### Abstract

We introduce a nearly automatic procedure to locate and count the quantum dots in images of kinesin motor assays. Our procedure employs an approximate likelihood estimator based on a two-component mixture model for the image data; the first component has a normal distribution, and the other component is distributed as a normal random variable plus an exponential random variable. The normal component has an unknown variance, which we model as a function of the mean. We use B-splines to estimate the variance function during a training run on a suitable image, and the estimate is used to process subsequent images. Parameter estimates are generated for each image along with estimates of standard errors, and the number of dots in the image is determined using an information criterion and likelihood ratio tests. Realistic simulations show that our procedure is robust and that it leads to accurate estimates, both of parameters and of standard errors.

Original language | English (US) |
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Pages (from-to) | 588-595 |

Number of pages | 8 |

Journal | Biometrics |

Volume | 67 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1 2011 |

Externally published | Yes |

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### Keywords

- Bio-imaging
- Fluorescence microscopy
- Kinesin motor protein
- Maximum likelihood
- Mixture model
- Quantum dot
- Spline
- Variance-function estimation

### ASJC Scopus subject areas

- Statistics and Probability
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

*Biometrics*,

*67*(2), 588-595. https://doi.org/10.1111/j.1541-0420.2010.01467.x