Representation via Probabilities: Models of Probabilistic Modeling

How do probabilistic models represent their targets and how do they allow us to learn about them? The answer to this question depends on a number of details, in particular on the meaning of the probabilities involved. To classify the options, a minimalist conception of representation (Su\'arez 2004) is adopted: Modelers devise substitutes (``sources'') of their targets and investigate them to infer something about the target. Probabilistic models allow us to infer probabilities about the target from probabilities about the source. This leads to a framework in which we can systematically distinguish between different models of probabilistic modeling. I develop a fully Bayesian view of probabilistic modeling, but I argue that, as an alternative, Bayesian degrees of belief about the target may be derived from ontic probabilities about the source. Remarkably, some accounts of ontic probabilities can avoid problems if they are supposed to apply to sources only.

Probabilistic approach to cloud and snow detection on Advanced Very High Resolution Radiometer (AVHRR) imagery

Derivation of probability estimates complementary to geophysical data sets has gained special attention over the last years. Information about a confidence level of provided physical quantities is required to construct an error budget of higher-level products and to correctly interpret final results of a particular analysis. Regarding the generation of products based on satellite data a common input consists of a cloud mask which allows discrimination between surface and cloud signals. Further the surface information is divided between snow and snow-free components. At any step of this discrimination process a misclassification in a cloud/snow mask propagates to higher-level products and may alter their usability. Within this scope a novel probabilistic cloud mask (PCM) algorithm suited for the 1 km × 1 km Advanced Very High Resolution Radiometer (AVHRR) data is proposed which provides three types of probability estimates between: cloudy/clear-sky, cloudy/snow and clear-sky/snow conditions. As opposed to the majority of available techniques which are usually based on the decision-tree approach in the PCM algorithm all spectral, angular and ancillary information is used in a single step to retrieve probability estimates from the precomputed look-up tables (LUTs). Moreover, the issue of derivation of a single threshold value for a spectral test was overcome by the concept of multidimensional information space which is divided into small bins by an extensive set of intervals. The discrimination between snow and ice clouds and detection of broken, thin clouds was enhanced by means of the invariant coordinate system (ICS) transformation. The study area covers a wide range of environmental conditions spanning from Iceland through central Europe to northern parts of Africa which exhibit diverse difficulties for cloud/snow masking algorithms. The retrieved PCM cloud classification was compared to the Polar Platform System (PPS) version 2012 and Moderate Resolution Imaging Spectroradiometer (MODIS) collection 6 cloud masks, SYNOP (surface synoptic observations) weather reports, Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) vertical feature mask version 3 and to MODIS collection 5 snow mask. The outcomes of conducted analyses proved fine detection skills of the PCM method with results comparable to or better than the reference PPS algorithm.

Probabilistic contingency learning with limbic or prefrontal damage

AB A fundamental capacity of the human brain is to learn relations (contingencies) between environmental stimuli and the consequences of their occurrence. Some contingencies are probabilistic; that is, they predict an event in some situations but not in all. Animal studies suggest that damage to limbic structures or the prefrontal cortex may disturb probabilistic learning. The authors studied the learning of probabilistic contingencies in amnesic patients with limbic lesions, patients with prefrontal cortex damage, and healthy controls. Across 120 trials, participants learned contingent relations between spatial sequences and a button press. Amnesic patients had learning comparable to that of control subjects but failed to indicate what they had learned. Across the last 60 trials, amnesic patients and control subjects learned to avoid a noncontingent choice better than frontal patients. These results indicate that probabilistic learning does not depend on the brain structures supporting declarative memory.

Cardiopulmonary performance testing using a robotics-assisted tilt table: Feasibility assessment in able-bodied subjects

BACKGROUND: Robotics-assisted tilt table technology was introduced for early rehabilitation of neurological patients. It provides cyclical stepping movement and physiological loading of the legs. The aim of the present study was to assess the feasibility of this type of device for peak cardiopulmonary performance testing using able-bodied subjects. METHODS: A robotics-assisted tilt table was augmented with force sensors in the thigh cuffs and a work rate estimation algorithm. A custom visual feedback system was employed to guide the subjects' work rate and to provide real time feedback of actual work rate. Feasibility assessment focused on: (i) implementation (technical feasibility), and (ii) responsiveness (was there a measurable, high-level cardiopulmonary reaction?). For responsiveness testing, each subject carried out an incremental exercise test to the limit of functional capacity with a work rate increment of 5 W/min in female subjects and 8 W/min in males. RESULTS: 11 able-bodied subjects were included (9 male, 2 female; age 29.6 ± 7.1 years: mean ± SD). Resting oxygen uptake (O_{2}) was 4.6 ± 0.7 mL/min/kg and O_{2}peak was 32.4 ± 5.1 mL/min/kg; this mean O_{2}peak was 81.1% of the predicted peak value for cycle ergometry. Peak heart rate (HRpeak) was 177.5 ± 9.7 beats/min; all subjects reached at least 85% of their predicted HRpeak value. Respiratory exchange ratio (RER) at O_{2}peak was 1.02 ± 0.07. Peak work rate) was 61.3 ± 15.1 W. All subjects reported a Borg CR10 value for exertion and leg fatigue of 7 or more. CONCLUSIONS: The robotics-assisted tilt table is deemed feasible for peak cardiopulmonary performance testing: the approach was found to be technically implementable and substantial cardiopulmonary responses were observed. Further testing in neurologically-impaired subjects is warranted.

Privacy Preserving Probabilistic Record Linkage (P3RL): a novel method for linking existing health-related data and maintaining participant confidentiality.

BACKGROUND Record linkage of existing individual health care data is an efficient way to answer important epidemiological research questions. Reuse of individual health-related data faces several problems: Either a unique personal identifier, like social security number, is not available or non-unique person identifiable information, like names, are privacy protected and cannot be accessed. A solution to protect privacy in probabilistic record linkages is to encrypt these sensitive information. Unfortunately, encrypted hash codes of two names differ completely if the plain names differ only by a single character. Therefore, standard encryption methods cannot be applied. To overcome these challenges, we developed the Privacy Preserving Probabilistic Record Linkage (P3RL) method. METHODS In this Privacy Preserving Probabilistic Record Linkage method we apply a three-party protocol, with two sites collecting individual data and an independent trusted linkage center as the third partner. Our method consists of three main steps: pre-processing, encryption and probabilistic record linkage. Data pre-processing and encryption are done at the sites by local personnel. To guarantee similar quality and format of variables and identical encryption procedure at each site, the linkage center generates semi-automated pre-processing and encryption templates. To retrieve information (i.e. data structure) for the creation of templates without ever accessing plain person identifiable information, we introduced a novel method of data masking. Sensitive string variables are encrypted using Bloom filters, which enables calculation of similarity coefficients. For date variables, we developed special encryption procedures to handle the most common date errors. The linkage center performs probabilistic record linkage with encrypted person identifiable information and plain non-sensitive variables. RESULTS In this paper we describe step by step how to link existing health-related data using encryption methods to preserve privacy of persons in the study. CONCLUSION Privacy Preserving Probabilistic Record linkage expands record linkage facilities in settings where a unique identifier is unavailable and/or regulations restrict access to the non-unique person identifiable information needed to link existing health-related data sets. Automated pre-processing and encryption fully protect sensitive information ensuring participant confidentiality. This method is suitable not just for epidemiological research but also for any setting with similar challenges.

Comparison of peak cardiopulmonary performance parameters on a robotics-assisted tilt table, a cycle and a treadmill

Robotics-assisted tilt table (RATT) technology provides body support, cyclical stepping movement and physiological loading. This technology can potentially be used to facilitate the estimation of peak cardiopulmonary performance parameters in patients who have neurological or other problems that may preclude testing on a treadmill or cycle ergometer. The aim of the study was to compare the magnitude of peak cardiopulmonary performance parameters including peak oxygen uptake (VO2peak) and peak heart rate (HRpeak) obtained from a robotics-assisted tilt table (RATT), a cycle ergometer and a treadmill. The strength of correlations between the three devices, test-retest reliability and repeatability were also assessed. Eighteen healthy subjects performed six maximal exercise tests, with two tests on each of the three exercise modalities. Data from the second tests were used for the comparative and correlation analyses. For nine subjects, test-retest reliability and repeatability of VO2peak and HRpeak were assessed. Absolute VO2peak from the RATT, the cycle ergometer and the treadmill was (mean (SD)) 2.2 (0.56), 2.8 (0.80) and 3.2 (0.87) L/min, respectively (p < 0.001). HRpeak from the RATT, the cycle ergometer and the treadmill was 168 (9.5), 179 (7.9) and 184 (6.9) beats/min, respectively (p < 0.001). VO2peak and HRpeak from the RATT vs the cycle ergometer and the RATT vs the treadmill showed strong correlations. Test-retest reliability and repeatability were high for VO2peak and HRpeak for all devices. The results demonstrate that the RATT is a valid and reliable device for exercise testing. There is potential for the RATT to be used in severely impaired subjects who cannot use the standard modalities.

First steps towards probabilistic justification logic

In this article, we introduce the probabilistic justification logic PJ, a logic in which we can reason about the probability of justification statements. We present its syntax and semantics, and establish a strong completeness theorem. Moreover, we investigate the relationship between PJ and the logic of uncertain justifications.

Feasibility of cardiopulmonary exercise testing and training using a robotics-assisted tilt table in dependent-ambulatory stroke patients

BACKGROUND: We evaluated the feasibility of an augmented robotics-assisted tilt table (RATT) for incremental cardiopulmonary exercise testing (CPET) and exercise training in dependent-ambulatory stroke patients. METHODS: Stroke patients (Functional Ambulation Category ≤ 3) underwent familiarization, an incremental exercise test (IET) and a constant load test (CLT) on separate days. A RATT equipped with force sensors in the thigh cuffs, a work rate estimation algorithm and real-time visual feedback to guide the exercise work rate was used. Feasibility assessment considered technical feasibility, patient tolerability, and cardiopulmonary responsiveness. RESULTS: Eight patients (4 female) aged 58.3 ± 9.2 years (mean ± SD) were recruited and all completed the study. For IETs, peak oxygen uptake (V'O2peak), peak heart rate (HRpeak) and peak work rate (WRpeak) were 11.9 ± 4.0 ml/kg/min (45 % of predicted V'O2max), 117 ± 32 beats/min (72 % of predicted HRmax) and 22.5 ± 13.0 W, respectively. Peak ratings of perceived exertion (RPE) were on the range "hard" to "very hard". All 8 patients reached their limit of functional capacity in terms of either their cardiopulmonary or neuromuscular performance. A ventilatory threshold (VT) was identified in 7 patients and a respiratory compensation point (RCP) in 6 patients: mean V'O2 at VT and RCP was 8.9 and 10.7 ml/kg/min, respectively, which represent 75 % (VT) and 85 % (RCP) of mean V'O2peak. Incremental CPET provided sufficient information to satisfy the responsiveness criteria and identification of key outcomes in all 8 patients. For CLTs, mean steady-state V'O2 was 6.9 ml/kg/min (49 % of V'O2 reserve), mean HR was 90 beats/min (56 % of HRmax), RPEs were > 2, and all patients maintained the active work rate for 10 min: these values meet recommended intensity levels for bouts of training. CONCLUSIONS: The augmented RATT is deemed feasible for incremental cardiopulmonary exercise testing and exercise training in dependent-ambulatory stroke patients: the approach was found to be technically implementable, acceptable to the patients, and it showed substantial cardiopulmonary responsiveness. This work has clinical implications for patients with severe disability who otherwise are not able to be tested.

Submaximal cardiopulmonary thresholds on a robotics-assisted tilt table, a cycle and a treadmill: a comparative analysis

BACKGROUND: The robotics-assisted tilt table (RATT), including actuators for tilting and cyclical leg movement, is used for rehabilitation of severely disabled neurological patients. Following further engineering development of the system, i.e. the addition of force sensors and visual bio-feedback, patients can actively participate in exercise testing and training on the device. Peak cardiopulmonary performance parameters were previously investigated, but it also important to compare submaximal parameters with standard devices. The aim of this study was to evaluate the feasibility of the RATT for estimation of submaximal exercise thresholds by comparison with a cycle ergometer and a treadmill. METHODS: 17 healthy subjects randomly performed six maximal individualized incremental exercise tests, with two tests on each of the three exercise modalities. The ventilatory anaerobic threshold (VAT) and respiratory compensation point (RCP) were determined from breath-by-breath data. RESULTS: VAT and RCP on the RATT were lower than the cycle ergometer and the treadmill: oxygen uptake (V'O2) at VAT was [mean (SD)] 1.2 (0.3), 1.5 (0.4) and 1.6 (0.5) L/min, respectively (p < 0.001); V'O2 at RCP was 1.7 (0.4), 2.3 (0.8) and 2.6 (0.9) L/min, respectively (p = 0.001). High correlations for VAT and RCP were found between the RATT vs the cycle ergometer and RATT vs the treadmill (R on the range 0.69-0.80). VAT and RCP demonstrated excellent test-retest reliability for all three devices (ICC from 0.81 to 0.98). Mean differences between the test and retest values on each device were close to zero. The ventilatory equivalent for O2 at VAT for the RATT and cycle ergometer were similar and both were higher than the treadmill. The ventilatory equivalent for CO2 at RCP was similar for all devices. Ventilatory equivalent parameters demonstrated fair-to-excellent reliability and repeatability. CONCLUSIONS: It is feasible to use the RATT for estimation of submaximal exercise thresholds: VAT and RCP on the RATT were lower than the cycle ergometer and the treadmill, but there were high correlations between the RATT vs the cycle ergometer and vs the treadmill. Repeatability and test-retest reliability of all submaximal threshold parameters from the RATT were comparable to those of standard devices.

Predicting the onset of psychosis in patients at clinical high risk: practical guide to probabilistic prognostic reasoning

Prediction of psychosis in patients at clinical high risk (CHR) has become a mainstream focus of clinical and research interest worldwide. When using CHR instruments for clinical purposes, the predicted outcome is but only a probability; and, consequently, any therapeutic action following the assessment is based on probabilistic prognostic reasoning. Yet, probabilistic reasoning makes considerable demands on the clinicians. We provide here a scholarly practical guide summarising the key concepts to support clinicians with probabilistic prognostic reasoning in the CHR state. We review risk or cumulative incidence of psychosis in, person-time rate of psychosis, Kaplan-Meier estimates of psychosis risk, measures of prognostic accuracy, sensitivity and specificity in receiver operator characteristic curves, positive and negative predictive values, Bayes’ theorem, likelihood ratios, potentials and limits of real-life applications of prognostic probabilistic reasoning in the CHR state. Understanding basic measures used for prognostic probabilistic reasoning is a prerequisite for successfully implementing the early detection and prevention of psychosis in clinical practice. Future refinement of these measures for CHR patients may actually influence risk management, especially as regards initiating or withholding treatment.

The Complexity of Non-Iterated Probabilistic Justification Logic

The logic PJ is a probabilistic logic defined by adding (noniterated) probability operators to the basic justification logic J. In this paper we establish upper and lower bounds for the complexity of the derivability problem in the logic PJ. The main result of the paper is that the complexity of the derivability problem in PJ remains the same as the complexity of the derivability problem in the underlying logic J, which is π[p/2] -complete. This implies that the probability operators do not increase the complexity of the logic, although they arguably enrich the expressiveness of the language.

Probabilistic Justification Logic

We present a probabilistic justification logic, PPJ, to study rational belief, degrees of belief and justifications. We establish soundness and completeness for PPJ and show that its satisfiability problem is decidable. In the last part we use PPJ to provide a solution to the lottery paradox.

Investigation of robotics-assisted tilt table technology for cardiopulmonary exercise testing in stroke patients

Due to the lack of exercise testing devices that can be employed in stroke patients with severe disability, the aim of this PhD research was to investigate the clinical feasibility of using a robotics-assisted tilt table (RATT) as a method for cardiopulmonary exercise testing (CPET) and exercise training in stroke patients. For this purpose, the RATT was augmented with force sensors, a visual feedback system and a work rate calculation algorithm. As the RATT had not been used previously for CPET, the first phase of this project focused on a feasibility study in 11 healthy able-bodied subjects. The results demonstrated substantial cardiopulmonary responses, no complications were found, and the method was deemed feasible. The second phase was to analyse validity and test-retest reliability of the primary CPET parameters obtained from the RATT in 18 healthy able-bodied subjects and to compare the outcomes to those obtained from standard exercise testing devices (a cycle ergometer and a treadmill). The results demonstrated that peak oxygen uptake (V'O2peak) and oxygen uptake at the submaximal exercise thresholds on the RATT were ̴20% lower than for the cycle ergometer and ̴30% lower than on the treadmill. A very high correlation was found between the RATT vs the cycle ergometer V'O2peak and the RATT vs the treadmill V'O2peak. Test-retest reliability of CPET parameters obtained from the RATT were similarly high to those for standard exercise testing devices. These findings suggested that the RATT is a valid and reliable device for CPET and that it has potential to be used in severely impaired patients. Thus, the third phase was to investigate using the RATT for CPET and exercise training in 8 severely disabled stroke patients. The method was technically implementable, well tolerated by the patients, and substantial cardiopulmonary responses were observed. Additionally, all patients could exercise at the recommended training intensity for 10 min bouts. Finally, an investigation of test-retest reliability and four-week changes in cardiopulmonary fitness was carried out in 17 stroke patients with various degrees of disability. Good to excellent test-retest reliability and repeatability were found for the main CPET variables. There was no significant difference in most CPET parameters over four weeks. In conclusion, based on the demonstrated validity, reliability and repeatability, the RATT was found to be a feasible and appropriate alternative exercise testing and training device for patients who have limitations for use of standard devices.