scholarly journals Predictive Bayesian selection of multistep Markov chains, applied to the detection of the hot hand and other statistical dependencies in free throws

2019 ◽  
Vol 6 (3) ◽  
pp. 182174
Author(s):  
Joshua C. Chang
Keyword(s):  
Markov Chains ◽  
Predictive Accuracy ◽  
Single Step ◽  
Information Criteria ◽  
Discrete State ◽  
Hitting Probability ◽  
Free Throw ◽  
Hot Hand ◽  
Two Parameters ◽  
Selection Of

Consider the problem of modelling memory effects in discrete-state random walks using higher-order Markov chains. This paper explores cross-validation and information criteria as proxies for a model’s predictive accuracy. Our objective is to select, from data, the number of prior states of recent history upon which a trajectory is statistically dependent. Through simulations, I evaluate these criteria in the case where data are drawn from systems with fixed orders of history, noting trends in the relative performance of the criteria. As a real-world illustrative example of these methods, this manuscript evaluates the problem of detecting statistical dependencies in shot outcomes in free throw shooting. Over three National Basketball Association (NBA) seasons analysed, several players exhibited statistical dependencies in free throw hitting probability of various types—hot handedness, cold handedness and error correction. For the 2013–2014 to 2015–2016 NBA seasons, I detected statistical dependencies in 23% of all player-seasons. Focusing on a single player, in two of these three seasons, LeBron James shot a better percentage after an immediate miss than otherwise. Conditioning on the previous outcome makes for a more-predictive model than treating free throw makes as independent. When extended specifically to LeBron James' 2016–2017 season, a model depending on the previous shot (single-step Markovian) does not clearly beat a model with independent outcomes. An error-correcting variable length model of two parameters, where James shoots a higher percentage after a missed free throw than otherwise, is more predictive than either model.

On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions

1996 ◽  
Vol 33 (3) ◽  
pp. 640-653 ◽  
Author(s):  
Tobias Rydén
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Continuous Time ◽  
Poisson Processes ◽  
Hitting Times ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Minimum Number ◽  
Markov Modulated ◽  
Two Parameters

An aggregated Markov chain is a Markov chain for which some states cannot be distinguished from each other by the observer. In this paper we consider the identifiability problem for such processes in continuous time, i.e. the problem of determining whether two parameters induce identical laws for the observable process or not. We also study the order of a continuous-time aggregated Markov chain, which is the minimum number of states needed to represent it. In particular, we give a lower bound on the order. As a by-product, we obtain results of this kind also for Markov-modulated Poisson processes, i.e. doubly stochastic Poisson processes whose intensities are directed by continuous-time Markov chains, and phase-type distributions, which are hitting times in finite-state Markov chains.

scholarly journals Probability Models for Assessing Effectiveness of Advertising Channels in the Internet Environment

2018 ◽  
pp. 209-215
Keyword(s):  
Graph Theory ◽  
Markov Chains ◽  
Markov Processes ◽  
The Internet ◽  
Probability Models ◽  
Method Of Calculation ◽  
Internet Environment ◽  
The Impact ◽  
Theory Of Graphs ◽  
Selection Of

Nowadays, marketing specialists simultaneously use several channels to attract visitors to websites. There is a difficulty in assessing not only the efficiency and conversion of each channel separately, but also in their interconnection. The problem occurs when users visit a website from several sources and only after that do the key action. To assess the effectiveness and selection of the most optimal channels, different models of attribution are used. The models are reviewed in the article. However, we propose to use multi-channel attribution, which provides an aggregate assessment of multi-channel sequences, taking into account that they are interdependent. The purpose of the paper is to create an attribution model that comprehensively evaluates multi-channel sequences and shows the effect of each channel on the conversion. The presented model of attribution can be based on the theory of graphs or Markov chains. The first method of calculation is more visual, the second (based on Markov chains) allows for work with a large amount of data. As a result, a model of multi-channel attribution was presented, which is based on Markov processes or graph theory. It allows for maximum comprehensive assessing of the impact of each channel on the conversion. On the basis of the two methods, calculations were carried out, confirming the adequacy of the model used for the tasks assigned.

Closed-Form Synthesis of Force-Generating Planar Four-Bar Linkages

1995 ◽  
Author(s):  
R. Randall Soper ◽  
Michael Scardina ◽  
Paul Tidwell ◽  
Charles Reinholtz ◽  
Michael A. Lo Presti
Keyword(s):  
Closed Form ◽  
The Other ◽  
Design Parameters ◽  
Synthesis Methods ◽  
Function Generator ◽  
Mechanical Advantage ◽  
Nonlinear Mechanical ◽  
Two Parameters ◽  
Selection Of ◽  
Weight Force

Abstract This paper presents a technique for synthesizing four-bar linkages to produce a specified resisting force or torque. The resisting energy is provided by a weight acting on the other grounded link. The linkage serves as a nonlinear mechanical advantage function generator. Force and velocity synthesis methods have been extensively discussed in the literature. The general approach, however, has been to assume that the specified force or velocity occurs at a prescribed position. This results in the loss of design parameters that are being used unnecessarily to control position. In this application, force input to the linkage is specified as a function of only the input link position and the magnitude and direction of the weight force. Mechanical advantage synthesis can be achieved at as many as seven precision points. The method presented in this paper allows free selection of two parameters and viewing one infinity of solutions.

Development of a new empirical method for Tunnel Squeezing Classification (TSC)

2020 ◽  
Vol 53 (4) ◽  
pp. 655-660 ◽  
Author(s):  
Hadi Farhadian ◽  
Arash Nikvar-Hassani
Keyword(s):  
Quality Index ◽  
Empirical Method ◽  
Point Of View ◽  
Geological Hazard ◽  
Case Histories ◽  
Proposed Model ◽  
Two Parameters ◽  
Classification Tool ◽  
Selection Of

The characterization of squeezing phenomena as a geological hazard is of great importance because squeezing has a crucial role in the selection of the route and type of tunnels and in the characteristics of the excavation device. Tunnel squeezing is also the basis for the designation and construction of tunnelling-related structures. We present a new tunnel squeezing classification tool to predict tunnel squeezing based on two parameters: Q, the tunnelling quality index; and H, the depth of the tunnel. We used data collected from published papers to train the model; these data included 225 case histories from different countries, including Andorra, India, Iran, Japan, Nepal, Spain, Turkey and Venezuela. Validation of the model indicated that our tunnel squeezing classification tool is more accurate than the speculative and analytical methods currently in use. The proposed model will help tunnelling experts to classify tunnelling media from the point of view of squeezing hazards.

State aggregation and discrete-state Markov chains embedded in a class of point processes

1995 ◽  
Vol 32 (01) ◽  
pp. 39-51
Author(s):  
Xi-Ren Cao
Keyword(s):  
Markov Chains ◽  
Poisson Process ◽  
Point Process ◽  
Point Processes ◽  
Marked Point ◽  
Practical Importance ◽  
Marked Point Process ◽  
Interarrival Time ◽  
Discrete State ◽  
State Aggregation

One result that is of both theoretical and practical importance regarding point processes is the method of thinning. The basic idea of this method is that under some conditions, there exists an embedded Poisson process in any point process such that all its arrival points form a sub-sequence of the Poisson process. We extend this result by showing that on the embedded Poisson process of a uni- or multi-variable marked point process in which interarrival time distributions may depend on the marks, one can define a Markov chain with a discrete state that characterizes the stage of the interarrival times. This implies that one can construct embedded Markov chains with countable state spaces for the state processes of many practical systems that can be modeled by such point processes.

scholarly journals Antipneumococcal Activities of Two Novel Macrolides, GW 773546 and GW 708408, Compared with Those of Erythromycin, Azithromycin, Clarithromycin, Clindamycin, and Telithromycin

2004 ◽  
Vol 48 (11) ◽  
pp. 4103-4112 ◽  
Author(s):  
Vlatka Matic ◽  
Klaudia Kosowska ◽  
Bulent Bozdogan ◽  
Linda M. Kelly ◽  
Kathy Smith ◽  
...  
Keyword(s):  
Ribosomal Protein ◽  
Protein Sequence ◽  
Single Step ◽  
23S Rrna ◽  
Susceptible Parent ◽  
Rrna Sequence ◽  
Resistant Strains ◽  
Resistant Mutants ◽  
Rrna Sequences ◽  
Selection Of

ABSTRACT The MICs of GW 773546, GW 708408, and telithromycin for 164 macrolide-susceptible and 161 macrolide-resistant pneumococci were low. The MICs of GW 773546, GW 708408, and telithromycin for macrolide-resistant strains were similar, irrespective of the resistance genotypes of the strains. Clindamycin was active against all macrolide-resistant strains except those with erm(B) and one strain with a 23S rRNA mutation. GW 773546, GW 708408, and telithromycin at two times their MICs were bactericidal after 24 h for 7 to 8 of 12 strains. Serial passages of 12 strains in the presence of sub-MICs yielded 54 mutants, 29 of which had changes in the L4 or L22 protein or the 23S rRNA sequence. Among the macrolide-susceptible strains, resistant mutants developed most rapidly after passage in the presence of clindamycin, GW 773546, erythromycin, azithromycin, and clarithromycin and slowest after passage in the presence of GW 708408 and telithromycin. Selection of strains for which MICs were ≥0.5 μg/ml from susceptible parents occurred only with erythromycin, azithromycin, clarithromycin, and clindamycin; 36 resistant clones from susceptible parent strains had changes in the sequences of the L4 or L22 protein or 23S rRNA. No mef(E) strains yielded resistant clones after passage in the presence of erythromycin and azithromycin. Selection with GW 773546, GW 708408, telithromycin, and clindamycin in two mef(E) strains did not raise the erythromycin, azithromycin, and clarithromycin MICs more than twofold. There were no change in the ribosomal protein (L4 or L22) or 23S rRNA sequences for 15 of 18 mutants selected for macrolide resistance; 3 mutants had changes in the L22-protein sequence. GW 773546, GW 708408, and telithromycin selected clones for which MICs were 0.03 to >2.0 μg/ml. Single-step studies showed mutation frequencies <5.0 × 10−10 to 3.5 × 10−7 for GW 773546, GW 708408, and telithromycin for macrolide-susceptible strains and 1.1 × 10−7 to >4.3 × 10−3 for resistant strains. The postantibiotic effects of GW 773546, GW 708408, and telithromycin were 2.4 to 9.8 h.

scholarly journals Dual Targeting of DNA Gyrase and Topoisomerase IV: Target Interactions of Garenoxacin (BMS-284756, T-3811ME), a New Desfluoroquinolone

2002 ◽  
Vol 46 (11) ◽  
pp. 3370-3380 ◽  
Author(s):  
Dilek Ince ◽  
Xiamei Zhang ◽  
L. Christine Silver ◽  
David C. Hooper
Keyword(s):  
Inhibitory Concentration ◽  
Efflux Pump ◽  
Fold Increase ◽  
Single Step ◽  
The Novel ◽  
Wild Type ◽  
Topoisomerase Iv ◽  
Dual Targeting ◽  
Resistant Mutants ◽  
Selection Of

ABSTRACT We determined the target enzyme interactions of garenoxacin (BMS-284756, T-3811ME), a novel desfluoroquinolone, in Staphylococcus aureus by genetic and biochemical studies. We found garenoxacin to be four- to eightfold more active than ciprofloxacin against wild-type S. aureus. A single topoisomerase IV or gyrase mutation caused only a 2- to 4-fold increase in the MIC of garenoxacin, whereas a combination of mutations in both loci caused a substantial increase (128-fold). Overexpression of the NorA efflux pump had minimal effect on resistance to garenoxacin. With garenoxacin at twice the MIC, selection of resistant mutants (<7.4 × 10−12 to 4.0 × 10−11) was 5 to 6 log units less than that with ciprofloxacin. Mutations inside or outside the quinolone resistance-determining regions (QRDR) of either topoisomerase IV, or gyrase, or both were selected in single-step mutants, suggesting dual targeting of topoisomerase IV and gyrase. Three of the novel mutations were shown by genetic experiments to be responsible for resistance. Studies with purified topoisomerase IV and gyrase from S. aureus also showed that garenoxacin had similar activity against topoisomerase IV and gyrase (50% inhibitory concentration, 1.25 to 2.5 and 1.25 μg/ml, respectively), and although its activity against topoisomerase IV was 2-fold greater than that of ciprofloxacin, its activity against gyrase was 10-fold greater. This study provides the first genetic and biochemical data supporting the dual targeting of topoisomerase IV and gyrase in S. aureus by a quinolone as well as providing genetic proof for the expansion of the QRDRs to include the 5′ terminus of grlB and the 3′ terminus of gyrA.

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