A Casual View of Multi-Layer Perceptrons as Probability Models

This chapter contains many classroom activities and demonstrations to help students understand basic probability calculations, including conditional probability and Bayes rule. Many of the activities alert students to misconceptions about randomness. They create dramatic settings where the instructor discerns real coin flips from fake ones, students modify dice and coins in order to load them, students “accused” of lying based on the outcome of an inaccurate simulated lie detector face their classmates. Additionally, probability models of real outcomes offer good value: first we can do the probability calculations, and then can go back and discuss the potential flaws of the model.

Download Full-text

Expert Uncertainty and the Use of Subjective-Probability Models

Journal of Applied Statistics ◽

10.1080/02664768100000003 ◽

1981 ◽

Vol 8 (1) ◽

pp. 26-56

Author(s):

J M Dickey

Keyword(s):

Subjective Probability ◽

Probability Models

Download Full-text

Probability logic: A model-theoretic perspective

Journal of Logic and Computation ◽

10.1093/logcom/exaa066 ◽

2020 ◽

Author(s):

M Pourmahdian ◽

R Zoghifard

Keyword(s):

Characterization Theorem ◽

Expressive Power ◽

Probability Logic ◽

Theoretic Analysis ◽

Compactness Property ◽

Probability Models ◽

Finitely Additive Probability ◽

Additive Probability ◽

Basic Probability ◽

Abstract Logics

Abstract This paper provides some model-theoretic analysis for probability (modal) logic ($PL$). It is known that this logic does not enjoy the compactness property. However, by passing into the sublogic of $PL$, namely basic probability logic ($BPL$), it is shown that this logic satisfies the compactness property. Furthermore, by drawing some special attention to some essential model-theoretic properties of $PL$, a version of Lindström characterization theorem is investigated. In fact, it is verified that probability logic has the maximal expressive power among those abstract logics extending $PL$ and satisfying both the filtration and disjoint unions properties. Finally, by alternating the semantics to the finitely additive probability models ($\mathcal{F}\mathcal{P}\mathcal{M}$) and introducing positive sublogic of $PL$ including $BPL$, it is proved that this sublogic possesses the compactness property with respect to $\mathcal{F}\mathcal{P}\mathcal{M}$.

Download Full-text

Why is syphilis rising in Europe? Multi-level modelling of alternative hypotheses in 31 countries

European Journal of Public Health ◽

10.1093/eurpub/ckaa165.534 ◽

2020 ◽

Vol 30 (Supplement_5) ◽

Author(s):

A Mendez-Lopez ◽

D Stuckler ◽

T Noori ◽

J C Semenza

Keyword(s):

Risky Sexual Behavior ◽

Population Level ◽

Internet Survey ◽

Probability Models ◽

Syphilis Infection ◽

Detection Rates ◽

Substantial Impact ◽

Multi Level ◽

Sex With Men ◽

Linear Probability

Abstract Background Syphilis transmission has increased markedly over the past two decades in Europe, concentrated in men who have sex with men. We test alternative potential social and behavioral individual- and population-level determinants of this resurgence. Methods Two rounds of the cross-sectional European Men who have sex with men Internet Survey (EMIS 2010 and 2017, n = 272,902) were used to fit multi-level linear probability models to evaluate determinants of the incidence of self-reported syphilis, capturing risky sexual behaviours and pre-exposure prophylaxis use, among others, adjusting for potential sociodemographic confounders. Results Self-reported syphilis incidence rates rose by about 1.8 percentage points (within the last 12 months) and 3.9 (within the last 5 years) between the 2010 and 2017 waves, after adjusting for sociodemographic factors. HIV status was a major risk factor for syphilis infection (27.6 ppt higher incident rate, 95%CI: 24.7 to 30.5). A dose-response relationship was observed between greater numbers of condomless non-steady partners and syphilis infection, with more than 10 partners estimating increases in the probability of diagnosis of over 25 ppt (11-20 partners vs none: 24.5 ppt, 95%CI: 20.5 to 28.5); further, we observed evidence of mediation for number of condomless non-steady partners, which attenuated the estimated rise in 2017 vs 2010 by about 35%. STI testing uptake also accounted for a substantial increase in syphilis incidence signaling higher detection rates over time. While country-level PrEP use was linked to greater number of condomless partners, there was no substantial impact of population-wide factors, including GDP and PrEP use, on overall syphilis trends. Conclusions Risky sexual behavior changes, particularly condomless sex with non-steady partners, appears to be a major contributing factor to rising syphilis incidence. Further research is needed to understand what accounts for this substantial behavior change. Key messages Increased number of condomless non-steady partners accounts for a substantial rise in syphilis trends. Population-level PrEP use was linked to increasing numbers of condomless non-steady partners but had no substantial impact on overall syphilis trends.

Download Full-text

Stochastic Natural Vibration Analyses of Free-Form Shells

Applied Sciences ◽

10.3390/app9153168 ◽

2019 ◽

Vol 9 (15) ◽

pp. 3168

Author(s):

Bingbing San ◽

Yunlong Ma ◽

Zhi Xiao ◽

Dongming Feng ◽

Liwei Yin

Keyword(s):

Elastic Modulus ◽

Shape Optimization ◽

Shell Thickness ◽

Natural Vibration ◽

Natural Frequencies ◽

Vibration Characteristics ◽

Free Form ◽

Probability Models ◽

Geometric Imperfection ◽

Natural Vibration Characteristics

This work investigates the natural vibration characteristics of free-form shells when considering the influence of uncertainties, including initial geometric imperfection, shell thickness deviation, and elastic modulus deviation. Herein, free-form shell models are generated while using a self-coded optimization algorithm. The Latin hypercube sampling (LHS) method is used to draw the samplings of uncertainties with respect to their stochastic probability models. ANSYS finite element (FE) software is adopted to analyze the natural vibration characteristics and compute the natural frequencies. The mean values, standard deviations, and cumulative distributions functions (CDFs) of the first three natural frequencies are obtained. The partial correlation coefficient is adopted to rank the significances of uncertainty factors. The study reveals that, for the free-form shells that were investigated in this study, the natural frequencies is a random quantity with a normal distribution; elastic modulus deviation imposes the greatest effect on natural frequencies; shell thickness ranks the second; geometrical imperfection ranks the last, with a much lower weight than the other two factors, which illustrates that the shape of the studied free-form shells is robust in term of natural vibration characteristics; when the supported edges are fixed during the shape optimization, the stochastic characteristics do not significantly change during the shape optimization process.

Download Full-text