In the analysis of spatial point patterns, an important role is played by statistical tests based on simulation envelopes, such as the envelope of simulations of Ripley's K function. Recent ecological literature has correctly pointed out a common error in the interpretation of simulation envelopes. However, this has led to a widespread belief that the tests themselves are invalid. On the contrary, envelope‐based statistical tests are correct statistical procedures, under appropriate conditions. In this paper, we explain the principles of Monte Carlo tests and their correct interpretation, canvas the benefits of graphical procedures, measure the statistical performance of several popular tests, and make practical recommendations. There are several caveats including the under‐recognized problem that Monte Carlo tests of goodness of fit are probably conservative if the model parameters have to be estimated from data. Finally, we discuss whether graphs of simulation envelopes can be used to infer the scale of spatial interaction.

We develop statistical methods for analysing a pattern of points on a region of the sphere, including intensity modelling and estimation, summary functions such as the K function, point process models, and model-fitting techniques. The methods are demonstrated by analysing a dataset giving the sky positions of galaxies.

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We describe a case of mixed liposarcoma of the axilla presenting as a high grade undifferentiated sarcoma with areas of well-differentiated and myxoid liposarcoma. MRI demonstrated a lobulated, septated intermuscular mass with marked heterogeneous gadolinium enhancement. A small focus of the tumor demonstrated fat suppressed signal more characteristic of well-differentiated liposarcoma. Pathologic analysis following wide local excision revealed a large, high grade sarcomatous component with highly pleomorphic cells with a thin rim of well-differentiated and myxoid liposarcoma on histologic examination. Dedifferentiated liposarcomas arising outside of the retroperitoneum are very rare, as are dedifferentiated liposarcomas arising from a histologically mixed liposarcoma. In this regard, this case illustrates an unusual combination of tumor location and histology which, to our knowledge, has not previously been reported.

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