Speckle suppression and elimination are very important to improve the visual quality of ultrasound image and the diagnostic ability of the diseases. An effective technique of image denoising based on discrete wavelet transform is to employ a Bayesian maximum a posteriori (MAP) estimator. To suppress and remove the speckle noise using MAP estimator effectively, it must assign correctly the shrinkage function based on appropriate probability density functions (PDFs) for the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise. In this paper, we introduce a new closed-form shrinkage function that is an analytical solution of a Bayesian MAP estimator for despeckling of the ultrasound images effectively in wavelet domain. We employ a Cauchy prior and Gaussian PDF to model the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise, respectively. Firstly, we derive the CauchyShrinkGMAP that is a closed-form shrinkage function. In addition, we estimate the noise variance and parameter of MAP estimator. Next, we evaluate the despeckling performance of wavelet image denoising method using the CauchyShrinkGMAP compared to various despeckling method using median and Wiener filters, hard and soft thresholding and GaussShrinkGMAP and MCMAP3N shrinkage function. The experiment results show that PSNR of new closed-form shrinkage function is highest, MSE is smallest, and the correlation coefficient ([Formula: see text]) and SSIM are closer to one than the other existing image denoising methods for noisy synthetic ultrasound images at different speckle noise levels. Also, experiment results show that ENL of new closed-form shrinkage function is highest and that of EN and SD is smallest than the other existing image denoising methods for noisy real ultrasound image.

The detection of multiple faults in a Bayesian setting using dynamic programming approaches

Inspired by the need for improving the reliability and safety of complex dynamic systems, this paper tackles the multiple faults detection problem using Dynamic Programming (DP) based methods under the Bayesian framework. These methods include (i) Maximum-A-Posteriori (MAP) estimator approach, (ii) Monte Carlo Markov Chain (MCMC) posteriors, (iii) Set Membership (SM) approach, (iv) probability of fault and (v) alternative methods. Using Bernoulli and Poisson priors, the Bayesian DP-type MAP estimate of all unknown parameters is presented. To derive the posterior distributions of Bayesian point estimations, the MCMC method is applied. For the SM approach, the Bayesian feasible parameter space is derived, as Bayesian confidence interval. The SM criteria are proposed to detect multiple faults which also reduces the Bayesian complexity of MAP estimator. For online fault detection, using the Bayesian model selection technique and the MAP estimator, the DP-based probability of faults is given, serving as a Bayesian early warning system. Since running DP algorithms is a time-consuming, alternative methods are also proposed using the modified MAP estimator. These methods use iterative approximations of MAP estimates, via the application of an iterative Expectation–Maximization algorithm technique. Numerical simulations are conducted and analysed to evaluate the performance of the proposed methods.

A limited sampling strategy to estimate exposure of once-daily modified release tacrolimus in renal transplant recipients using linear regression analysis and comparison with Bayesian population pharmacokinetics in different cohorts.

Tacrolimus has a narrow therapeutic window. Measuring trough level (C0) as surrogate for drug exposure (AUC) in renal transplant recipients has limitations. Therefore, limited sampling strategies (LSS's) have been developed. For the newer modified release, once-daily formulation (Tac QD) LSS's are based on either linear regression analysis (LRA) or population pharmacokinetics with maximum a posteriori Bayesian (MAPB) estimation. The predictive performances of both methods were compared, also to LSS's as described in literature. LSS's (maximally three sampling time points) were developed for Tac QD from full 24-h sampling by LRA in 27 Caucasian, stable renal transplant recipients. Performance for accuracy (mean absolute prediction error < 10%) and precision (root mean squared error < 15%) was quantified also after MAPB estimation in two independent groups (early and late post-transplant, n = 12 each). LRA determined a single 8hours post-dose measurement (C8) to fulfil predefined criteria for accuracy (MAPE 3.41%) and precision (RMSE 4.28%). The best LSS contained C2, C8 and C12 for the stable (MAPE 2.42%, RMSE 3.1%) and the early post-transplant group (MAPE 2.46%, RMSE 3.14%). LRA did not include C0 for any LSS, unless it was forced into the model. MAPB estimation showed similar performance. In renal transplant patients, sampling in the elimination phase (C8) accurately predicted Tac QD exposure, contrary to C0. The 3-point sampling C2, C8 and C12 had the best performance and is also valid early post-transplant. These LSS's were similarly predictive with MAPB estimation. Dried blood spot could facilitate late sampling in clinical practice.

An Analysis of Period and Cohort Mortality Shocks in International Data

This article uses Bayesian maximum a posteriori (BMAP) estimation to fit a cohort-based mortality model that applies the Gompertz mortality law to fixed cohorts across different periods (rather than the more usual application to fixed periods across different cohorts). Period effects are then estimated as residuals. In this approach, cohort effects can be viewed as a proxy for causes of death with long latency, which have become relatively more important in recent decades in richer countries. We estimate the model independently using male and female adult population mortality data in 31 countries. We are able to associate historical events with many of the observed period and cohort shocks, most notably the 1918 flu epidemic, and find striking geographical and cultural correlations in the results. We find that after 1960, the variance of period mortality shocks has declined by an average factor of 5 in most of the countries we examine. Over the same period, cohort shocks appear to have become a more important factor causing changes in mortality than period shocks. We also find that period and cohort shocks appear to be driven by different underlying factors. Our results have important implications for stochastic mortality modeling, and may explain why stochastic mortality models that rely largely on period mortality shocks struggle to generate sufficient variation in mortality rates. Our results will also be useful to those who construct reinsurance portfolios, those who issue or trade longevity-linked securities, and those who study the origins of human mortality.

ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging

In electrocardiographic imaging (ECGI), one solves the inverse problem of electrocardiography (ECG) to reconstruct equivalent cardiac sources based on the body surface potential measurements and a mathematical model of the torso. Due to attenuation and spatial smoothing within the torso, this inverse problem is ill-posed. Among many regularization approaches used in the ECG literature to overcome this ill-posedness, statistical techniques have received great attention because of their flexibility to represent the data, and ability to provide performance evaluation tools for quantification of uncertainties and errors in the model. However, despite their potential to accurately reconstruct the equivalent cardiac sources, one major challenge in these methods is how to best utilize the prior information available in terms of training data. In this paper, we address the question of how to define the prior probability distributions (pdf) of the sources and the error terms so that we can obtain more accurate and robust inverse solutions. We employ two methods, maximum likelihood (ML) and maximum a posteriori (MAP), for estimating the model parameters such as the prior pdfs, error pdfs, and the state-transition matrix, based on the same training data. These model parameters are then used for the state-space representation and estimation of the epicardial potentials, which constitute the equivalent cardiac sources in this study. The performances of ML- and MAP-based model parameter estimation methods are evaluated qualitatively and quantitatively at various noise levels and geometric disturbances using two different simulated datasets. Bayesian MAP estimation, which is also a well-known statistical inversion technique, and Tikhonov regularization, which can be formulated as a special and simplified version of Bayesian MAP estimation, have been included here for comparison with the Kalman filtering method. Our results show that the state-space approach outperforms Bayesian MAP estimation in all cases; ML yields accurate results when the test and training beats come from the same physiological model, but MAP is superior to ML, especially if the test and training beats are from different physiological models. Graphical Abstract ML and MAP estimation of parameters for the Kalman filter and smoother applied to electrocardiographic imaging.

A novel image fusion algorithm based on 2D scale-mixing complex wavelet transform and Bayesian MAP estimation for multimodal medical images

In this paper, we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform (2D-SMCWT). The fusion of the detail 2D-SMCWT coefficients is performed via a Bayesian Maximum a Posteriori (MAP) approach by considering a trivariate statistical model for the local neighboring of 2D-SMCWT coefficients. For the approximation coefficients, a new fusion rule based on the Principal Component Analysis (PCA) is applied. We conduct several experiments using three different groups of multimodal medical images to evaluate the performance of the proposed method. The obtained results prove the superiority of the proposed method over the state of the art fusion methods in terms of visual quality and several commonly used metrics. Robustness of the proposed method is further tested against different types of noise. The plots of fusion metrics establish the accuracy of the proposed fusion method.

Congested Link Inference Algorithms in Dynamic Routing IP Network

The performance descending of current congested link inference algorithms is obviously in dynamic routing IP network, such as the most classical algorithm CLINK. To overcome this problem, based on the assumptions of Markov property and time homogeneity, we build a kind of Variable Structure Discrete Dynamic Bayesian (VSDDB) network simplified model of dynamic routing IP network. Under the simplified VSDDB model, based on the Bayesian Maximum A Posteriori (BMAP) and Rest Bayesian Network Model (RBNM), we proposed an Improved CLINK (ICLINK) algorithm. Considering the concurrent phenomenon of multiple link congestion usually happens, we also proposed algorithm CLILRS (Congested Link Inference algorithm based on Lagrangian Relaxation Subgradient) to infer the set of congested links. We validated our results by the experiments of analogy, simulation, and actual Internet.

Single Snapshot Detection and Estimation of Reflections From Room Impulse Responses in the Spherical Harmonic Domain

We study the detection and estimation of the parameters related to the deterministic model of the reflections of room impulse responses measured with a spherical microphone array. More specifically, we investigate the problem of detecting and estimating several reflections of a single snapshot of data in the spherical harmonic (SH) domain with four detection and four estimation methods, presented previously in the array processing research. Three of the estimation methods are based on Bayesian Maximum a Posteriori (MAP) estimation, and they employ a prior normal distribution on the signals. The estimation methods are compared with the deterministic maximum likelihood (DML) method [Tervo & Politis 2015]. In the detection task, two information criteria-based methods, minimum description length (MDL) and Akaike information criteria (AIC), a normalized likelihood (NL) based method, and a Bayesian detection scheme (BDS) are explored. The experiments study the performance of the methods with simulated and real data experiments. The simulation results show that the MAP estimation methods have a lower root mean squared error (RMSE) than DML in the reflection signal amplitude estimation, but all three have similar performance in the direction of arrival (DOA) and noise variance estimation, although in general RMSE of DOA estimation of MAP methods is slightly lower that that of DML. In addition, in the detection task, the BDS and AIC are the most robust against additive noise, and NL and AIC have the best detection rate when more than two reflections are simulated. The results of the real data experiments show that all the estimation methods have similar performance for DOA and noise variance estimation, while the Bayesian MAP methods have a clearly lower RMSE for reflection signal amplitude estimation than DML. In total, NL has the highest detection rate in the real data experiments.

SAR Image Despeckling Based on a Mixture of Gaussian Distributions with Local Parameters and Multiscale Edge Detection in Lapped Transform Domain

A new Lapped transform domain SAR image despeckling algorithm using a two-state Gaussian mixture probability density function that uses local parameters for the mixture model, is proposed. The use of lapped orthogonal transform (LOT) is motivated by its low computational complexity and robustness to oversmoothing. It is shown that the dyadic rearranged LOT coefficients of logarithmically transformed SAR images can be well approximated using two-state Gaussian mixture distribution compared to Laplacian, Gamma, generalized Gaussian and Cauchy distributions, based on the Kolmogorov–Smirnov (KS) goodness of fit test. The LOT coefficients of speckle noise are modeled using zero mean Gaussian distributions. A maximum a posteriori (MAP) estimator within Bayesian framework is developed using this proposed prior distribution and is used to restore the noisy LOT coefficients. The parameters of mixture distribution are estimated using the expectation-maximization algorithm. This paper presents a new technique to identify LOT modulus maxima which allows us to classify LOT coefficients into the edge and non edge coefficients. The classified edge coefficients are kept unmodified by the proposed algorithm whereas the noise-free estimates of non-edge coefficients are obtained using Bayesian MAP estimator developed using two state Gaussian mixture distribution with local parameters. Finally the proposed technique is combined with the cycle spinning scheme to further improve the despeckling performance. Experimental results show that the proposed method very efficiently reduces speckle in homogeneous regions while preserving more edge structures compared to some recent well known methods.

A high quality single-image super-resolution algorithm based on linear Bayesian MAP estimation with sparsity prior

This paper proposes a novel single-image super-resolution algorithm based on linear Bayesian maximum a posteriori (MAP) estimation and sparse representation. Starting from constructing several probability distribution priors in representation vector, we develop a linear Bayesian MAP estimator to acquire the most probable high-resolution (HR) image behind the low-resolution (LR) observation. Our new algorithm involves three main steps: (1) obtaining an initial estimate of the HR image via bi-cubic interpolation algorithm, (2) performing sparse coding on the initial estimate to get the representation vector and its support, (3) using the MAP estimator to restore the desired representation vector and then reconstructing the HR output. Simulated results show that the proposed method can achieve a more competitive performance both in subjective visual quality and in peak-signal-to-noise ratio (PSNR) and structural similarity (SSIM) measures, compared with other state-of-the-art super-resolution methods.

A novel image denoising algorithm using linear Bayesian MAP estimation based on sparse representation

A novel image denoising algorithm using linear Bayesian maximum a posteriori (MAP) estimation based on sparse representation model is proposed. Starting from constructing prior probability distribution in representation vector, a linear Bayesian MAP estimator is constructed in order to acquire the most probable one behind the observations, which is adaptive to solve the generalized image inverse problems. Furthermore, a practical closed-form solution by affording some plausible approximations is obtained, and thus image denoising as a specialization can be easily solved. With our new method, we first extract all possible patches from noisy images and classify them to several sub-groups by their structural patterns, then train a different dictionary per each using the K-SVD algorithm, following by estimating corresponding parameters in MAP estimator. The final denoised image is obtained by applying denoising on each sub-group based on the estimator and averaging these outputs together. Simulated results show that the proposed method achieves a very competitive performance both in subjective visual quality and objective PSNR value, compared with other state-of-the-art denoising algorithms.

Directionlet-based method using the Gaussian mixture prior to SAR image despeckling

In this article, a new denoising algorithm is proposed based on the directionlet transform and the maximum a posteriori (MAP) estimation. The detailed directionlet coefficients of the logarithmically transformed noise-free image are considered to be Gaussian mixture probability density functions (PDFs) with zero means, and the speckle noise in the directionlet domain is modelled as additive noise with a Gaussian distribution. Then, we develop a Bayesian MAP estimator using these assumed prior distributions. Because the estimator that is the solution of the MAP equation is a function of the parameters of the assumed mixture PDF models, the expectation-maximization (EM) algorithm is also utilized to estimate the parameters, including weight factors and variances. Finally, the noise-free SAR image is restored from the estimated coefficients yielded by the MAP estimator. Experimental results show that the directionlet-based MAP method can be successfully applied to images and real synthetic aperture radar images to denoise speckle.

Fusing cluster-centric feature similarities for face recognition in video sequences

The emergence of video has presented new challenges to the problem of face recognition. Most of the existing methods are focused towards the use of either representative exemplars or image sets to summarize videos. There is little work as to how they can be combined effectively to harness their individual strengths. In this paper, we investigate a new dual-feature approach to face recognition in video sequences that unifies feature similarities derived within local appearance-based clusters. Relevant similarity matching involving exemplar points and cluster subspaces are comprehensively modeled within a Bayesian maximum-a posteriori (MAP) classification framework. An extensive performance evaluation of the proposed method on three face video datasets have demonstrated promising results.

Influence of Erroneous Patient Records on Population Pharmacokinetic Modeling and Individual Bayesian Estimation

Observational data sets can be used for population pharmacokinetic (PK) modeling. However, these data sets are generally less precisely recorded than experimental data sets. This article aims to investigate the influence of erroneous records on population PK modeling and individual maximum a posteriori Bayesian (MAPB) estimation. A total of 1123 patient records of neonates who were administered vancomycin were used for population PK modeling by iterative 2-stage Bayesian (ITSB) analysis. Cut-off values for weighted residuals were tested for exclusion of records from the analysis. A simulation study was performed to assess the influence of erroneous records on population modeling and individual MAPB estimation. Also the cut-off values for weighted residuals were tested in the simulation study. Errors in registration have limited the influence on outcomes of population PK modeling but can have detrimental effects on individual MAPB estimation. A population PK model created from a data set with many registration errors has little influence on subsequent MAPB estimates for precisely recorded data. A weighted residual value of 2 for concentration measurements has good discriminative power for identification of erroneous records. ITSB analysis and its individual estimates are hardly affected by most registration errors. Large registration errors can be detected by weighted residuals of concentration.

Bayesian image interpolation using Markov random fields driven by visually relevant image features

In this paper we present a Markov Random Field (MRF) based image interpolation procedure suited to both noise-free and noisy measurements. Specifically, after introducing a MRF characterized by means of a novel complex line process representing the visually relevant image features, we derive the global Maximum A Posteriori (MAP) interpolator under the hypothesis of spatially variant additive Gaussian noise. Besides, we derive a closed form local Bayesian MAP interpolator, on the base of which we develop a suboptimal, computationally efficient, single pass interpolation procedure. Numerical simulations demonstrate that the interpolation procedure outperforms state-of-the-art techniques, from both a subjective and objective point of view, in the case of noise-free and noisy measurements.

Spatial cluster detection using dynamic programming

BackgroundThe task of spatial cluster detection involves finding spatial regions where some property deviates from the norm or the expected value. In a probabilistic setting this task can be expressed as finding a region where some event is significantly more likely than usual. Spatial cluster detection is of interest in fields such as biosurveillance, mining of astronomical data, military surveillance, and analysis of fMRI images. In almost all such applications we are interested both in the question of whether a cluster exists in the data, and if it exists, we are interested in finding the most accurate characterization of the cluster.MethodsWe present a general dynamic programming algorithm for grid-based spatial cluster detection. The algorithm can be used for both Bayesian maximum a-posteriori (MAP) estimation of the most likely spatial distribution of clusters and Bayesian model averaging over a large space of spatial cluster distributions to compute the posterior probability of an unusual spatial clustering. The algorithm is explained and evaluated in the context of a biosurveillance application, specifically the detection and identification of Influenza outbreaks based on emergency department visits. A relatively simple underlying model is constructed for the purpose of evaluating the algorithm, and the algorithm is evaluated using the model and semi-synthetic test data.ResultsWhen compared to baseline methods, tests indicate that the new algorithm can improve MAP estimates under certain conditions: the greedy algorithm we compared our method to was found to be more sensitive to smaller outbreaks, while as the size of the outbreaks increases, in terms of area affected and proportion of individuals affected, our method overtakes the greedy algorithm in spatial precision and recall. The new algorithm performs on-par with baseline methods in the task of Bayesian model averaging.ConclusionsWe conclude that the dynamic programming algorithm performs on-par with other available methods for spatial cluster detection and point to its low computational cost and extendability as advantages in favor of further research and use of the algorithm.