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.

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.

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.

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.

Implicit probabilistic sequence learning: Correlated streams and sequence length matter

We investigated whether a pure perceptual stream is sufficient for probabilistic sequence learning to occur within a single session or whether correlated streams are necessary, whether learning is affected by the transition probability between sequence elements, and how the sequence length influences learning. In each of three experiments, we used six horizontally arranged stimulus displays which consisted of randomly ordered bigrams xo and ox. The probability of the next possible target location out of two was either .50/.50 or .75/.25 and was marked by an underline. In Experiment 1, a left vs. right key response was required for the x of a marked bigram in the pure perceptual learning condition and a response key press corresponding to the marked bigram location (out of 6) was required in the correlated streams condition (i.e., the ring, middle, or index finger of the left and right hand, respectively). The same probabilistic 3-element sequence was used in both conditions. Learning occurred only in the correlated streams condition. In Experiment 2, we investigated whether sequence length affected learning correlated sequences by contrasting the 3-elements sequence with a 6-elements sequence. Significant sequence learning occurred in all conditions. In Experiment 3, we removed a potential confound, that is, the sequence of hand changes. Under these conditions, learning occurred for the 3-element sequence only and transition probability did not affect the amount of learning. Together, these results indicate that correlated streams are necessary for probabilistic sequence learning within a single session and that sequence length can reduce the chances for learning to occur.

Probabilistic models for the prediction of a ship performance in dynamic ice

We introduce two probabilistic, data-driven models that predict a ship's speed and the situations where a ship is probable to get stuck in ice based on the joint effect of ice features such as the thickness and concentration of level ice, ice ridges, rafted ice, moreover ice compression is considered. To develop the models to datasets were utilized. First, the data from the Automatic Identification System about the performance of a selected ship was used. Second, a numerical ice model HELMI, developed in the Finnish Meteorological Institute, provided information about the ice field. The relations between the ice conditions and ship movements were established using Bayesian learning algorithms. The case study presented in this paper considers a single and unassisted trip of an ice-strengthened bulk carrier between two Finnish ports in the presence of challenging ice conditions, which varied in time and space. The obtained results show good prediction power of the models. This means, on average 80% for predicting the ship's speed within specified bins, and above 90% for predicting cases where a ship may get stuck in ice. We expect this new approach to facilitate the safe and effective route selection problem for ice-covered waters where the ship performance is reflected in the objective function.

A probabilistic model estimating oil spill clean-up costs - a case study for the Gulf of Finland

Existing models estimating oil spill costs at sea are based on data from the past, and they usually lack a systematic approach. This make them passive, and limits their ability to forecast the effect of the changes in the oil combating fleet or location of a spill on the oil spill costs. In this paper we make an attempt towards the development of a probabilistic and systematic model estimating the costs of clean-up operations for the Gulf of Finland. For this purpose we utilize expert knowledge along with the available data and information from literature. Then, the obtained information is combined into a framework with the use of a Bayesian Belief Networks. Due to lack of data, we validate the model by comparing its results with existing models, with which we found good agreement. We anticipate that the presented model can contribute to the cost-effective oil-combating fleet optimization for the Gulf of Finland. It can also facilitate the accident consequences estimation in the framework of formal safety assessment (FSA).

Probabilistic Atlas Based Segmentation Using Affine Moment Descriptors and Graph-Cuts

We show a procedure for constructing a probabilistic atlas based on affine moment descriptors. It uses a normalization procedure over the labeled atlas. The proposed linear registration is defined by closed-form expressions involving only geometric moments. This procedure applies both to atlas construction as atlas-based segmentation. We model the likelihood term for each voxel and each label using parametric or nonparametric distributions and the prior term is determined by applying the vote-rule. The probabilistic atlas is built with the variability of our linear registration. We have two segmentation strategy: a) it applies the proposed affine registration to bring the target image into the coordinate frame of the atlas or b) the probabilistic atlas is non-rigidly aligning with the target image, where the probabilistic atlas is previously aligned to the target image with our affine registration. Finally, we adopt a graph cut - Bayesian framework for implementing the atlas-based segmentation.