Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

A Probabilistic Approach to the Primary Visual Cortex

What can the statistical structure of natural images teach us about the human brain? Even though the visual cortex is one of the most studied parts of the brain, surprisingly little is known about how exactly images are processed to leave us with a coherent percept of the world around us, so we can recognize a friend or drive on a crowded street without any effort. By constructing probabilistic models of natural images, the goal of this thesis is to understand the structure of the stimulus that is the raison d etre for the visual system. Following the hypothesis that the optimal processing has to be matched to the structure of that stimulus, we attempt to derive computational principles, features that the visual system should compute, and properties that cells in the visual system should have. Starting from machine learning techniques such as principal component analysis and independent component analysis we construct a variety of sta- tistical models to discover structure in natural images that can be linked to receptive field properties of neurons in primary visual cortex such as simple and complex cells. We show that by representing images with phase invariant, complex cell-like units, a better statistical description of the vi- sual environment is obtained than with linear simple cell units, and that complex cell pooling can be learned by estimating both layers of a two-layer model of natural images. We investigate how a simplified model of the processing in the retina, where adaptation and contrast normalization take place, is connected to the nat- ural stimulus statistics. Analyzing the effect that retinal gain control has on later cortical processing, we propose a novel method to perform gain control in a data-driven way. Finally we show how models like those pre- sented here can be extended to capture whole visual scenes rather than just small image patches. By using a Markov random field approach we can model images of arbitrary size, while still being able to estimate the model parameters from the data.

A probabilistic approach to the problem of electron localization in disordered systems and sharpness of the mobility edge

By applying the theory of the asymptotic distribution of extremes and a certain stability criterion to the question of the domain of convergence in the probability sense, of the renormalized perturbation expansion (RPE) for the site self-energy in a cellularly disordered system, an expression has been obtained in closed form for the probability of nonconvergence of the RPE on the real-energy axis. Hence, the intrinsic mobility mu (E) as a function of the carrier energy E is deduced to be given by mu (E)= mu 0exp(-exp( mod E mod -Ec) Delta ), where Ec is a nominal 'mobility edge' and Delta is the width of the random site-energy distribution. Thus mobility falls off sharply but continuously for mod E mod >Ec, in contradistinction with the notion of an abrupt 'mobility edge' proposed by Cohen et al. and Mott. Also, the calculated electrical conductivity shows a temperature dependence in qualitative agreement with experiments on disordered semiconductors.

Technological-forecasting and research inputs in area of birth-control technology

Technological forecasting, defined as quantified probabilistic prediction of timings and degree of change in the technological parameters, capabilities desirability or needs at different times in the future, is applied to birth control technology (BCT) as a means of revealing the paths of most promising research through identifying the necessary points for breakthroughs. The present status of BCT in the areas of pills and the IUD, male contraceptives, immumological approaches, post-coital pills, abortion, sterilization, luteolytic agents, laser technologies, and control of the sex of the child, are each summarized and evaluated in turn. Fine mapping is done to identify the most potentially promising areas of BCT. These include efforts to make oral contraception easier, improvement of the design of the IUD, clinical evaluation of the male contraceptive danazol, the effecting of biochemical changes in the seminal fluid, and researching of immunological approaches and the effects of other new drugs such as prostaglandins. The areas that require immediate and large research inputs are oral contraception and the IUD. On the basis of population and technological forecasts, it is deduced that research efforts could most effectively aid countries like India through the immediate production of an oral contraceptive pill or IUD with long-lasting effects. Development of a pill for males or an immunization against pre gnancy would also have a significant impact. However, the major impediment to birth control programs to date is attitudes, which must be changed through education.

Efficient probabilistic contingency analysis through a stability measure considering wind perturbation

The integration of stochastic wind power has accentuated a challenge for power system stability assessment. Since the power system is a time-variant system under wind generation fluctuations, pure time-domain simulations are difficult to provide real-time stability assessment. As a result, the worst-case scenario is simulated to give a very conservative assessment of system transient stability. In this study, a probabilistic contingency analysis through a stability measure method is proposed to provide a less conservative contingency analysis which covers 5-min wind fluctuations and a successive fault. This probabilistic approach would estimate the transfer limit of a critical line for a given fault with stochastic wind generation and active control devices in a multi-machine system. This approach achieves a lower computation cost and improved accuracy using a new stability measure and polynomial interpolation, and is feasible for online contingency analysis.

Development of probabilistic understanding in fourth grade

We analyzed the development of 4th-grade students’ understanding of the transition from experimental relative frequencies of outcomes to theoretical probabilities with a focus on the foundational statistical concepts of variation and expectation. We report students’ initial and changing expectations of the outcomes of tossing one and two coins, how they related the relative frequency from their physical and computersimulated trials to the theoretical probability, and how they created and interpreted theoretical probability models. Findings include students’ progression from an initial apparent equiprobability bias in predicting outcomes of tossing two coins through to representing the outcomes of increasing the number of trials. After observing the decreasing variation from the theoretical probability as the sample size increased, students developed a deeper understanding of the relationship between relative frequency of outcomes and theoretical probability as well as their respective associations with variation and expectation. Students’ final models indicated increasing levels of probabilistic understanding.

Probabilistic Inductive Querying Using ProbLog

We study how probabilistic reasoning and inductive querying can be combined within ProbLog, a recent probabilistic extension of Prolog. ProbLog can be regarded as a database system that supports both probabilistic and inductive reasoning through a variety of querying mechanisms. After a short introduction to ProbLog, we provide a survey of the different types of inductive queries that ProbLog supports, and show how it can be applied to the mining of large biological networks.

Probabilistic evaluation of seismic soil liquefaction potential based on SPT data

The performance-based liquefaction potential analysis was carried out in the present study to estimate the liquefaction return period for Bangalore, India, through a probabilistic approach. In this approach, the entire range of peak ground acceleration (PGA) and earthquake magnitudes was used in the evaluation of liquefaction return period. The seismic hazard analysis for the study area was done using probabilistic approach to evaluate the peak horizontal acceleration at bed rock level. Based on the results of the multichannel analysis of surface wave, it was found that the study area belonged to site class D. The PGA values for the study area were evaluated for site class D by considering the local site effects. The soil resistance for the study area was characterized using the standard penetration test (SPT) values obtained from 450 boreholes. These SPT data along with the PGA values obtained from the probabilistic seismic hazard analysis were used to evaluate the liquefaction return period for the study area. The contour plot showing the spatial variation of factor of safety against liquefaction and the corrected SPT values required for preventing liquefaction for a return period of 475 years at depths of 3 and 6 m are presented in this paper. The entire process of liquefaction potential evaluation, starting from collection of earthquake data, identifying the seismic sources, evaluation of seismic hazard and the assessment of liquefaction return period were carried out, and the entire analysis was done based on the probabilistic approach.

Essays on Financial Analyst Forecasts and Recommendations

The trade of the financial analyst is currently a much-debated issue in today’s media. As a large part of the investment analysis is conducted under the broker firms’ regime, the incentives of the financial analyst and the investor do not always align. The broker firm’s commercial incentives may be to maximise its commission from securities trading and underwriting fees. The purpose of this thesis is to extend our understanding of the work of a financial analyst, the incentives he faces and how these affect his actions. The first essay investigates how the economic significance of the coverage of a particular firm impacts the analysts’ accuracy of estimation. The hypothesis is that analysts put more effort in analysing firms with a relatively higher trading volume, as these firms usually yield higher commissions. The second essay investigates how analysts interpret new financial statement information. The essay shows that analysts underreact or overreact to prior reported earnings, depending on the short-term pattern in reported earnings. The third essay investigates the possible investment value in Finnish stock recommendations, issued by sell side analysts. It is established that consensus recommendations issued on Finnish stocks contain investment value. Further, the investment value in consensus recommendations improves significantly through the exclusion of recommendations issued by banks. The fourth essay investigates investors’ behaviour prior to financial analysts’ earnings forecast revisions. Lately, the financial press have reported cases were financial analysts warn their preferred clients of possible earnings forecast revisions. However, in the light of the empirical results, it appears that the problem of analysts leaking information to some selected customers does not appear systematically on the Finnish stock market.

Probabilistic Analysis of Cracking Moment of Reinforced Concrete Beams

Probabilistic analysis of cracking moment from 22 simply supported reinforced concrete beams is performed. When the basic variables follow the distribution considered in this study, the cracking moment of a beam is found to follow a normal distribution. An expression is derived, for characteristic cracking moment, which will be useful in examining reinforced concrete beams for a limit state of cracking.

Flow forecasts in general planning of municipal water and sewage works

Vuorokausivirtaaman ennustaminen yhdyskuntien vesi- ja viemärilaitosten yleissuunnittelussa.

The Skill of ECMWF Medium-Range Forecasts during the Year of Tropical Convection 2008

This study uses the European Centre for Medium-Range Weather Forecasts (ECMWF) model-generated high-resolution 10-day-long predictions for the Year of Tropical Convection (YOTC) 2008. Precipitation forecast skills of the model over the tropics are evaluated against the Tropical Rainfall Measuring Mission (TRMM) estimates. It has been shown that the model was able to capture the monthly to seasonal mean features of tropical convection reasonably. Northward propagation of convective bands over the Bay of Bengal was also forecasted realistically up to 5 days in advance, including the onset phase of the monsoon during the first half of June 2008. However, large errors exist in the daily datasets especially for longer lead times over smaller domains. For shorter lead times (less than 4-5 days), forecast errors are much smaller over the oceans than over land. Moreover, the rate of increase of errors with lead time is rapid over the oceans and is confined to the regions where observed precipitation shows large day-to-day variability. It has been shown that this rapid growth of errors over the oceans is related to the spatial pattern of near-surface air temperature. This is probably due to the one-way air-sea interaction in the atmosphere-only model used for forecasting. While the prescribed surface temperature over the oceans remain realistic at shorter lead times, the pattern and hence the gradient of the surface temperature is not altered with change in atmospheric parameters at longer lead times. It has also been shown that the ECMWF model had considerable difficulties in forecasting very low and very heavy intensity of precipitation over South Asia. The model has too few grids with ``zero'' precipitation and heavy (>40 mm day(-1)) precipitation. On the other hand, drizzle-like precipitation is too frequent in the model compared to that in the TRMM datasets. Further analysis shows that a major source of error in the ECMWF precipitation forecasts is the diurnal cycle over the South Asian monsoon region. The peak intensity of precipitation in the model forecasts over land (ocean) appear about 6 (9) h earlier than that in the observations. Moreover, the amplitude of the diurnal cycle is much higher in the model forecasts compared to that in the TRMM estimates. It has been seen that the phase error of the diurnal cycle increases with forecast lead time. The error in monthly mean 3-hourly precipitation forecasts is about 2-4 times of the error in the daily mean datasets. Thus, effort should be given to improve the phase and amplitude forecast of the diurnal cycle of precipitation from the model.

Probabilistic extension to realistic abductive reasoning model

In this paper, we give a method for probabilistic assignment to the Realistic Abductive Reasoning Model, The knowledge is assumed to be represented in the form of causal chaining, namely, hyper-bipartite network. Hyper-bipartite network is the most generalized form of knowledge representation for which, so far, there has been no way of assigning probability to the explanations, First, the inference mechanism using realistic abductive reasoning model is briefly described and then probability is assigned to each of the explanations so as to pick up the explanations in the decreasing order of plausibility.

A checking method for probabilistic seismic-hazard assessment: case studies on three cities

The conventional Cornell's source-based approach of probabilistic seismic-hazard assessment (PSHA) has been employed all around the world, whilst many studies often rely on the use of computer packages such as FRISK (McGuire FRISK-a computer program for seismic risk analysis. Open-File Report 78-1007, United States Geological Survey, Department of Interior, Washington 1978) and SEISRISK III (Bender and Perkins SEISRISK III-a computer program for seismic hazard estimation, Bulletin 1772. United States Geological Survey, Department of Interior, Washington 1987). A ``black-box'' syndrome may be resulted if the user of the software does not have another simple and robust PSHA method that can be used to make comparisons. An alternative method for PSHA, namely direct amplitude-based (DAB) approach, has been developed as a heuristic and efficient method enabling users to undertake their own sanity checks on outputs from computer packages. This paper experiments the application of the DAB approach for three cities in China, Iran, and India, respectively, and compares with documented results computed by the source-based approach. Several insights regarding the procedure of conducting PSHA have also been obtained, which could be useful for future seismic-hazard studies.